Research ArticleTHz-SAR Vibrating Target Imaging via the Bayesian Method

Bin Deng Xin-yun Wang Cheng-guang Wu Yu-liang Qin and Hong-qiang Wang

College of Electronic Science and Engineering National University of Defense Technology 157 Deya Road Changsha 410073 China

Correspondence should be addressed to Bin Deng sagitdeng163com

Received 18 September 2016 Revised 7 January 2017 Accepted 22 January 2017 Published 19 February 2017

Academic Editor Lorenzo Crocco

Copyright copy 2017 Bin Deng et alThis is an open access article distributed under theCreative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Target vibration bears important information for target recognition and terahertz due to significant micro-Doppler effects hasstrong advantages for remotely sensing vibrations In this paper the imaging characteristics of vibrating targets with THz-SAR areat first analyzed An improved algorithm based on an excellent Bayesian approach that is the expansion-compression variance-component (ExCoV) method has been proposed for reconstructing scattering coefficients of vibrating targets which providesmore robust and efficient initialization and overcomes the deficiencies of sidelobes as well as artifacts arising from the traditionalcorrelation method A real vibration measurement experiment of idle cars was performed to validate the range model SimulatedSAR data of vibrating targets and a tank model in a real background in 220GHz show good performance at low SNR Rapidlyevolving high-power terahertz devices will offer viable THz-SAR application at a distance of several kilometers

1 Introduction

Vibration is one of the commonest motions in nature suchas the vibration of a car engine the bumping of a caron a rude road the chest movement caused by heart beatand breath and the arm swing of a walking terrorist Thecharacteristics of vibration differ greatly for different targetsFor example the vibration amplitude of different types oftanks or armored cars ranges from several millimeters toseveral centimeters and the vibration frequency ranges fromseveral hertz to several decades hertz The exact valuesare closely related to the vehicle type size and structureIn addition the remote sensing of vibration is helpful forgathering the road condition information [1] One can seethat vibration contains subtle and stable information oftargets The vibration parameters once extracted can playan important role in target recognition which will open upa new range of applications in battlefield reconnaissanceprecision seeking traffic surveillance and antiterrorist tasks

Detecting vibrating targets on the ground with syntheticaperture radar (SAR) is an emerging subject in the remotesensing communityDirect SAR imaging for vibrating targetshowever will result in ghosts in the image due to theperiodic micro-Doppler modulation [2] which cannot beovercome by the SAR ground moving target indication(SARGMTI) techniques Relevant researches on SAR target

vibration have been carried out internationally since 1995[3] and our group started the study early in 2006 inChina and defined it together with rotating target detec-tion and imaging as SARmicromotion target indication(SARMMTI) [4] Recent works on it are mainly focused onthe vibrating target phenomenology or vibrationrsquos influencevibrating target detection micro-Doppler analysis as wellas extraction and real vibration sensing experiments Onthe phenomenology main conclusion is that vibration givesrise to high frequency phase and paired echoes in the timedomain to micro-Doppler in the frequency domain and toghosts [2] fence [5] bowknot [6] or fuzzballs [7] in theimage domain On the detection the main methods includethe generalized likelihood ratio test and cyclostationaryspectrum density method [8ndash10] or the multiantenna baseddisplaced phase center antenna (DPCA) and along-trackinterferometry (ATI)methods [11ndash14]On themicro-Doppleranalysis and extraction time-frequency analysis [12] and thefractional Fourier transform (FrFT) [15] are predominant andthe pulse-repetition-interval transform [16] can also providegood results On the experiments X-band APY-6 [17] Ku-band Lynx [18] andmmWMEMPHIS [12] radar systems havebeen utilizedThe basic viability of vibration sensing has beenproven but two main problems have yet to be addressed(1) Experimental data show that minor vibrations with theamplitude under several millimeters cannot be detected even

HindawiInternational Journal of Antennas and PropagationVolume 2017 Article ID 3706925 10 pageshttpsdoiorg10115520173706925

2 International Journal of Antennas and Propagation

by mmW radars [12] (2) Few researches on vibrating targetimaging have been done Although the phase compensationmethod and the Doppler keystone transform [19] can beused for imaging they are mainly useful to point scatteringtargets and the range cell migration of vibrating targets isstill difficult to be corrected The MLE imaging method [20]proposed previously by us can directly model the echo signaland then estimate scattering centers of vibrating targets butis essentially of the high-dimensional nonlinear optimizationproblem with ill condition and it is impossible to obtain theglobal minimum without using prior information

To solve problem (1) we introduce terahertz wave intoSAR for vibration sensing Due to the shorter wavelengthterahertz wave is more sensitive to micromotions making iteasier to detect vibrating targetsThe emission power of solid-state and vacuum electronics terahertz devices approaches toseveral decadeWatts according to the DARPA terahertz elec-tronics program As there is serious atmosphere attenuationthe emission power is sufficient to meet the needs of airborneterahertz radar for operating range of several kilometers atthe frequencies of 220GHz or 330GHz atmosphere windowsIn 2012 the US DARPA proposed a project called VideoSAR (ViSAR) [21] and the frequency band around 230GHzwas chosen prophesying realization of THz-SAR To solveproblem (2) we convert vibrating target imaging to the prob-lem of sparse representation and the expansion-compressionvariance-component (ExCoV) method is utilized to obtainthe scattering coefficients of vibrating targets The ExCoVmethod is of sparse Bayesian learning (SBL) [22] but it ismore effective and has less parameters than the traditionalSBL and is promising to efficiently solve the high-dimensionaloptimization problems In this paper we will modify theinitial iteration in ExCoV that is superseding pseudoinverseby correlation processing to improve efficiency and stabilityThe simulated data of vibrating point targets and a tankmodelat 220GHz will validate the performance of the proposedalgorithm

2 Models of THz-SAR Vibrating Targets

As illustrated in Figure 1 the radar moves at velocity119881119886Thenat slow time 119905 it moves to

1199101015840 = 119881119886119905 = 119877119888 tan 120579 asymp 119877119888120579 (1)

We could see that 120579 has the similar meaning as slowtime 119905 and thus the symbol 120579119905 may be more appropriatenevertheless it is abandoned for brevity Now consideringan arbitrary moving target let vector 120578 represent the targetmotion parameters such as the initial position (119909 119910) velocityand vibration frequency 120578 can thus be regarded as theidentification code of a target Suppose that when the radarmoves to 1199101015840 = 119877119888120579 or 120579 for simplicity the target of 120578moves to(119909120578120579 119910120578120579) and then the target range model is

119877120578 (120579) = radic(119877119888 + 119909120578120579)2 + (1199101015840 + 119910120578120579)2

asymp radic1198772119888 + 11991010158402 + 119909120578120579 cos 120579 + 119910120578120579 sin 120579(2)

where the approximation is a result of plane waves that isin Figure 1(b) |119875119879| asymp |1198751198791015840| = |119875119874| + |1198741198791015840| = radic1198772119888 + 11991010158402 +119909120578120579 cos 120579 + 119910120578120579 sin 120579

Spotlight SAR echoes of the target could then be repre-sented in the wavenumber domain as

119904 (119870 120579 120578) = 119875 (119870) exp [minus119895119870radic1198772119888 + 11991010158402]sdot exp [minus119895119870 (119909120578120579 cos 120579 + 119910120578120579sin120579)]

(3)

where 119870 = 4120587120582 = 4120587119891119888 is the two way wavenumber 119888 isthe speed of light 120582 is the wavelength 119891 is the frequency119870119862 = 4120587120582119862 = 4120587119891119862119888 is the center wavenumber 120582119862 isthe carrier wavelength 119891119862 is the carrier frequency and 119875(119870)is the Fourier transform of the transmitted signal Supposemultiple targets exit recall that 120578 is the identification code ofa target and thus we use 119886(120578) as the scattering coefficient ofthe target with respect to 120578Then the total echoes of all targetscan be expressed in terms of integration as

119878total (119870 120579) = int 119886 (120578) 119904 (119870 120579 120578) d120578 (4)

In (3) 119875(119870) and exp[minus119895119870radic1198772119888 + 11991010158402] contain nounknowns and hence they can be compensated forrange compression (multiplication by 119875lowast(119870)) and motioncompensation (multiplication by exp[119895119870radic1198772119888 + 11991010158402]) Thusthe first two terms of 119904(sdot) in (3) disappear and then the targetsignal model becomes

119866 (119870 120579)= int 119886 (120578) exp [minus119895119870 (119909120578120579 cos 120579 + 119910120578120579 sin 120579)] d120578 (5)

Note (5) is a Fredholm integral equation of the first kindWhen the target experiences vibration the real vehicle

vibration frequencies have complex components and thevibration frequencies also differ for its parts such as theroof and the bumper [12] However it can be regarded as asynthesis of simple harmonic vibrations as measured for twoidle cars which can be seen later in the experiment sectionConsidering only one frequency component for simplicityand without loss of generality we have

119909120578120579 = 119909 + 119903 cos (2120587119891119898119905 + 1205930) 119910120578120579 = 119910 + 119903 sin (2120587119891119898119905 + 1205930) (6)

where vibration parameters compose a parameter vector

120578def= [119909 119910 119903 119891119898 1205930]119879 (7)

and (119909 119910) is the center of the vibration axis 119903 is the effectivevibration amplitude 119891119898 is the vibration frequency and 1205930 isthe initial phase at 119905 = 0 By the way (6) can also be used tomodel target rotations

International Journal of Antennas and Propagation 3

x

yo

T

P

Rc

(x120578120579 y120578120579)

120579

y998400 = Vat

(a)

x

yoT

Py998400

Rc

T998400

120579

(x120578120579 y120578120579)

(b)

oO120579

Ky

K

ky

kx Kx

KC

(c)

Figure 1 Spotlight SAR moving target geometry (a) slant plane view (b) plane wave approximation (c) wavenumber-domain view

Substituting (6) into (5) discretizing the result andadding noise yield

119866 (119870 120579) = 119868sum119894=1

119886119894 sdot 119890119870120579 (120578119894) + V119894 (8)

where 119868 is the number of vibrating targets (it can also includestationary body points by just setting 119903 or 119891119898 to zero andcan include no target by setting 119886119894 to zero) 119886119894 denotes thescattering coefficient of the 119894th target and

119890119870120579 (120578119894)def= exp (minus119895119870119909119894 cos 120579 minus 119895119870119910119894 sin 120579)

sdot exp(minus119895119870119903119894 cos(2120587119891119898119894119877119888119881119886 tan 120579 + 1205930119894)) (9)

During the derivation of (9) 119905 = 119877119888 tan 120579119881119886 from (1) and2120587119891119898119877119888119881119886 ≫ 1 have been usedIn (9) we can clearly see that there is an additional

exponential component that is the last term representingtarget vibration in (9) when compared with the stationaryscattering center model Note119870 and 120579 can also be discretizedinto 119872 and 119873 values respectively and therefore (8) can beexpressed in a matrix form as

g = Φa + k (10)

where

g = [119866 (1198701 1205791) 119866 (1198701 1205792) 119866 (119870119872 120579119873)]119879 a def= [1198861 1198862 119886119868]119879 v def= [V1 V2 V119868]119879

Φ =[[[[[[[[

11989011987011205791 (1205781) 11989011987011205791 (1205782) sdot sdot sdot 11989011987011205791 (120578119868)11989011987011205792 (1205781) 11989011987011205792 (1205782) sdot sdot sdot 11989011987011987711205792 (120578119868) sdot sdot sdot sdot sdot sdot119890119870119872120579119873 (1205781) 119890119870119872120579119873 (1205782) sdot sdot sdot 119890119870119872120579119873 (120578119868)

]]]]]]]]

(11)

From (10) the imaging or scattering coefficient recon-struction problem can be regarded as an inverse problem ofsolving linear equations

What deserves special mention is that the unknown 120578 hasalso been discretized into 1205781 1205782 120578119868 which are located ata high-dimensional cubic grid and therefore Φ contains nounknowns

3 The Influence of Target Vibration onTHZ-SAR Image

It is well known that vibrating targets cannot be focusedin microwave SAR images and a ghost image will generallyresult according to the paired echo principle We now try toanalyze THz-SAR image characteristics of vibrating targetsThe space between ghosts is a constant [2]

Δ119910 = 1198911198981205821198621198771198882119881119886 (12)

For THz-SAR Δ119910 will decrease by a commensurateamount compared with microwave SAR since 120582119862 is signifi-cantly smaller than the wavelength at X-band or mmWband

Note the azimuth resolution 120588119886 = 1205821198621198771198882119881119886119879119897 where119879119897 isthe coherent processing interval (CPI) and the space in pixelor resolution cell can be expressed as

Δ119910120588119886 = 119891119898119879119897 (13)

It is apparent that the space in pixel or resolution cell hasno relation with the frequency band However 119879119897 needed forthe same resolution as microwave SAR is reduced for THz-SAR For typical parameter values Δ119910120588119886 le 1 which statesthat the ghosts are not resolvable and line segment results

According to Carsonrsquos rule [22] the ghost number plusthe real target is

119873 asymp 8120587119903120582119862 + 3 (14)

From (12) and (14) the length of the ghost image or theline segment in azimuth is

Δ119871 = Δ119910119873 = (8120587119903 + 3120582119862) 1198911198981198771198882119881119886 (15)

4 International Journal of Antennas and Propagation

Equation (15) makes it clear that Δ119871 will decrease whenthe frequency moves to the terahertz band

4 Vibrating Target Imaging viathe Improved ExCoV Method

In order to solve (8) we model the pdf of THz-SAR echovector g given a and 1205902 using the standard additive Gaussiannoise model

119901 (g | a 1205902) = 119873(gΦa 1205902C) (16)

where C is a known positive definite symmetric matrix ofsize119872119873times119872119873 1205902 is an unknown noise-variance parameterand 1205902C is the noise covariance matrix The SBL employsa Gaussian prior on the signal with a distinct variancecomponent on each signal element

119901 (119886119894 120574119894) = 119873 (0 120574119894) = (2120587120574119894)minus12 exp(minus 11988621198942120574119894) 119894 = 1 119868

(17)

However we have known according to the sparse recov-ery theory and a priori knowledge that in most real-worldcases only a few elements of a have significant magnitudesand that the remaining elements are either strictly zerosor close to zeros [23] Therefore the prior distribution (17)did not capture the signal key feature that is sparsity Onthe contrary the ExCoV method assigns distinct variancecomponents to the candidates for significant signal elementsand uses only one common variance-component parameterto account for the variability of the rest of signal coefficients[24] LetΛ be the full index set in the signal and let the size be119868 Denote A as the set of indices of the signal elements withdistinct variance components and the size as 119898A and definethe complementary index set B = ΛAwith cardinality119898B =119868 minus 119898A Accordingly we partition Φ and a into submatricesΦA and ΦB and subvectors aA andaB Then the followingprior model for the signal coefficients is adopted

119901 (a | 120575A 1205742) = 119901 (aA | 120575A) sdot 119901 (aB | 1205742)= 119873(aA 0119898Atimes1 119863A (120575A))sdot 119873 (aB 0119898Btimes1 119863B (1205742))

(18)

where 119863A(120575A) = diag 1205752A1 1205752A2 1205752A119898A and 119863B(1205742) =1205742I119898B are the signal covariance matrices and the variancecomponents 1205752A1 1205752A2 1205752A119898A for aA are distinct whilethe common variance 1205742 accounts for the variability ofaB Assume that the signal variance components 120575A and1205742 are unknown and define the set of all unknowns 120579 =(A 120575A 1205742 1205902) and then the marginal pdf of the observationsg given 120579 is [24]

119901 (g | 120579) = int119901 (g | a 1205902) sdot 119901 (a | 120575A 1205742) da= 119873(g 0119872119873times1 119875minus1 (120579))

(19)

where 119875(120579) is the inverse covariance matrix of g given 120579Clearly 119901(g | 120579) provides generalized maximum-likelihood(GML) estimation of 120579 The GML estimation of 119901(g |a 1205902)119901(a | 120575A 1205742) proceeds for obtaining the only unknown aas the image The whole estimation process is iteratively real-ized via applying the ExCoV algorithm and the iteration willterminate when A does not change between two consecutivecycles [24]

ExCoV has demonstrated an excellent algorithm forsolving linear equations arising from the real world especiallyfrom the radar field [25] Compared to SBL (SBL-EM SBL-Type II VBSBL and ESBL) SpaRSA and CoSaMP it has thesmallest mean-square error (MSE) in the low signal-to-noiseratio (SNR) and the second highest computation efficiency(not better than CoSaMP whose MSE is large) It beginswith an initialization followed by complex iterations Theinitialization provides the starting point for the following iter-ations and thus plays an important part for fast convergenceThe original ExCoVutilizesMoore-Penrose pseudoinverse toinitialize the parameters that is

a(0) = Φ119867 (ΦΦ119867)minus1 g (20)

where 119867 denotes complex conjugation The first 119898(0)A largestelements of a(0) are found to initialize A

However ΦΦ119867 is usually rank deficient for real radarproblems and hence ΦΦ119867 is not inversible resulting inwrong estimation of a(0) An example is shown in Figure 2(a)We recognize that ΦΦ119867 denotes autocorrelation and cross-correlation of the measurement matrix and will give a sinc-shaped system response (ΦΦ119867)minus1 is just the inverse sincresponse which is an identity matrix in ideal condition torealize super-resolution estimation of a Thus we abandonthis term and obtain a more robust efficient and simplerestimation than (20) as

a(0) = Φ119867g (21)

which can also be called correlation imaging back projectionimaging ormultidimensionalmatched filtering imagingTheestimation is displayed in Figure 2(b)

5 Experiment Results

51 Vibration Measurement Results of Two Idle Cars We atfirst measured the vibration of two cars that is a Mengshicar and a Nissan car whose engines were running idlyby a frequency-modulated continuous wave (FMCW) radaras Figures 3(a) and 3(b) show The carrier frequency is25GHz and the bandwidth is 2GHz which results in a 75 cmresolution in rangeThe phase 120593(119905) is measured and thereforethe vibration range 119903 can be obtained by 119903(119905) = 120593(119905)(1198884120587)after the phase filtering and the DC being eliminated asshown in Figure 3(c) Finally the vibration spectra can beobtained simply by the Fourier transform of 119903(119905) as displayedin Figure 3(d) From the spectra it can clearly be seen thatonly few strong vibration frequency components about 2sim3for our subjects exist for idle cars Therefore one can model

International Journal of Antennas and Propagation 5

Azimuth (m)

Rang

e (m

)

minus04minus0200204minus04

minus03

minus02

minus01

0

01

02

03

04

(a)

Rang

e (m

)

Azimuth (m)minus04minus0200204

minus04

minus03

minus02

minus01

0

01

02

03

04

(b)

Figure 2 Initial imaging of a vibrating target at (0 0) by different methods (the arrow points to the maxima and the true maximum is locatedat (0 0)) (a) Moore-Penrose pseudoinverse and (b) correlation

(a) (b)

04 05 06 07 08minus006

minus004

minus002

0

002

004

006

008

Time (s)

Rang

e (m

m)

Stationary Mengshi carIdle Mengshi carIdle Nissan car

(c)

0 10 20 30 40

02

04

06

08

1

Frequency (Hz)

Am

plitu

de

Mengshi carNissan car

(d)

Figure 3 Vibration measurement results of two idle cars (a) Mengshi car (b) Nissan car (c) vibration amplitude versus time (d) vibrationspectra

6 International Journal of Antennas and Propagation

Azimuth (m)minus3minus2minus10123

minus08

minus06

minus04

minus02

0

02

04

06

08

Rang

e (m

)

(a)

Azimuth (m)

Rang

e (m

)

minus3minus2minus10123

minus08

minus06

minus04

minus02

0

02

04

06

08

(b)

Figure 4 SAR images of a vibrating point target with the vibration amplitude 1mm and frequency 1Hz without refocusing (a) X-band (b)THz band (220GHz)

the vibration by the synthesis of simple harmonic vibrationsIn the paper we only use one component for simplicity andwithout loss of generality

52 THz-SAR Imaging Results of Simulated Vibrating TargetsWe proceed to conduct the following numerical experimentas real experiments are right now not available due to lowpower of our THz source available to validate the algorithmproposed THz-SAR system parameters are given in Table 1The experiment includes comparison of vibrating targetimages in microwave and terahertz bands and imaging ofvibrating point targets as well as a tank model

521 Comparison of Vibrating Target Images in Microwaveand Terahertz Bands Figure 4 provides a good representa-tion of original image characteristics of a vibrating targetin different bands For the X-band the resolution is 015mand 028m in range and azimuth respectively Only a fewghosts are present in the image as Figure 4(a) shows andthe ghosts bear strong resemblance to stationary point targetsor their sidelobes hence difficult to discriminate betweenvibration and stillness In contrast the vibrating target takeson a line segment in the THz-SAR image as Figure 4(b)depicts Clearly terahertz can enforce the vibrating targetimage feature and therefore is expected to be used as the bestband for vibration sensing In addition the line segment inFigure 4(b) also consists of ghosts while the spacing betweenwhich is so near in the terahertz regime that is not resolvedas (13) predicts

522 Vibrating Point Target Imaging For quantitativelyanalyzing the performance of the algorithm proposed weuse three point targets in the experiment herein whoseparameters are shown in Table 1 The images formulated bythe polar format algorithm (PFA) are displayed in Figure 5where the stationary target is well focused at the bottomwhilethe two vibrating ones are blurred into segments

Azimuth (m)

Rang

e (m

)

minus3minus2minus10123

minus08

minus06

minus04

minus02

0

02

04

06

08

12

3

Figure 5 THz-SAR image of point targets in Table 2 withoutrefocusing

Table 1 THz-SAR parameters

Mode Spotlight CPI 05 sCarrier frequency 220GHz Bandwidth 10GHzSlant angle 0∘ Platform velocity 80msRange resolution 0015m Azimuth resolution 0051m

Nowwe employ the correlationmethod and the improvedExCoV to reconstruct vibrating target scattering coefficientshence obtaining their refocused images The imaged sizeis just set 08m times 08m both with 004m grid spacingfor the memory as well as computation time costs andthe sparse sampling rate is 40 implying that compressivesensing is utilized together with ExCoV Multidimensionalimages are obtained with the dimension in accord with120578

def= [119909 119910 119903 119891119898 1205930]119879 and parts of their slices along the

International Journal of Antennas and Propagation 7

minus04minus0200204 minus04minus0200204 minus04minus0200204 minus04minus0200204

minus04minus0200204 minus04minus0200204 minus04minus0200204 minus04minus0200204

Rang

e (m

)Ra

nge (

m)

Rang

e (m

)Ra

nge (

m)

minus04minus0200204 minus04minus0200204 minus04minus0200204 minus04minus0200204

minus04minus0200204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

Azimuth (m)Azimuth (m)Azimuth (m)Azimuth (m)minus04minus0200204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus0200204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus0200204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

1

2

3

fm = 27Hzfm = 26Hzfm = 25Hzfm = 0Hz

r=

0m

r=

000

5m

r=

000

6m

r=

000

7m

Figure 6 THz-SAR image of point targets in Table 2 under minus10 dB SNR refocused via correlation imaging

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

Rang

e (m

)Ra

nge (

m)

Rang

e (m

)Ra

nge (

m)

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

Azimuth (m) Azimuth (m) Azimuth (m) Azimuth (m)

1

2

3

fm = 0Hz fm = 25Hz fm = 26Hz fm = 27Hz

r=

0m

r=

000

5m

r=

000

6m

r=

000

7m

Figure 7 THz-SAR image of point targets in Table 2 under minus10 dB SNR refocused via ExCoV imaging

vibration frequency 119891119898 and amplitude 119903 are shown in Figures6 and 7 Clearly the ExCoV method provides better imagingresults while the image by the correlation method showshigh sidelobes and generates some artifacts for the stationarytarget From the location of the focused image slices inFigure 7 one can readily estimate the vibration parameters

We define the root MSE (RMSE) between the recon-structed scattering coefficient and the true values that isRMSE = a minus aa where a denotes the true valuesto test the algorithm performance 100 times Monte Carlosimulations are conducted for each SNR value to obtainFigure 8 indicating that RMSE drops sharply with SNR

Excellent performance can be realized in low SNR andFigure 7 is an example of minus10 dB SNR

523 Vibrating Tank Model Imaging A real SAR imagearound the Isleta Lake in New Mexico (Figure 9(b)) isdownloaded from the Sandia Cooperation website and isused to generate the scene echoes [26] Then a simulatedvibrating tank model (Figure 9(a)) is fed into the scenewith the size 037m times 02m times 018m (length by widthby height) and with the vibration frequency 25Hz andamplitude 0005m Its images when stationary and vibratingare shown in Figures 9(c) and 9(d)The refocused image slice

8 International Journal of Antennas and Propagation

minus20 minus10 0 10

025

03

035

04

045

05

SNR (dB)

RMSE

Figure 8 The RMSE versus SNR for the ExCoV method

(a) (b)

Azimuth (m)

Rang

e (m

)

minus05005

minus08

minus06

minus04

minus02

0

02

04

06

08

(c)

Azimuth (m)

Rang

e (m

)

minus05005

minus08

minus06

minus04

minus02

0

02

04

06

08

(d)

Figure 9 Simulated THz-SAR images of the tank model when stationary and vibrating respectively (a) Tank model (b) Isleta Lake in NewMexico used as the background (c) image of stationary tank model (d) image of vibrating tank model

Table 2 Point target parameters

Target number Azimuth Range Vibration frequency Vibration amplitude1 (stationary) 02m minus02m 0 02 (vibrating) 0 0 25Hz 0006m3 (vibrating) minus02m 02m 26Hz 0007m

International Journal of Antennas and Propagation 9

Azimuth (m)

Rang

e (m

)

minus04minus0200204minus04

minus03

minus02

minus01

0

01

02

03

04

Figure 10 THz-SAR image slice of the vibrating tank model on theIsleta Lake background refocused by the ExCoV method

is displayed in Figure 10 and the location of the slice indicatesthe correct vibration frequency and amplitude In reality thevibrating parameters will take on estimation error due toparameter grid mismatch which remains to be explored infuture investigations

6 Conclusion

Terahertz has significant advantages of remote vibration sens-ing over microwave bands In this paper the THz-SAR echomodel of vibrating targets has been establishedTheir imagingcharacteristics with THz-SAR are analyzed and the mainfeatures of vibrating point targets are segments consistingof unresolvable ghosts An improved algorithm based onExCoV withmore robust and efficient initialization has beenproposed in the sparse Bayesian framework for reconstruct-ing scattering coefficients Data of vibrating targets and a tankmodel in a real background has been simulated at 220GHzand the reconstructed images show good performance atlow SNR The algorithm proposed can also overcome thedeficiencies of sidelobes and artifacts arising from traditionalcorrelation (or back projection) imaging method as com-pared in Figures 6 and 7 In fact the algorithm begins withcorrelation and can be treated as combination of ExCoVand correlation Terahertz together with the sparse Bayesiantheory shows a viable and most promising alternative toremote sensing of minor vibrations in particular with rapidlyevolving of solid-state and high-power electric-vacuum tera-hertz devices Although the Bayesian method provides a finesolution to vibrating target imaging algorithms with higherefficiency to realize video-rate THz-SAR imaging are stillto be studied in future especially when multiple vibrationcomponents are taken into account

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The paper is supported by the National Natural ScienceFoundation for Young Scientists of China under Grants61302148 and 61571011

References

[1] S Baumgartner G Krieger K Bethke and S Zuev ldquoTrafficmonitoring with SAR implications of target accelerationrdquo inProceedings of the European Conference on Synthetic ApertureRadar (EUSAR rsquo06) May 2006

[2] X Li B Deng Y Qin H Wang and Y Li ldquoThe influence oftarget micromotion on SAR and GMTIrdquo IEEE Transactions onGeoscience and Remote Sensing vol 49 no 7 pp 2738ndash27512011

[3] E F Stockburger and D N Held ldquoInterferometric movingground target imagingrdquo in Proceedings of the IEEE 1995 Inter-national Radar Conference pp 438ndash443 Alexandria Va USA1995

[4] B Deng G Wu Y Qin H Wang and X Li ldquoSARMMTIAn extension to conventional SARGMTI and a combinationof SAR and micromotion techniquesrdquo in Proceedings of the IETInternational Radar Conference pp 42ndash45 Guilin China April2009

[5] B Deng Y Qin H Wang and Y Li ldquoAngular extent effect ofmicromotion target in SAR image by polar format algorithmrdquoJournal of Systems Engineering and Electronics vol 25 no 3Article ID 6850221 pp 428ndash433 2014

[6] B Deng H-Q Wang Y-L Qin S Zhu and X Li ldquoRotatingparabolic-reflector antenna target in SAR data model char-acteristics and parameter estimationrdquo International Journal ofAntennas and Propagation vol 2013 Article ID 583865 13pages 2013

[7] D B Andre D Blacknell D G Muff and M R NottinghamldquoThe physics of vibrating scatterers in SAR imageryrdquo in SPIEProceedings of the Algorithms for Synthetic Aperture RadarImagery XVIII SPIE Orlando Fla USA April 2011

[8] B Deng H-Q Wang X Li Y-L Qin and J-T WangldquoGeneralised likelihood ratio test detector for micro-motiontargets in synthetic aperture radar raw signalsrdquo IET RadarSonar and Navigation vol 5 no 5 pp 528ndash535 2011

[9] W G Carrara R S Goodman and R M Majewski SpotlightSynthetic Aperture Radar Signal Processing Algorithms ArtechHouse Norwood Mass USA 1995

[10] N S Subotic B J Thelen and D A Carrara ldquoCyclostationarysignalmodels for the detection and characterization of vibratingobjects in SAR datardquo in Proceedings of the Conference Record ofthe 32nd Asilomar Conference on Signals Systems amp Computers(ACSSC rsquo98) vol 2 pp 1304ndash1308 November 1998

[11] Y Chen B Deng H Wang Y Qin and J Ding ldquoVibrationtarget detection and vibration parameters estimation based onthe DPCA technique in dual-channel SARrdquo Science ChinaInformation Sciences vol 55 no 10 pp 2281ndash2291 2012

[12] M Ruegg E Meier and D Nuesch ldquoVibration and rotationin millimeter-wave SARrdquo IEEE Transactions on Geoscience andRemote Sensing vol 45 no 2 pp 293ndash304 2007

[13] W Zhang C Tong Q Zhang Y Zhang and X ZhangldquoExtraction of vibrating features with dual-channel fixed-receiver bistatic SARrdquo IEEE Geoscience and Remote SensingLetters vol 9 no 3 pp 507ndash511 2012

10 International Journal of Antennas and Propagation

[14] W Zhang C Tong L Ren X Chen and X Zhang ldquoBistaticmicro-Doppler radar signatures of vibrating targets with along-track interferometryrdquo in Proceedings of the 4th IEEE Interna-tional Symposium on Microwave Antenna Propagation andEMC Technologies for Wireless Communications (MAPE rsquo11) pp505ndash508 Beijing China November 2011

[15] Q Wang M Pepin A Wright et al ldquoReduction of vibration-induced artifacts in synthetic aperture radar imageryrdquo IEEETransactions on Geoscience and Remote Sensing vol 52 no 6pp 3063ndash3073 2014

[16] B Deng Y-L Qin H-Q Wang X Li and H Li ldquoPulse-repetition-interval transform-based vibrating target detectionand estimation in synthetic aperture radarrdquo IET Signal Process-ing vol 6 no 6 pp 551ndash558 2012

[17] T Sparr and B Krane ldquoMicro-Doppler analysis of vibratingtargets in SARrdquo IEE ProceedingsmdashRadar Sonar and Navigationvol 150 no 4 pp 277ndash283 2003

[18] Q Wang M Pepin R J Beach et al ldquoSAR-based vibrationestimation using the discrete fractional Fourier transformrdquoIEEE Transactions on Geoscience and Remote Sensing vol 50no 10 pp 4145ndash4156 2012

[19] Y Zhang J Sun P Lei and W Hong ldquoSAR-based pairedecho focusing and suppression of vibrating targetsrdquo IEEETransactions on Geoscience and Remote Sensing vol 52 no 12pp 7593ndash7605 2014

[20] Y Qin B Deng Z Huang and W Su ldquoHybrid micromotion-scattering center model for synthetic aperture radar micro-motion target imagingrdquo Journal of Systems Engineering andElectronics vol 24 no 6 pp 931ndash937 2013

[21] H B Wallace ldquoVideo synthetic aperture radar (ViSAR)rdquoDARPA 2012

[22] R G Wiley The Interception and Analysis of Radar SignalsArtch House Bristol UK 2006

[23] J Ender ldquoA brief review of compressive sensing applied toradarrdquo in Proceedings of the 14th International Radar Symposium(IRS rsquo13) pp 3ndash16 Dresden Germany June 2013

[24] K Qiu and A Dogandzic ldquoVariance-component based sparsesignal reconstruction and model selectionrdquo IEEE Transactionson Signal Processing vol 58 no 6 pp 2935ndash2952 2010

[25] W G Su H Q Wang B Deng and R J Wang ldquoSparseBayesian SAR imaging of moving target via the excov methodrdquoin Proceedings of the IEEE Workshop on Statistical SignalProcessing pp 448ndash451 June-July 2014

[26] B Deng Y Qin Y Li H Wang and X Li ldquoFast simulation ofraw signals from natural scenes for squint stripmap SARrdquo inProceedings of the Asia-Pacific Conference on Synthetic ApertureRadar (APSAR rsquo09) pp 235ndash238 IEEE Xian China October2009

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpswwwhindawicom

VLSI Design

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Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

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Advances inOptoElectronics

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Volume 2014

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SensorsJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

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Navigation and Observation

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DistributedSensor Networks

International Journal of

International Journal of Antennas and Propagation 3

x

yo

T

P

Rc

(x120578120579 y120578120579)

120579

y998400 = Vat

(a)

x

yoT

Py998400

Rc

T998400

120579

(x120578120579 y120578120579)

(b)

oO120579

Ky

K

ky

kx Kx

KC

(c)

Figure 1 Spotlight SAR moving target geometry (a) slant plane view (b) plane wave approximation (c) wavenumber-domain view

Substituting (6) into (5) discretizing the result andadding noise yield

119866 (119870 120579) = 119868sum119894=1

119886119894 sdot 119890119870120579 (120578119894) + V119894 (8)

where 119868 is the number of vibrating targets (it can also includestationary body points by just setting 119903 or 119891119898 to zero andcan include no target by setting 119886119894 to zero) 119886119894 denotes thescattering coefficient of the 119894th target and

119890119870120579 (120578119894)def= exp (minus119895119870119909119894 cos 120579 minus 119895119870119910119894 sin 120579)

sdot exp(minus119895119870119903119894 cos(2120587119891119898119894119877119888119881119886 tan 120579 + 1205930119894)) (9)

During the derivation of (9) 119905 = 119877119888 tan 120579119881119886 from (1) and2120587119891119898119877119888119881119886 ≫ 1 have been usedIn (9) we can clearly see that there is an additional

exponential component that is the last term representingtarget vibration in (9) when compared with the stationaryscattering center model Note119870 and 120579 can also be discretizedinto 119872 and 119873 values respectively and therefore (8) can beexpressed in a matrix form as

g = Φa + k (10)

where

g = [119866 (1198701 1205791) 119866 (1198701 1205792) 119866 (119870119872 120579119873)]119879 a def= [1198861 1198862 119886119868]119879 v def= [V1 V2 V119868]119879

Φ =[[[[[[[[

11989011987011205791 (1205781) 11989011987011205791 (1205782) sdot sdot sdot 11989011987011205791 (120578119868)11989011987011205792 (1205781) 11989011987011205792 (1205782) sdot sdot sdot 11989011987011987711205792 (120578119868) sdot sdot sdot sdot sdot sdot119890119870119872120579119873 (1205781) 119890119870119872120579119873 (1205782) sdot sdot sdot 119890119870119872120579119873 (120578119868)

]]]]]]]]

(11)

From (10) the imaging or scattering coefficient recon-struction problem can be regarded as an inverse problem ofsolving linear equations

What deserves special mention is that the unknown 120578 hasalso been discretized into 1205781 1205782 120578119868 which are located ata high-dimensional cubic grid and therefore Φ contains nounknowns

3 The Influence of Target Vibration onTHZ-SAR Image

It is well known that vibrating targets cannot be focusedin microwave SAR images and a ghost image will generallyresult according to the paired echo principle We now try toanalyze THz-SAR image characteristics of vibrating targetsThe space between ghosts is a constant [2]

Δ119910 = 1198911198981205821198621198771198882119881119886 (12)

For THz-SAR Δ119910 will decrease by a commensurateamount compared with microwave SAR since 120582119862 is signifi-cantly smaller than the wavelength at X-band or mmWband

Note the azimuth resolution 120588119886 = 1205821198621198771198882119881119886119879119897 where119879119897 isthe coherent processing interval (CPI) and the space in pixelor resolution cell can be expressed as

Δ119910120588119886 = 119891119898119879119897 (13)

It is apparent that the space in pixel or resolution cell hasno relation with the frequency band However 119879119897 needed forthe same resolution as microwave SAR is reduced for THz-SAR For typical parameter values Δ119910120588119886 le 1 which statesthat the ghosts are not resolvable and line segment results

According to Carsonrsquos rule [22] the ghost number plusthe real target is

119873 asymp 8120587119903120582119862 + 3 (14)

From (12) and (14) the length of the ghost image or theline segment in azimuth is

Δ119871 = Δ119910119873 = (8120587119903 + 3120582119862) 1198911198981198771198882119881119886 (15)

4 International Journal of Antennas and Propagation

Equation (15) makes it clear that Δ119871 will decrease whenthe frequency moves to the terahertz band

4 Vibrating Target Imaging viathe Improved ExCoV Method

In order to solve (8) we model the pdf of THz-SAR echovector g given a and 1205902 using the standard additive Gaussiannoise model

119901 (g | a 1205902) = 119873(gΦa 1205902C) (16)

where C is a known positive definite symmetric matrix ofsize119872119873times119872119873 1205902 is an unknown noise-variance parameterand 1205902C is the noise covariance matrix The SBL employsa Gaussian prior on the signal with a distinct variancecomponent on each signal element

119901 (119886119894 120574119894) = 119873 (0 120574119894) = (2120587120574119894)minus12 exp(minus 11988621198942120574119894) 119894 = 1 119868

(17)

However we have known according to the sparse recov-ery theory and a priori knowledge that in most real-worldcases only a few elements of a have significant magnitudesand that the remaining elements are either strictly zerosor close to zeros [23] Therefore the prior distribution (17)did not capture the signal key feature that is sparsity Onthe contrary the ExCoV method assigns distinct variancecomponents to the candidates for significant signal elementsand uses only one common variance-component parameterto account for the variability of the rest of signal coefficients[24] LetΛ be the full index set in the signal and let the size be119868 Denote A as the set of indices of the signal elements withdistinct variance components and the size as 119898A and definethe complementary index set B = ΛAwith cardinality119898B =119868 minus 119898A Accordingly we partition Φ and a into submatricesΦA and ΦB and subvectors aA andaB Then the followingprior model for the signal coefficients is adopted

119901 (a | 120575A 1205742) = 119901 (aA | 120575A) sdot 119901 (aB | 1205742)= 119873(aA 0119898Atimes1 119863A (120575A))sdot 119873 (aB 0119898Btimes1 119863B (1205742))

(18)

where 119863A(120575A) = diag 1205752A1 1205752A2 1205752A119898A and 119863B(1205742) =1205742I119898B are the signal covariance matrices and the variancecomponents 1205752A1 1205752A2 1205752A119898A for aA are distinct whilethe common variance 1205742 accounts for the variability ofaB Assume that the signal variance components 120575A and1205742 are unknown and define the set of all unknowns 120579 =(A 120575A 1205742 1205902) and then the marginal pdf of the observationsg given 120579 is [24]

119901 (g | 120579) = int119901 (g | a 1205902) sdot 119901 (a | 120575A 1205742) da= 119873(g 0119872119873times1 119875minus1 (120579))

(19)

where 119875(120579) is the inverse covariance matrix of g given 120579Clearly 119901(g | 120579) provides generalized maximum-likelihood(GML) estimation of 120579 The GML estimation of 119901(g |a 1205902)119901(a | 120575A 1205742) proceeds for obtaining the only unknown aas the image The whole estimation process is iteratively real-ized via applying the ExCoV algorithm and the iteration willterminate when A does not change between two consecutivecycles [24]

ExCoV has demonstrated an excellent algorithm forsolving linear equations arising from the real world especiallyfrom the radar field [25] Compared to SBL (SBL-EM SBL-Type II VBSBL and ESBL) SpaRSA and CoSaMP it has thesmallest mean-square error (MSE) in the low signal-to-noiseratio (SNR) and the second highest computation efficiency(not better than CoSaMP whose MSE is large) It beginswith an initialization followed by complex iterations Theinitialization provides the starting point for the following iter-ations and thus plays an important part for fast convergenceThe original ExCoVutilizesMoore-Penrose pseudoinverse toinitialize the parameters that is

a(0) = Φ119867 (ΦΦ119867)minus1 g (20)

where 119867 denotes complex conjugation The first 119898(0)A largestelements of a(0) are found to initialize A

However ΦΦ119867 is usually rank deficient for real radarproblems and hence ΦΦ119867 is not inversible resulting inwrong estimation of a(0) An example is shown in Figure 2(a)We recognize that ΦΦ119867 denotes autocorrelation and cross-correlation of the measurement matrix and will give a sinc-shaped system response (ΦΦ119867)minus1 is just the inverse sincresponse which is an identity matrix in ideal condition torealize super-resolution estimation of a Thus we abandonthis term and obtain a more robust efficient and simplerestimation than (20) as

a(0) = Φ119867g (21)

which can also be called correlation imaging back projectionimaging ormultidimensionalmatched filtering imagingTheestimation is displayed in Figure 2(b)

5 Experiment Results

51 Vibration Measurement Results of Two Idle Cars We atfirst measured the vibration of two cars that is a Mengshicar and a Nissan car whose engines were running idlyby a frequency-modulated continuous wave (FMCW) radaras Figures 3(a) and 3(b) show The carrier frequency is25GHz and the bandwidth is 2GHz which results in a 75 cmresolution in rangeThe phase 120593(119905) is measured and thereforethe vibration range 119903 can be obtained by 119903(119905) = 120593(119905)(1198884120587)after the phase filtering and the DC being eliminated asshown in Figure 3(c) Finally the vibration spectra can beobtained simply by the Fourier transform of 119903(119905) as displayedin Figure 3(d) From the spectra it can clearly be seen thatonly few strong vibration frequency components about 2sim3for our subjects exist for idle cars Therefore one can model

International Journal of Antennas and Propagation 5

Azimuth (m)

Rang

e (m

)

minus04minus0200204minus04

minus03

minus02

minus01

0

01

02

03

04

(a)

Rang

e (m

)

Azimuth (m)minus04minus0200204

minus04

minus03

minus02

minus01

0

01

02

03

04

(b)

Figure 2 Initial imaging of a vibrating target at (0 0) by different methods (the arrow points to the maxima and the true maximum is locatedat (0 0)) (a) Moore-Penrose pseudoinverse and (b) correlation

(a) (b)

04 05 06 07 08minus006

minus004

minus002

0

002

004

006

008

Time (s)

Rang

e (m

m)

Stationary Mengshi carIdle Mengshi carIdle Nissan car

(c)

0 10 20 30 40

02

04

06

08

1

Frequency (Hz)

Am

plitu

de

Mengshi carNissan car

(d)

Figure 3 Vibration measurement results of two idle cars (a) Mengshi car (b) Nissan car (c) vibration amplitude versus time (d) vibrationspectra

6 International Journal of Antennas and Propagation

Azimuth (m)minus3minus2minus10123

minus08

minus06

minus04

minus02

0

02

04

06

08

Rang

e (m

)

(a)

Azimuth (m)

Rang

e (m

)

minus3minus2minus10123

minus08

minus06

minus04

minus02

0

02

04

06

08

(b)

Figure 4 SAR images of a vibrating point target with the vibration amplitude 1mm and frequency 1Hz without refocusing (a) X-band (b)THz band (220GHz)

the vibration by the synthesis of simple harmonic vibrationsIn the paper we only use one component for simplicity andwithout loss of generality

52 THz-SAR Imaging Results of Simulated Vibrating TargetsWe proceed to conduct the following numerical experimentas real experiments are right now not available due to lowpower of our THz source available to validate the algorithmproposed THz-SAR system parameters are given in Table 1The experiment includes comparison of vibrating targetimages in microwave and terahertz bands and imaging ofvibrating point targets as well as a tank model

521 Comparison of Vibrating Target Images in Microwaveand Terahertz Bands Figure 4 provides a good representa-tion of original image characteristics of a vibrating targetin different bands For the X-band the resolution is 015mand 028m in range and azimuth respectively Only a fewghosts are present in the image as Figure 4(a) shows andthe ghosts bear strong resemblance to stationary point targetsor their sidelobes hence difficult to discriminate betweenvibration and stillness In contrast the vibrating target takeson a line segment in the THz-SAR image as Figure 4(b)depicts Clearly terahertz can enforce the vibrating targetimage feature and therefore is expected to be used as the bestband for vibration sensing In addition the line segment inFigure 4(b) also consists of ghosts while the spacing betweenwhich is so near in the terahertz regime that is not resolvedas (13) predicts

522 Vibrating Point Target Imaging For quantitativelyanalyzing the performance of the algorithm proposed weuse three point targets in the experiment herein whoseparameters are shown in Table 1 The images formulated bythe polar format algorithm (PFA) are displayed in Figure 5where the stationary target is well focused at the bottomwhilethe two vibrating ones are blurred into segments

Azimuth (m)

Rang

e (m

)

minus3minus2minus10123

minus08

minus06

minus04

minus02

0

02

04

06

08

12

3

Figure 5 THz-SAR image of point targets in Table 2 withoutrefocusing

Table 1 THz-SAR parameters

Mode Spotlight CPI 05 sCarrier frequency 220GHz Bandwidth 10GHzSlant angle 0∘ Platform velocity 80msRange resolution 0015m Azimuth resolution 0051m

Nowwe employ the correlationmethod and the improvedExCoV to reconstruct vibrating target scattering coefficientshence obtaining their refocused images The imaged sizeis just set 08m times 08m both with 004m grid spacingfor the memory as well as computation time costs andthe sparse sampling rate is 40 implying that compressivesensing is utilized together with ExCoV Multidimensionalimages are obtained with the dimension in accord with120578

def= [119909 119910 119903 119891119898 1205930]119879 and parts of their slices along the

International Journal of Antennas and Propagation 7

minus04minus0200204 minus04minus0200204 minus04minus0200204 minus04minus0200204

minus04minus0200204 minus04minus0200204 minus04minus0200204 minus04minus0200204

Rang

e (m

)Ra

nge (

m)

Rang

e (m

)Ra

nge (

m)

minus04minus0200204 minus04minus0200204 minus04minus0200204 minus04minus0200204

minus04minus0200204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

Azimuth (m)Azimuth (m)Azimuth (m)Azimuth (m)minus04minus0200204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus0200204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus0200204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

1

2

3

fm = 27Hzfm = 26Hzfm = 25Hzfm = 0Hz

r=

0m

r=

000

5m

r=

000

6m

r=

000

7m

Figure 6 THz-SAR image of point targets in Table 2 under minus10 dB SNR refocused via correlation imaging

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

Rang

e (m

)Ra

nge (

m)

Rang

e (m

)Ra

nge (

m)

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

Azimuth (m) Azimuth (m) Azimuth (m) Azimuth (m)

1

2

3

fm = 0Hz fm = 25Hz fm = 26Hz fm = 27Hz

r=

0m

r=

000

5m

r=

000

6m

r=

000

7m

Figure 7 THz-SAR image of point targets in Table 2 under minus10 dB SNR refocused via ExCoV imaging

vibration frequency 119891119898 and amplitude 119903 are shown in Figures6 and 7 Clearly the ExCoV method provides better imagingresults while the image by the correlation method showshigh sidelobes and generates some artifacts for the stationarytarget From the location of the focused image slices inFigure 7 one can readily estimate the vibration parameters

We define the root MSE (RMSE) between the recon-structed scattering coefficient and the true values that isRMSE = a minus aa where a denotes the true valuesto test the algorithm performance 100 times Monte Carlosimulations are conducted for each SNR value to obtainFigure 8 indicating that RMSE drops sharply with SNR

Excellent performance can be realized in low SNR andFigure 7 is an example of minus10 dB SNR

523 Vibrating Tank Model Imaging A real SAR imagearound the Isleta Lake in New Mexico (Figure 9(b)) isdownloaded from the Sandia Cooperation website and isused to generate the scene echoes [26] Then a simulatedvibrating tank model (Figure 9(a)) is fed into the scenewith the size 037m times 02m times 018m (length by widthby height) and with the vibration frequency 25Hz andamplitude 0005m Its images when stationary and vibratingare shown in Figures 9(c) and 9(d)The refocused image slice

8 International Journal of Antennas and Propagation

minus20 minus10 0 10

025

03

035

04

045

05

SNR (dB)

RMSE

Figure 8 The RMSE versus SNR for the ExCoV method

(a) (b)

Azimuth (m)

Rang

e (m

)

minus05005

minus08

minus06

minus04

minus02

0

02

04

06

08

(c)

Azimuth (m)

Rang

e (m

)

minus05005

minus08

minus06

minus04

minus02

0

02

04

06

08

(d)

Figure 9 Simulated THz-SAR images of the tank model when stationary and vibrating respectively (a) Tank model (b) Isleta Lake in NewMexico used as the background (c) image of stationary tank model (d) image of vibrating tank model

Table 2 Point target parameters

Target number Azimuth Range Vibration frequency Vibration amplitude1 (stationary) 02m minus02m 0 02 (vibrating) 0 0 25Hz 0006m3 (vibrating) minus02m 02m 26Hz 0007m

International Journal of Antennas and Propagation 9

Azimuth (m)

Rang

e (m

)

minus04minus0200204minus04

minus03

minus02

minus01

0

01

02

03

04

Figure 10 THz-SAR image slice of the vibrating tank model on theIsleta Lake background refocused by the ExCoV method

is displayed in Figure 10 and the location of the slice indicatesthe correct vibration frequency and amplitude In reality thevibrating parameters will take on estimation error due toparameter grid mismatch which remains to be explored infuture investigations

6 Conclusion

Terahertz has significant advantages of remote vibration sens-ing over microwave bands In this paper the THz-SAR echomodel of vibrating targets has been establishedTheir imagingcharacteristics with THz-SAR are analyzed and the mainfeatures of vibrating point targets are segments consistingof unresolvable ghosts An improved algorithm based onExCoV withmore robust and efficient initialization has beenproposed in the sparse Bayesian framework for reconstruct-ing scattering coefficients Data of vibrating targets and a tankmodel in a real background has been simulated at 220GHzand the reconstructed images show good performance atlow SNR The algorithm proposed can also overcome thedeficiencies of sidelobes and artifacts arising from traditionalcorrelation (or back projection) imaging method as com-pared in Figures 6 and 7 In fact the algorithm begins withcorrelation and can be treated as combination of ExCoVand correlation Terahertz together with the sparse Bayesiantheory shows a viable and most promising alternative toremote sensing of minor vibrations in particular with rapidlyevolving of solid-state and high-power electric-vacuum tera-hertz devices Although the Bayesian method provides a finesolution to vibrating target imaging algorithms with higherefficiency to realize video-rate THz-SAR imaging are stillto be studied in future especially when multiple vibrationcomponents are taken into account

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The paper is supported by the National Natural ScienceFoundation for Young Scientists of China under Grants61302148 and 61571011

References

[1] S Baumgartner G Krieger K Bethke and S Zuev ldquoTrafficmonitoring with SAR implications of target accelerationrdquo inProceedings of the European Conference on Synthetic ApertureRadar (EUSAR rsquo06) May 2006

[2] X Li B Deng Y Qin H Wang and Y Li ldquoThe influence oftarget micromotion on SAR and GMTIrdquo IEEE Transactions onGeoscience and Remote Sensing vol 49 no 7 pp 2738ndash27512011

[3] E F Stockburger and D N Held ldquoInterferometric movingground target imagingrdquo in Proceedings of the IEEE 1995 Inter-national Radar Conference pp 438ndash443 Alexandria Va USA1995

[4] B Deng G Wu Y Qin H Wang and X Li ldquoSARMMTIAn extension to conventional SARGMTI and a combinationof SAR and micromotion techniquesrdquo in Proceedings of the IETInternational Radar Conference pp 42ndash45 Guilin China April2009

[5] B Deng Y Qin H Wang and Y Li ldquoAngular extent effect ofmicromotion target in SAR image by polar format algorithmrdquoJournal of Systems Engineering and Electronics vol 25 no 3Article ID 6850221 pp 428ndash433 2014

[6] B Deng H-Q Wang Y-L Qin S Zhu and X Li ldquoRotatingparabolic-reflector antenna target in SAR data model char-acteristics and parameter estimationrdquo International Journal ofAntennas and Propagation vol 2013 Article ID 583865 13pages 2013

[7] D B Andre D Blacknell D G Muff and M R NottinghamldquoThe physics of vibrating scatterers in SAR imageryrdquo in SPIEProceedings of the Algorithms for Synthetic Aperture RadarImagery XVIII SPIE Orlando Fla USA April 2011

[8] B Deng H-Q Wang X Li Y-L Qin and J-T WangldquoGeneralised likelihood ratio test detector for micro-motiontargets in synthetic aperture radar raw signalsrdquo IET RadarSonar and Navigation vol 5 no 5 pp 528ndash535 2011

[9] W G Carrara R S Goodman and R M Majewski SpotlightSynthetic Aperture Radar Signal Processing Algorithms ArtechHouse Norwood Mass USA 1995

[10] N S Subotic B J Thelen and D A Carrara ldquoCyclostationarysignalmodels for the detection and characterization of vibratingobjects in SAR datardquo in Proceedings of the Conference Record ofthe 32nd Asilomar Conference on Signals Systems amp Computers(ACSSC rsquo98) vol 2 pp 1304ndash1308 November 1998

[11] Y Chen B Deng H Wang Y Qin and J Ding ldquoVibrationtarget detection and vibration parameters estimation based onthe DPCA technique in dual-channel SARrdquo Science ChinaInformation Sciences vol 55 no 10 pp 2281ndash2291 2012

[12] M Ruegg E Meier and D Nuesch ldquoVibration and rotationin millimeter-wave SARrdquo IEEE Transactions on Geoscience andRemote Sensing vol 45 no 2 pp 293ndash304 2007

[13] W Zhang C Tong Q Zhang Y Zhang and X ZhangldquoExtraction of vibrating features with dual-channel fixed-receiver bistatic SARrdquo IEEE Geoscience and Remote SensingLetters vol 9 no 3 pp 507ndash511 2012

10 International Journal of Antennas and Propagation

[14] W Zhang C Tong L Ren X Chen and X Zhang ldquoBistaticmicro-Doppler radar signatures of vibrating targets with along-track interferometryrdquo in Proceedings of the 4th IEEE Interna-tional Symposium on Microwave Antenna Propagation andEMC Technologies for Wireless Communications (MAPE rsquo11) pp505ndash508 Beijing China November 2011

[15] Q Wang M Pepin A Wright et al ldquoReduction of vibration-induced artifacts in synthetic aperture radar imageryrdquo IEEETransactions on Geoscience and Remote Sensing vol 52 no 6pp 3063ndash3073 2014

[16] B Deng Y-L Qin H-Q Wang X Li and H Li ldquoPulse-repetition-interval transform-based vibrating target detectionand estimation in synthetic aperture radarrdquo IET Signal Process-ing vol 6 no 6 pp 551ndash558 2012

[17] T Sparr and B Krane ldquoMicro-Doppler analysis of vibratingtargets in SARrdquo IEE ProceedingsmdashRadar Sonar and Navigationvol 150 no 4 pp 277ndash283 2003

[18] Q Wang M Pepin R J Beach et al ldquoSAR-based vibrationestimation using the discrete fractional Fourier transformrdquoIEEE Transactions on Geoscience and Remote Sensing vol 50no 10 pp 4145ndash4156 2012

[19] Y Zhang J Sun P Lei and W Hong ldquoSAR-based pairedecho focusing and suppression of vibrating targetsrdquo IEEETransactions on Geoscience and Remote Sensing vol 52 no 12pp 7593ndash7605 2014

[20] Y Qin B Deng Z Huang and W Su ldquoHybrid micromotion-scattering center model for synthetic aperture radar micro-motion target imagingrdquo Journal of Systems Engineering andElectronics vol 24 no 6 pp 931ndash937 2013

[21] H B Wallace ldquoVideo synthetic aperture radar (ViSAR)rdquoDARPA 2012

[22] R G Wiley The Interception and Analysis of Radar SignalsArtch House Bristol UK 2006

[23] J Ender ldquoA brief review of compressive sensing applied toradarrdquo in Proceedings of the 14th International Radar Symposium(IRS rsquo13) pp 3ndash16 Dresden Germany June 2013

[24] K Qiu and A Dogandzic ldquoVariance-component based sparsesignal reconstruction and model selectionrdquo IEEE Transactionson Signal Processing vol 58 no 6 pp 2935ndash2952 2010

[25] W G Su H Q Wang B Deng and R J Wang ldquoSparseBayesian SAR imaging of moving target via the excov methodrdquoin Proceedings of the IEEE Workshop on Statistical SignalProcessing pp 448ndash451 June-July 2014

[26] B Deng Y Qin Y Li H Wang and X Li ldquoFast simulation ofraw signals from natural scenes for squint stripmap SARrdquo inProceedings of the Asia-Pacific Conference on Synthetic ApertureRadar (APSAR rsquo09) pp 235ndash238 IEEE Xian China October2009

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

4 International Journal of Antennas and Propagation

Equation (15) makes it clear that Δ119871 will decrease whenthe frequency moves to the terahertz band

4 Vibrating Target Imaging viathe Improved ExCoV Method

In order to solve (8) we model the pdf of THz-SAR echovector g given a and 1205902 using the standard additive Gaussiannoise model

119901 (g | a 1205902) = 119873(gΦa 1205902C) (16)

where C is a known positive definite symmetric matrix ofsize119872119873times119872119873 1205902 is an unknown noise-variance parameterand 1205902C is the noise covariance matrix The SBL employsa Gaussian prior on the signal with a distinct variancecomponent on each signal element

119901 (119886119894 120574119894) = 119873 (0 120574119894) = (2120587120574119894)minus12 exp(minus 11988621198942120574119894) 119894 = 1 119868

(17)

However we have known according to the sparse recov-ery theory and a priori knowledge that in most real-worldcases only a few elements of a have significant magnitudesand that the remaining elements are either strictly zerosor close to zeros [23] Therefore the prior distribution (17)did not capture the signal key feature that is sparsity Onthe contrary the ExCoV method assigns distinct variancecomponents to the candidates for significant signal elementsand uses only one common variance-component parameterto account for the variability of the rest of signal coefficients[24] LetΛ be the full index set in the signal and let the size be119868 Denote A as the set of indices of the signal elements withdistinct variance components and the size as 119898A and definethe complementary index set B = ΛAwith cardinality119898B =119868 minus 119898A Accordingly we partition Φ and a into submatricesΦA and ΦB and subvectors aA andaB Then the followingprior model for the signal coefficients is adopted

119901 (a | 120575A 1205742) = 119901 (aA | 120575A) sdot 119901 (aB | 1205742)= 119873(aA 0119898Atimes1 119863A (120575A))sdot 119873 (aB 0119898Btimes1 119863B (1205742))

(18)

where 119863A(120575A) = diag 1205752A1 1205752A2 1205752A119898A and 119863B(1205742) =1205742I119898B are the signal covariance matrices and the variancecomponents 1205752A1 1205752A2 1205752A119898A for aA are distinct whilethe common variance 1205742 accounts for the variability ofaB Assume that the signal variance components 120575A and1205742 are unknown and define the set of all unknowns 120579 =(A 120575A 1205742 1205902) and then the marginal pdf of the observationsg given 120579 is [24]

119901 (g | 120579) = int119901 (g | a 1205902) sdot 119901 (a | 120575A 1205742) da= 119873(g 0119872119873times1 119875minus1 (120579))

(19)

where 119875(120579) is the inverse covariance matrix of g given 120579Clearly 119901(g | 120579) provides generalized maximum-likelihood(GML) estimation of 120579 The GML estimation of 119901(g |a 1205902)119901(a | 120575A 1205742) proceeds for obtaining the only unknown aas the image The whole estimation process is iteratively real-ized via applying the ExCoV algorithm and the iteration willterminate when A does not change between two consecutivecycles [24]

ExCoV has demonstrated an excellent algorithm forsolving linear equations arising from the real world especiallyfrom the radar field [25] Compared to SBL (SBL-EM SBL-Type II VBSBL and ESBL) SpaRSA and CoSaMP it has thesmallest mean-square error (MSE) in the low signal-to-noiseratio (SNR) and the second highest computation efficiency(not better than CoSaMP whose MSE is large) It beginswith an initialization followed by complex iterations Theinitialization provides the starting point for the following iter-ations and thus plays an important part for fast convergenceThe original ExCoVutilizesMoore-Penrose pseudoinverse toinitialize the parameters that is

a(0) = Φ119867 (ΦΦ119867)minus1 g (20)

where 119867 denotes complex conjugation The first 119898(0)A largestelements of a(0) are found to initialize A

However ΦΦ119867 is usually rank deficient for real radarproblems and hence ΦΦ119867 is not inversible resulting inwrong estimation of a(0) An example is shown in Figure 2(a)We recognize that ΦΦ119867 denotes autocorrelation and cross-correlation of the measurement matrix and will give a sinc-shaped system response (ΦΦ119867)minus1 is just the inverse sincresponse which is an identity matrix in ideal condition torealize super-resolution estimation of a Thus we abandonthis term and obtain a more robust efficient and simplerestimation than (20) as

a(0) = Φ119867g (21)

which can also be called correlation imaging back projectionimaging ormultidimensionalmatched filtering imagingTheestimation is displayed in Figure 2(b)

5 Experiment Results

51 Vibration Measurement Results of Two Idle Cars We atfirst measured the vibration of two cars that is a Mengshicar and a Nissan car whose engines were running idlyby a frequency-modulated continuous wave (FMCW) radaras Figures 3(a) and 3(b) show The carrier frequency is25GHz and the bandwidth is 2GHz which results in a 75 cmresolution in rangeThe phase 120593(119905) is measured and thereforethe vibration range 119903 can be obtained by 119903(119905) = 120593(119905)(1198884120587)after the phase filtering and the DC being eliminated asshown in Figure 3(c) Finally the vibration spectra can beobtained simply by the Fourier transform of 119903(119905) as displayedin Figure 3(d) From the spectra it can clearly be seen thatonly few strong vibration frequency components about 2sim3for our subjects exist for idle cars Therefore one can model

International Journal of Antennas and Propagation 5

Azimuth (m)

Rang

e (m

)

minus04minus0200204minus04

minus03

minus02

minus01

0

01

02

03

04

(a)

Rang

e (m

)

Azimuth (m)minus04minus0200204

minus04

minus03

minus02

minus01

0

01

02

03

04

(b)

Figure 2 Initial imaging of a vibrating target at (0 0) by different methods (the arrow points to the maxima and the true maximum is locatedat (0 0)) (a) Moore-Penrose pseudoinverse and (b) correlation

(a) (b)

04 05 06 07 08minus006

minus004

minus002

0

002

004

006

008

Time (s)

Rang

e (m

m)

Stationary Mengshi carIdle Mengshi carIdle Nissan car

(c)

0 10 20 30 40

02

04

06

08

1

Frequency (Hz)

Am

plitu

de

Mengshi carNissan car

(d)

Figure 3 Vibration measurement results of two idle cars (a) Mengshi car (b) Nissan car (c) vibration amplitude versus time (d) vibrationspectra

6 International Journal of Antennas and Propagation

Azimuth (m)minus3minus2minus10123

minus08

minus06

minus04

minus02

0

02

04

06

08

Rang

e (m

)

(a)

Azimuth (m)

Rang

e (m

)

minus3minus2minus10123

minus08

minus06

minus04

minus02

0

02

04

06

08

(b)

Figure 4 SAR images of a vibrating point target with the vibration amplitude 1mm and frequency 1Hz without refocusing (a) X-band (b)THz band (220GHz)

the vibration by the synthesis of simple harmonic vibrationsIn the paper we only use one component for simplicity andwithout loss of generality

52 THz-SAR Imaging Results of Simulated Vibrating TargetsWe proceed to conduct the following numerical experimentas real experiments are right now not available due to lowpower of our THz source available to validate the algorithmproposed THz-SAR system parameters are given in Table 1The experiment includes comparison of vibrating targetimages in microwave and terahertz bands and imaging ofvibrating point targets as well as a tank model

521 Comparison of Vibrating Target Images in Microwaveand Terahertz Bands Figure 4 provides a good representa-tion of original image characteristics of a vibrating targetin different bands For the X-band the resolution is 015mand 028m in range and azimuth respectively Only a fewghosts are present in the image as Figure 4(a) shows andthe ghosts bear strong resemblance to stationary point targetsor their sidelobes hence difficult to discriminate betweenvibration and stillness In contrast the vibrating target takeson a line segment in the THz-SAR image as Figure 4(b)depicts Clearly terahertz can enforce the vibrating targetimage feature and therefore is expected to be used as the bestband for vibration sensing In addition the line segment inFigure 4(b) also consists of ghosts while the spacing betweenwhich is so near in the terahertz regime that is not resolvedas (13) predicts

522 Vibrating Point Target Imaging For quantitativelyanalyzing the performance of the algorithm proposed weuse three point targets in the experiment herein whoseparameters are shown in Table 1 The images formulated bythe polar format algorithm (PFA) are displayed in Figure 5where the stationary target is well focused at the bottomwhilethe two vibrating ones are blurred into segments

Azimuth (m)

Rang

e (m

)

minus3minus2minus10123

minus08

minus06

minus04

minus02

0

02

04

06

08

12

3

Figure 5 THz-SAR image of point targets in Table 2 withoutrefocusing

Table 1 THz-SAR parameters

Mode Spotlight CPI 05 sCarrier frequency 220GHz Bandwidth 10GHzSlant angle 0∘ Platform velocity 80msRange resolution 0015m Azimuth resolution 0051m

Nowwe employ the correlationmethod and the improvedExCoV to reconstruct vibrating target scattering coefficientshence obtaining their refocused images The imaged sizeis just set 08m times 08m both with 004m grid spacingfor the memory as well as computation time costs andthe sparse sampling rate is 40 implying that compressivesensing is utilized together with ExCoV Multidimensionalimages are obtained with the dimension in accord with120578

def= [119909 119910 119903 119891119898 1205930]119879 and parts of their slices along the

International Journal of Antennas and Propagation 7

minus04minus0200204 minus04minus0200204 minus04minus0200204 minus04minus0200204

minus04minus0200204 minus04minus0200204 minus04minus0200204 minus04minus0200204

Rang

e (m

)Ra

nge (

m)

Rang

e (m

)Ra

nge (

m)

minus04minus0200204 minus04minus0200204 minus04minus0200204 minus04minus0200204

minus04minus0200204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

Azimuth (m)Azimuth (m)Azimuth (m)Azimuth (m)minus04minus0200204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus0200204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus0200204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

1

2

3

fm = 27Hzfm = 26Hzfm = 25Hzfm = 0Hz

r=

0m

r=

000

5m

r=

000

6m

r=

000

7m

Figure 6 THz-SAR image of point targets in Table 2 under minus10 dB SNR refocused via correlation imaging

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

Rang

e (m

)Ra

nge (

m)

Rang

e (m

)Ra

nge (

m)

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

Azimuth (m) Azimuth (m) Azimuth (m) Azimuth (m)

1

2

3

fm = 0Hz fm = 25Hz fm = 26Hz fm = 27Hz

r=

0m

r=

000

5m

r=

000

6m

r=

000

7m

Figure 7 THz-SAR image of point targets in Table 2 under minus10 dB SNR refocused via ExCoV imaging

vibration frequency 119891119898 and amplitude 119903 are shown in Figures6 and 7 Clearly the ExCoV method provides better imagingresults while the image by the correlation method showshigh sidelobes and generates some artifacts for the stationarytarget From the location of the focused image slices inFigure 7 one can readily estimate the vibration parameters

We define the root MSE (RMSE) between the recon-structed scattering coefficient and the true values that isRMSE = a minus aa where a denotes the true valuesto test the algorithm performance 100 times Monte Carlosimulations are conducted for each SNR value to obtainFigure 8 indicating that RMSE drops sharply with SNR

Excellent performance can be realized in low SNR andFigure 7 is an example of minus10 dB SNR

523 Vibrating Tank Model Imaging A real SAR imagearound the Isleta Lake in New Mexico (Figure 9(b)) isdownloaded from the Sandia Cooperation website and isused to generate the scene echoes [26] Then a simulatedvibrating tank model (Figure 9(a)) is fed into the scenewith the size 037m times 02m times 018m (length by widthby height) and with the vibration frequency 25Hz andamplitude 0005m Its images when stationary and vibratingare shown in Figures 9(c) and 9(d)The refocused image slice

8 International Journal of Antennas and Propagation

minus20 minus10 0 10

025

03

035

04

045

05

SNR (dB)

RMSE

Figure 8 The RMSE versus SNR for the ExCoV method

(a) (b)

Azimuth (m)

Rang

e (m

)

minus05005

minus08

minus06

minus04

minus02

0

02

04

06

08

(c)

Azimuth (m)

Rang

e (m

)

minus05005

minus08

minus06

minus04

minus02

0

02

04

06

08

(d)

Figure 9 Simulated THz-SAR images of the tank model when stationary and vibrating respectively (a) Tank model (b) Isleta Lake in NewMexico used as the background (c) image of stationary tank model (d) image of vibrating tank model

Table 2 Point target parameters

Target number Azimuth Range Vibration frequency Vibration amplitude1 (stationary) 02m minus02m 0 02 (vibrating) 0 0 25Hz 0006m3 (vibrating) minus02m 02m 26Hz 0007m

International Journal of Antennas and Propagation 9

Azimuth (m)

Rang

e (m

)

minus04minus0200204minus04

minus03

minus02

minus01

0

01

02

03

04

Figure 10 THz-SAR image slice of the vibrating tank model on theIsleta Lake background refocused by the ExCoV method

is displayed in Figure 10 and the location of the slice indicatesthe correct vibration frequency and amplitude In reality thevibrating parameters will take on estimation error due toparameter grid mismatch which remains to be explored infuture investigations

6 Conclusion

Terahertz has significant advantages of remote vibration sens-ing over microwave bands In this paper the THz-SAR echomodel of vibrating targets has been establishedTheir imagingcharacteristics with THz-SAR are analyzed and the mainfeatures of vibrating point targets are segments consistingof unresolvable ghosts An improved algorithm based onExCoV withmore robust and efficient initialization has beenproposed in the sparse Bayesian framework for reconstruct-ing scattering coefficients Data of vibrating targets and a tankmodel in a real background has been simulated at 220GHzand the reconstructed images show good performance atlow SNR The algorithm proposed can also overcome thedeficiencies of sidelobes and artifacts arising from traditionalcorrelation (or back projection) imaging method as com-pared in Figures 6 and 7 In fact the algorithm begins withcorrelation and can be treated as combination of ExCoVand correlation Terahertz together with the sparse Bayesiantheory shows a viable and most promising alternative toremote sensing of minor vibrations in particular with rapidlyevolving of solid-state and high-power electric-vacuum tera-hertz devices Although the Bayesian method provides a finesolution to vibrating target imaging algorithms with higherefficiency to realize video-rate THz-SAR imaging are stillto be studied in future especially when multiple vibrationcomponents are taken into account

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The paper is supported by the National Natural ScienceFoundation for Young Scientists of China under Grants61302148 and 61571011

References

[1] S Baumgartner G Krieger K Bethke and S Zuev ldquoTrafficmonitoring with SAR implications of target accelerationrdquo inProceedings of the European Conference on Synthetic ApertureRadar (EUSAR rsquo06) May 2006

[2] X Li B Deng Y Qin H Wang and Y Li ldquoThe influence oftarget micromotion on SAR and GMTIrdquo IEEE Transactions onGeoscience and Remote Sensing vol 49 no 7 pp 2738ndash27512011

[3] E F Stockburger and D N Held ldquoInterferometric movingground target imagingrdquo in Proceedings of the IEEE 1995 Inter-national Radar Conference pp 438ndash443 Alexandria Va USA1995

[4] B Deng G Wu Y Qin H Wang and X Li ldquoSARMMTIAn extension to conventional SARGMTI and a combinationof SAR and micromotion techniquesrdquo in Proceedings of the IETInternational Radar Conference pp 42ndash45 Guilin China April2009

[5] B Deng Y Qin H Wang and Y Li ldquoAngular extent effect ofmicromotion target in SAR image by polar format algorithmrdquoJournal of Systems Engineering and Electronics vol 25 no 3Article ID 6850221 pp 428ndash433 2014

[6] B Deng H-Q Wang Y-L Qin S Zhu and X Li ldquoRotatingparabolic-reflector antenna target in SAR data model char-acteristics and parameter estimationrdquo International Journal ofAntennas and Propagation vol 2013 Article ID 583865 13pages 2013

[7] D B Andre D Blacknell D G Muff and M R NottinghamldquoThe physics of vibrating scatterers in SAR imageryrdquo in SPIEProceedings of the Algorithms for Synthetic Aperture RadarImagery XVIII SPIE Orlando Fla USA April 2011

[8] B Deng H-Q Wang X Li Y-L Qin and J-T WangldquoGeneralised likelihood ratio test detector for micro-motiontargets in synthetic aperture radar raw signalsrdquo IET RadarSonar and Navigation vol 5 no 5 pp 528ndash535 2011

[9] W G Carrara R S Goodman and R M Majewski SpotlightSynthetic Aperture Radar Signal Processing Algorithms ArtechHouse Norwood Mass USA 1995

[10] N S Subotic B J Thelen and D A Carrara ldquoCyclostationarysignalmodels for the detection and characterization of vibratingobjects in SAR datardquo in Proceedings of the Conference Record ofthe 32nd Asilomar Conference on Signals Systems amp Computers(ACSSC rsquo98) vol 2 pp 1304ndash1308 November 1998

[11] Y Chen B Deng H Wang Y Qin and J Ding ldquoVibrationtarget detection and vibration parameters estimation based onthe DPCA technique in dual-channel SARrdquo Science ChinaInformation Sciences vol 55 no 10 pp 2281ndash2291 2012

[12] M Ruegg E Meier and D Nuesch ldquoVibration and rotationin millimeter-wave SARrdquo IEEE Transactions on Geoscience andRemote Sensing vol 45 no 2 pp 293ndash304 2007

[13] W Zhang C Tong Q Zhang Y Zhang and X ZhangldquoExtraction of vibrating features with dual-channel fixed-receiver bistatic SARrdquo IEEE Geoscience and Remote SensingLetters vol 9 no 3 pp 507ndash511 2012

10 International Journal of Antennas and Propagation

[14] W Zhang C Tong L Ren X Chen and X Zhang ldquoBistaticmicro-Doppler radar signatures of vibrating targets with along-track interferometryrdquo in Proceedings of the 4th IEEE Interna-tional Symposium on Microwave Antenna Propagation andEMC Technologies for Wireless Communications (MAPE rsquo11) pp505ndash508 Beijing China November 2011

[15] Q Wang M Pepin A Wright et al ldquoReduction of vibration-induced artifacts in synthetic aperture radar imageryrdquo IEEETransactions on Geoscience and Remote Sensing vol 52 no 6pp 3063ndash3073 2014

[16] B Deng Y-L Qin H-Q Wang X Li and H Li ldquoPulse-repetition-interval transform-based vibrating target detectionand estimation in synthetic aperture radarrdquo IET Signal Process-ing vol 6 no 6 pp 551ndash558 2012

[17] T Sparr and B Krane ldquoMicro-Doppler analysis of vibratingtargets in SARrdquo IEE ProceedingsmdashRadar Sonar and Navigationvol 150 no 4 pp 277ndash283 2003

[18] Q Wang M Pepin R J Beach et al ldquoSAR-based vibrationestimation using the discrete fractional Fourier transformrdquoIEEE Transactions on Geoscience and Remote Sensing vol 50no 10 pp 4145ndash4156 2012

[19] Y Zhang J Sun P Lei and W Hong ldquoSAR-based pairedecho focusing and suppression of vibrating targetsrdquo IEEETransactions on Geoscience and Remote Sensing vol 52 no 12pp 7593ndash7605 2014

[20] Y Qin B Deng Z Huang and W Su ldquoHybrid micromotion-scattering center model for synthetic aperture radar micro-motion target imagingrdquo Journal of Systems Engineering andElectronics vol 24 no 6 pp 931ndash937 2013

[21] H B Wallace ldquoVideo synthetic aperture radar (ViSAR)rdquoDARPA 2012

[22] R G Wiley The Interception and Analysis of Radar SignalsArtch House Bristol UK 2006

[23] J Ender ldquoA brief review of compressive sensing applied toradarrdquo in Proceedings of the 14th International Radar Symposium(IRS rsquo13) pp 3ndash16 Dresden Germany June 2013

[24] K Qiu and A Dogandzic ldquoVariance-component based sparsesignal reconstruction and model selectionrdquo IEEE Transactionson Signal Processing vol 58 no 6 pp 2935ndash2952 2010

[25] W G Su H Q Wang B Deng and R J Wang ldquoSparseBayesian SAR imaging of moving target via the excov methodrdquoin Proceedings of the IEEE Workshop on Statistical SignalProcessing pp 448ndash451 June-July 2014

[26] B Deng Y Qin Y Li H Wang and X Li ldquoFast simulation ofraw signals from natural scenes for squint stripmap SARrdquo inProceedings of the Asia-Pacific Conference on Synthetic ApertureRadar (APSAR rsquo09) pp 235ndash238 IEEE Xian China October2009

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Antennas and Propagation 5

Azimuth (m)

Rang

e (m

)

minus04minus0200204minus04

minus03

minus02

minus01

0

01

02

03

04

(a)

Rang

e (m

)

Azimuth (m)minus04minus0200204

minus04

minus03

minus02

minus01

0

01

02

03

04

(b)

Figure 2 Initial imaging of a vibrating target at (0 0) by different methods (the arrow points to the maxima and the true maximum is locatedat (0 0)) (a) Moore-Penrose pseudoinverse and (b) correlation

(a) (b)

04 05 06 07 08minus006

minus004

minus002

0

002

004

006

008

Time (s)

Rang

e (m

m)

Stationary Mengshi carIdle Mengshi carIdle Nissan car

(c)

0 10 20 30 40

02

04

06

08

1

Frequency (Hz)

Am

plitu

de

Mengshi carNissan car

(d)

Figure 3 Vibration measurement results of two idle cars (a) Mengshi car (b) Nissan car (c) vibration amplitude versus time (d) vibrationspectra

6 International Journal of Antennas and Propagation

Azimuth (m)minus3minus2minus10123

minus08

minus06

minus04

minus02

0

02

04

06

08

Rang

e (m

)

(a)

Azimuth (m)

Rang

e (m

)

minus3minus2minus10123

minus08

minus06

minus04

minus02

0

02

04

06

08

(b)

Figure 4 SAR images of a vibrating point target with the vibration amplitude 1mm and frequency 1Hz without refocusing (a) X-band (b)THz band (220GHz)

the vibration by the synthesis of simple harmonic vibrationsIn the paper we only use one component for simplicity andwithout loss of generality

52 THz-SAR Imaging Results of Simulated Vibrating TargetsWe proceed to conduct the following numerical experimentas real experiments are right now not available due to lowpower of our THz source available to validate the algorithmproposed THz-SAR system parameters are given in Table 1The experiment includes comparison of vibrating targetimages in microwave and terahertz bands and imaging ofvibrating point targets as well as a tank model

521 Comparison of Vibrating Target Images in Microwaveand Terahertz Bands Figure 4 provides a good representa-tion of original image characteristics of a vibrating targetin different bands For the X-band the resolution is 015mand 028m in range and azimuth respectively Only a fewghosts are present in the image as Figure 4(a) shows andthe ghosts bear strong resemblance to stationary point targetsor their sidelobes hence difficult to discriminate betweenvibration and stillness In contrast the vibrating target takeson a line segment in the THz-SAR image as Figure 4(b)depicts Clearly terahertz can enforce the vibrating targetimage feature and therefore is expected to be used as the bestband for vibration sensing In addition the line segment inFigure 4(b) also consists of ghosts while the spacing betweenwhich is so near in the terahertz regime that is not resolvedas (13) predicts

522 Vibrating Point Target Imaging For quantitativelyanalyzing the performance of the algorithm proposed weuse three point targets in the experiment herein whoseparameters are shown in Table 1 The images formulated bythe polar format algorithm (PFA) are displayed in Figure 5where the stationary target is well focused at the bottomwhilethe two vibrating ones are blurred into segments

Azimuth (m)

Rang

e (m

)

minus3minus2minus10123

minus08

minus06

minus04

minus02

0

02

04

06

08

12

3

Figure 5 THz-SAR image of point targets in Table 2 withoutrefocusing

Table 1 THz-SAR parameters

Mode Spotlight CPI 05 sCarrier frequency 220GHz Bandwidth 10GHzSlant angle 0∘ Platform velocity 80msRange resolution 0015m Azimuth resolution 0051m

Nowwe employ the correlationmethod and the improvedExCoV to reconstruct vibrating target scattering coefficientshence obtaining their refocused images The imaged sizeis just set 08m times 08m both with 004m grid spacingfor the memory as well as computation time costs andthe sparse sampling rate is 40 implying that compressivesensing is utilized together with ExCoV Multidimensionalimages are obtained with the dimension in accord with120578

def= [119909 119910 119903 119891119898 1205930]119879 and parts of their slices along the

International Journal of Antennas and Propagation 7

minus04minus0200204 minus04minus0200204 minus04minus0200204 minus04minus0200204

minus04minus0200204 minus04minus0200204 minus04minus0200204 minus04minus0200204

Rang

e (m

)Ra

nge (

m)

Rang

e (m

)Ra

nge (

m)

minus04minus0200204 minus04minus0200204 minus04minus0200204 minus04minus0200204

minus04minus0200204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

Azimuth (m)Azimuth (m)Azimuth (m)Azimuth (m)minus04minus0200204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus0200204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus0200204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

1

2

3

fm = 27Hzfm = 26Hzfm = 25Hzfm = 0Hz

r=

0m

r=

000

5m

r=

000

6m

r=

000

7m

Figure 6 THz-SAR image of point targets in Table 2 under minus10 dB SNR refocused via correlation imaging

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

Rang

e (m

)Ra

nge (

m)

Rang

e (m

)Ra

nge (

m)

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

Azimuth (m) Azimuth (m) Azimuth (m) Azimuth (m)

1

2

3

fm = 0Hz fm = 25Hz fm = 26Hz fm = 27Hz

r=

0m

r=

000

5m

r=

000

6m

r=

000

7m

Figure 7 THz-SAR image of point targets in Table 2 under minus10 dB SNR refocused via ExCoV imaging

vibration frequency 119891119898 and amplitude 119903 are shown in Figures6 and 7 Clearly the ExCoV method provides better imagingresults while the image by the correlation method showshigh sidelobes and generates some artifacts for the stationarytarget From the location of the focused image slices inFigure 7 one can readily estimate the vibration parameters

We define the root MSE (RMSE) between the recon-structed scattering coefficient and the true values that isRMSE = a minus aa where a denotes the true valuesto test the algorithm performance 100 times Monte Carlosimulations are conducted for each SNR value to obtainFigure 8 indicating that RMSE drops sharply with SNR

Excellent performance can be realized in low SNR andFigure 7 is an example of minus10 dB SNR

523 Vibrating Tank Model Imaging A real SAR imagearound the Isleta Lake in New Mexico (Figure 9(b)) isdownloaded from the Sandia Cooperation website and isused to generate the scene echoes [26] Then a simulatedvibrating tank model (Figure 9(a)) is fed into the scenewith the size 037m times 02m times 018m (length by widthby height) and with the vibration frequency 25Hz andamplitude 0005m Its images when stationary and vibratingare shown in Figures 9(c) and 9(d)The refocused image slice

8 International Journal of Antennas and Propagation

minus20 minus10 0 10

025

03

035

04

045

05

SNR (dB)

RMSE

Figure 8 The RMSE versus SNR for the ExCoV method

(a) (b)

Azimuth (m)

Rang

e (m

)

minus05005

minus08

minus06

minus04

minus02

0

02

04

06

08

(c)

Azimuth (m)

Rang

e (m

)

minus05005

minus08

minus06

minus04

minus02

0

02

04

06

08

(d)

Figure 9 Simulated THz-SAR images of the tank model when stationary and vibrating respectively (a) Tank model (b) Isleta Lake in NewMexico used as the background (c) image of stationary tank model (d) image of vibrating tank model

Table 2 Point target parameters

Target number Azimuth Range Vibration frequency Vibration amplitude1 (stationary) 02m minus02m 0 02 (vibrating) 0 0 25Hz 0006m3 (vibrating) minus02m 02m 26Hz 0007m

International Journal of Antennas and Propagation 9

Azimuth (m)

Rang

e (m

)

minus04minus0200204minus04

minus03

minus02

minus01

0

01

02

03

04

Figure 10 THz-SAR image slice of the vibrating tank model on theIsleta Lake background refocused by the ExCoV method

is displayed in Figure 10 and the location of the slice indicatesthe correct vibration frequency and amplitude In reality thevibrating parameters will take on estimation error due toparameter grid mismatch which remains to be explored infuture investigations

6 Conclusion

Terahertz has significant advantages of remote vibration sens-ing over microwave bands In this paper the THz-SAR echomodel of vibrating targets has been establishedTheir imagingcharacteristics with THz-SAR are analyzed and the mainfeatures of vibrating point targets are segments consistingof unresolvable ghosts An improved algorithm based onExCoV withmore robust and efficient initialization has beenproposed in the sparse Bayesian framework for reconstruct-ing scattering coefficients Data of vibrating targets and a tankmodel in a real background has been simulated at 220GHzand the reconstructed images show good performance atlow SNR The algorithm proposed can also overcome thedeficiencies of sidelobes and artifacts arising from traditionalcorrelation (or back projection) imaging method as com-pared in Figures 6 and 7 In fact the algorithm begins withcorrelation and can be treated as combination of ExCoVand correlation Terahertz together with the sparse Bayesiantheory shows a viable and most promising alternative toremote sensing of minor vibrations in particular with rapidlyevolving of solid-state and high-power electric-vacuum tera-hertz devices Although the Bayesian method provides a finesolution to vibrating target imaging algorithms with higherefficiency to realize video-rate THz-SAR imaging are stillto be studied in future especially when multiple vibrationcomponents are taken into account

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The paper is supported by the National Natural ScienceFoundation for Young Scientists of China under Grants61302148 and 61571011

References

[1] S Baumgartner G Krieger K Bethke and S Zuev ldquoTrafficmonitoring with SAR implications of target accelerationrdquo inProceedings of the European Conference on Synthetic ApertureRadar (EUSAR rsquo06) May 2006

[2] X Li B Deng Y Qin H Wang and Y Li ldquoThe influence oftarget micromotion on SAR and GMTIrdquo IEEE Transactions onGeoscience and Remote Sensing vol 49 no 7 pp 2738ndash27512011

[3] E F Stockburger and D N Held ldquoInterferometric movingground target imagingrdquo in Proceedings of the IEEE 1995 Inter-national Radar Conference pp 438ndash443 Alexandria Va USA1995

[4] B Deng G Wu Y Qin H Wang and X Li ldquoSARMMTIAn extension to conventional SARGMTI and a combinationof SAR and micromotion techniquesrdquo in Proceedings of the IETInternational Radar Conference pp 42ndash45 Guilin China April2009

[5] B Deng Y Qin H Wang and Y Li ldquoAngular extent effect ofmicromotion target in SAR image by polar format algorithmrdquoJournal of Systems Engineering and Electronics vol 25 no 3Article ID 6850221 pp 428ndash433 2014

[6] B Deng H-Q Wang Y-L Qin S Zhu and X Li ldquoRotatingparabolic-reflector antenna target in SAR data model char-acteristics and parameter estimationrdquo International Journal ofAntennas and Propagation vol 2013 Article ID 583865 13pages 2013

[7] D B Andre D Blacknell D G Muff and M R NottinghamldquoThe physics of vibrating scatterers in SAR imageryrdquo in SPIEProceedings of the Algorithms for Synthetic Aperture RadarImagery XVIII SPIE Orlando Fla USA April 2011

[8] B Deng H-Q Wang X Li Y-L Qin and J-T WangldquoGeneralised likelihood ratio test detector for micro-motiontargets in synthetic aperture radar raw signalsrdquo IET RadarSonar and Navigation vol 5 no 5 pp 528ndash535 2011

[9] W G Carrara R S Goodman and R M Majewski SpotlightSynthetic Aperture Radar Signal Processing Algorithms ArtechHouse Norwood Mass USA 1995

[10] N S Subotic B J Thelen and D A Carrara ldquoCyclostationarysignalmodels for the detection and characterization of vibratingobjects in SAR datardquo in Proceedings of the Conference Record ofthe 32nd Asilomar Conference on Signals Systems amp Computers(ACSSC rsquo98) vol 2 pp 1304ndash1308 November 1998

[11] Y Chen B Deng H Wang Y Qin and J Ding ldquoVibrationtarget detection and vibration parameters estimation based onthe DPCA technique in dual-channel SARrdquo Science ChinaInformation Sciences vol 55 no 10 pp 2281ndash2291 2012

[12] M Ruegg E Meier and D Nuesch ldquoVibration and rotationin millimeter-wave SARrdquo IEEE Transactions on Geoscience andRemote Sensing vol 45 no 2 pp 293ndash304 2007

[13] W Zhang C Tong Q Zhang Y Zhang and X ZhangldquoExtraction of vibrating features with dual-channel fixed-receiver bistatic SARrdquo IEEE Geoscience and Remote SensingLetters vol 9 no 3 pp 507ndash511 2012

10 International Journal of Antennas and Propagation

[14] W Zhang C Tong L Ren X Chen and X Zhang ldquoBistaticmicro-Doppler radar signatures of vibrating targets with along-track interferometryrdquo in Proceedings of the 4th IEEE Interna-tional Symposium on Microwave Antenna Propagation andEMC Technologies for Wireless Communications (MAPE rsquo11) pp505ndash508 Beijing China November 2011

[15] Q Wang M Pepin A Wright et al ldquoReduction of vibration-induced artifacts in synthetic aperture radar imageryrdquo IEEETransactions on Geoscience and Remote Sensing vol 52 no 6pp 3063ndash3073 2014

[16] B Deng Y-L Qin H-Q Wang X Li and H Li ldquoPulse-repetition-interval transform-based vibrating target detectionand estimation in synthetic aperture radarrdquo IET Signal Process-ing vol 6 no 6 pp 551ndash558 2012

[17] T Sparr and B Krane ldquoMicro-Doppler analysis of vibratingtargets in SARrdquo IEE ProceedingsmdashRadar Sonar and Navigationvol 150 no 4 pp 277ndash283 2003

[18] Q Wang M Pepin R J Beach et al ldquoSAR-based vibrationestimation using the discrete fractional Fourier transformrdquoIEEE Transactions on Geoscience and Remote Sensing vol 50no 10 pp 4145ndash4156 2012

[19] Y Zhang J Sun P Lei and W Hong ldquoSAR-based pairedecho focusing and suppression of vibrating targetsrdquo IEEETransactions on Geoscience and Remote Sensing vol 52 no 12pp 7593ndash7605 2014

[20] Y Qin B Deng Z Huang and W Su ldquoHybrid micromotion-scattering center model for synthetic aperture radar micro-motion target imagingrdquo Journal of Systems Engineering andElectronics vol 24 no 6 pp 931ndash937 2013

[21] H B Wallace ldquoVideo synthetic aperture radar (ViSAR)rdquoDARPA 2012

[22] R G Wiley The Interception and Analysis of Radar SignalsArtch House Bristol UK 2006

[23] J Ender ldquoA brief review of compressive sensing applied toradarrdquo in Proceedings of the 14th International Radar Symposium(IRS rsquo13) pp 3ndash16 Dresden Germany June 2013

[24] K Qiu and A Dogandzic ldquoVariance-component based sparsesignal reconstruction and model selectionrdquo IEEE Transactionson Signal Processing vol 58 no 6 pp 2935ndash2952 2010

[25] W G Su H Q Wang B Deng and R J Wang ldquoSparseBayesian SAR imaging of moving target via the excov methodrdquoin Proceedings of the IEEE Workshop on Statistical SignalProcessing pp 448ndash451 June-July 2014

[26] B Deng Y Qin Y Li H Wang and X Li ldquoFast simulation ofraw signals from natural scenes for squint stripmap SARrdquo inProceedings of the Asia-Pacific Conference on Synthetic ApertureRadar (APSAR rsquo09) pp 235ndash238 IEEE Xian China October2009

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

6 International Journal of Antennas and Propagation

Azimuth (m)minus3minus2minus10123

minus08

minus06

minus04

minus02

0

02

04

06

08

Rang

e (m

)

(a)

Azimuth (m)

Rang

e (m

)

minus3minus2minus10123

minus08

minus06

minus04

minus02

0

02

04

06

08

(b)

Figure 4 SAR images of a vibrating point target with the vibration amplitude 1mm and frequency 1Hz without refocusing (a) X-band (b)THz band (220GHz)

the vibration by the synthesis of simple harmonic vibrationsIn the paper we only use one component for simplicity andwithout loss of generality

52 THz-SAR Imaging Results of Simulated Vibrating TargetsWe proceed to conduct the following numerical experimentas real experiments are right now not available due to lowpower of our THz source available to validate the algorithmproposed THz-SAR system parameters are given in Table 1The experiment includes comparison of vibrating targetimages in microwave and terahertz bands and imaging ofvibrating point targets as well as a tank model

521 Comparison of Vibrating Target Images in Microwaveand Terahertz Bands Figure 4 provides a good representa-tion of original image characteristics of a vibrating targetin different bands For the X-band the resolution is 015mand 028m in range and azimuth respectively Only a fewghosts are present in the image as Figure 4(a) shows andthe ghosts bear strong resemblance to stationary point targetsor their sidelobes hence difficult to discriminate betweenvibration and stillness In contrast the vibrating target takeson a line segment in the THz-SAR image as Figure 4(b)depicts Clearly terahertz can enforce the vibrating targetimage feature and therefore is expected to be used as the bestband for vibration sensing In addition the line segment inFigure 4(b) also consists of ghosts while the spacing betweenwhich is so near in the terahertz regime that is not resolvedas (13) predicts

522 Vibrating Point Target Imaging For quantitativelyanalyzing the performance of the algorithm proposed weuse three point targets in the experiment herein whoseparameters are shown in Table 1 The images formulated bythe polar format algorithm (PFA) are displayed in Figure 5where the stationary target is well focused at the bottomwhilethe two vibrating ones are blurred into segments

Azimuth (m)

Rang

e (m

)

minus3minus2minus10123

minus08

minus06

minus04

minus02

0

02

04

06

08

12

3

Figure 5 THz-SAR image of point targets in Table 2 withoutrefocusing

Table 1 THz-SAR parameters

Mode Spotlight CPI 05 sCarrier frequency 220GHz Bandwidth 10GHzSlant angle 0∘ Platform velocity 80msRange resolution 0015m Azimuth resolution 0051m

Nowwe employ the correlationmethod and the improvedExCoV to reconstruct vibrating target scattering coefficientshence obtaining their refocused images The imaged sizeis just set 08m times 08m both with 004m grid spacingfor the memory as well as computation time costs andthe sparse sampling rate is 40 implying that compressivesensing is utilized together with ExCoV Multidimensionalimages are obtained with the dimension in accord with120578

def= [119909 119910 119903 119891119898 1205930]119879 and parts of their slices along the

International Journal of Antennas and Propagation 7

minus04minus0200204 minus04minus0200204 minus04minus0200204 minus04minus0200204

minus04minus0200204 minus04minus0200204 minus04minus0200204 minus04minus0200204

Rang

e (m

)Ra

nge (

m)

Rang

e (m

)Ra

nge (

m)

minus04minus0200204 minus04minus0200204 minus04minus0200204 minus04minus0200204

minus04minus0200204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

Azimuth (m)Azimuth (m)Azimuth (m)Azimuth (m)minus04minus0200204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus0200204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus0200204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

1

2

3

fm = 27Hzfm = 26Hzfm = 25Hzfm = 0Hz

r=

0m

r=

000

5m

r=

000

6m

r=

000

7m

Figure 6 THz-SAR image of point targets in Table 2 under minus10 dB SNR refocused via correlation imaging

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

Rang

e (m

)Ra

nge (

m)

Rang

e (m

)Ra

nge (

m)

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

Azimuth (m) Azimuth (m) Azimuth (m) Azimuth (m)

1

2

3

fm = 0Hz fm = 25Hz fm = 26Hz fm = 27Hz

r=

0m

r=

000

5m

r=

000

6m

r=

000

7m

Figure 7 THz-SAR image of point targets in Table 2 under minus10 dB SNR refocused via ExCoV imaging

vibration frequency 119891119898 and amplitude 119903 are shown in Figures6 and 7 Clearly the ExCoV method provides better imagingresults while the image by the correlation method showshigh sidelobes and generates some artifacts for the stationarytarget From the location of the focused image slices inFigure 7 one can readily estimate the vibration parameters

We define the root MSE (RMSE) between the recon-structed scattering coefficient and the true values that isRMSE = a minus aa where a denotes the true valuesto test the algorithm performance 100 times Monte Carlosimulations are conducted for each SNR value to obtainFigure 8 indicating that RMSE drops sharply with SNR

Excellent performance can be realized in low SNR andFigure 7 is an example of minus10 dB SNR

523 Vibrating Tank Model Imaging A real SAR imagearound the Isleta Lake in New Mexico (Figure 9(b)) isdownloaded from the Sandia Cooperation website and isused to generate the scene echoes [26] Then a simulatedvibrating tank model (Figure 9(a)) is fed into the scenewith the size 037m times 02m times 018m (length by widthby height) and with the vibration frequency 25Hz andamplitude 0005m Its images when stationary and vibratingare shown in Figures 9(c) and 9(d)The refocused image slice

8 International Journal of Antennas and Propagation

minus20 minus10 0 10

025

03

035

04

045

05

SNR (dB)

RMSE

Figure 8 The RMSE versus SNR for the ExCoV method

(a) (b)

Azimuth (m)

Rang

e (m

)

minus05005

minus08

minus06

minus04

minus02

0

02

04

06

08

(c)

Azimuth (m)

Rang

e (m

)

minus05005

minus08

minus06

minus04

minus02

0

02

04

06

08

(d)

Figure 9 Simulated THz-SAR images of the tank model when stationary and vibrating respectively (a) Tank model (b) Isleta Lake in NewMexico used as the background (c) image of stationary tank model (d) image of vibrating tank model

Table 2 Point target parameters

Target number Azimuth Range Vibration frequency Vibration amplitude1 (stationary) 02m minus02m 0 02 (vibrating) 0 0 25Hz 0006m3 (vibrating) minus02m 02m 26Hz 0007m

International Journal of Antennas and Propagation 9

Azimuth (m)

Rang

e (m

)

minus04minus0200204minus04

minus03

minus02

minus01

0

01

02

03

04

Figure 10 THz-SAR image slice of the vibrating tank model on theIsleta Lake background refocused by the ExCoV method

is displayed in Figure 10 and the location of the slice indicatesthe correct vibration frequency and amplitude In reality thevibrating parameters will take on estimation error due toparameter grid mismatch which remains to be explored infuture investigations

6 Conclusion

Terahertz has significant advantages of remote vibration sens-ing over microwave bands In this paper the THz-SAR echomodel of vibrating targets has been establishedTheir imagingcharacteristics with THz-SAR are analyzed and the mainfeatures of vibrating point targets are segments consistingof unresolvable ghosts An improved algorithm based onExCoV withmore robust and efficient initialization has beenproposed in the sparse Bayesian framework for reconstruct-ing scattering coefficients Data of vibrating targets and a tankmodel in a real background has been simulated at 220GHzand the reconstructed images show good performance atlow SNR The algorithm proposed can also overcome thedeficiencies of sidelobes and artifacts arising from traditionalcorrelation (or back projection) imaging method as com-pared in Figures 6 and 7 In fact the algorithm begins withcorrelation and can be treated as combination of ExCoVand correlation Terahertz together with the sparse Bayesiantheory shows a viable and most promising alternative toremote sensing of minor vibrations in particular with rapidlyevolving of solid-state and high-power electric-vacuum tera-hertz devices Although the Bayesian method provides a finesolution to vibrating target imaging algorithms with higherefficiency to realize video-rate THz-SAR imaging are stillto be studied in future especially when multiple vibrationcomponents are taken into account

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The paper is supported by the National Natural ScienceFoundation for Young Scientists of China under Grants61302148 and 61571011

References

[1] S Baumgartner G Krieger K Bethke and S Zuev ldquoTrafficmonitoring with SAR implications of target accelerationrdquo inProceedings of the European Conference on Synthetic ApertureRadar (EUSAR rsquo06) May 2006

[2] X Li B Deng Y Qin H Wang and Y Li ldquoThe influence oftarget micromotion on SAR and GMTIrdquo IEEE Transactions onGeoscience and Remote Sensing vol 49 no 7 pp 2738ndash27512011

[3] E F Stockburger and D N Held ldquoInterferometric movingground target imagingrdquo in Proceedings of the IEEE 1995 Inter-national Radar Conference pp 438ndash443 Alexandria Va USA1995

[4] B Deng G Wu Y Qin H Wang and X Li ldquoSARMMTIAn extension to conventional SARGMTI and a combinationof SAR and micromotion techniquesrdquo in Proceedings of the IETInternational Radar Conference pp 42ndash45 Guilin China April2009

[5] B Deng Y Qin H Wang and Y Li ldquoAngular extent effect ofmicromotion target in SAR image by polar format algorithmrdquoJournal of Systems Engineering and Electronics vol 25 no 3Article ID 6850221 pp 428ndash433 2014

[6] B Deng H-Q Wang Y-L Qin S Zhu and X Li ldquoRotatingparabolic-reflector antenna target in SAR data model char-acteristics and parameter estimationrdquo International Journal ofAntennas and Propagation vol 2013 Article ID 583865 13pages 2013

[7] D B Andre D Blacknell D G Muff and M R NottinghamldquoThe physics of vibrating scatterers in SAR imageryrdquo in SPIEProceedings of the Algorithms for Synthetic Aperture RadarImagery XVIII SPIE Orlando Fla USA April 2011

[8] B Deng H-Q Wang X Li Y-L Qin and J-T WangldquoGeneralised likelihood ratio test detector for micro-motiontargets in synthetic aperture radar raw signalsrdquo IET RadarSonar and Navigation vol 5 no 5 pp 528ndash535 2011

[9] W G Carrara R S Goodman and R M Majewski SpotlightSynthetic Aperture Radar Signal Processing Algorithms ArtechHouse Norwood Mass USA 1995

[10] N S Subotic B J Thelen and D A Carrara ldquoCyclostationarysignalmodels for the detection and characterization of vibratingobjects in SAR datardquo in Proceedings of the Conference Record ofthe 32nd Asilomar Conference on Signals Systems amp Computers(ACSSC rsquo98) vol 2 pp 1304ndash1308 November 1998

[11] Y Chen B Deng H Wang Y Qin and J Ding ldquoVibrationtarget detection and vibration parameters estimation based onthe DPCA technique in dual-channel SARrdquo Science ChinaInformation Sciences vol 55 no 10 pp 2281ndash2291 2012

[12] M Ruegg E Meier and D Nuesch ldquoVibration and rotationin millimeter-wave SARrdquo IEEE Transactions on Geoscience andRemote Sensing vol 45 no 2 pp 293ndash304 2007

[13] W Zhang C Tong Q Zhang Y Zhang and X ZhangldquoExtraction of vibrating features with dual-channel fixed-receiver bistatic SARrdquo IEEE Geoscience and Remote SensingLetters vol 9 no 3 pp 507ndash511 2012

10 International Journal of Antennas and Propagation

[14] W Zhang C Tong L Ren X Chen and X Zhang ldquoBistaticmicro-Doppler radar signatures of vibrating targets with along-track interferometryrdquo in Proceedings of the 4th IEEE Interna-tional Symposium on Microwave Antenna Propagation andEMC Technologies for Wireless Communications (MAPE rsquo11) pp505ndash508 Beijing China November 2011

[15] Q Wang M Pepin A Wright et al ldquoReduction of vibration-induced artifacts in synthetic aperture radar imageryrdquo IEEETransactions on Geoscience and Remote Sensing vol 52 no 6pp 3063ndash3073 2014

[16] B Deng Y-L Qin H-Q Wang X Li and H Li ldquoPulse-repetition-interval transform-based vibrating target detectionand estimation in synthetic aperture radarrdquo IET Signal Process-ing vol 6 no 6 pp 551ndash558 2012

[17] T Sparr and B Krane ldquoMicro-Doppler analysis of vibratingtargets in SARrdquo IEE ProceedingsmdashRadar Sonar and Navigationvol 150 no 4 pp 277ndash283 2003

[18] Q Wang M Pepin R J Beach et al ldquoSAR-based vibrationestimation using the discrete fractional Fourier transformrdquoIEEE Transactions on Geoscience and Remote Sensing vol 50no 10 pp 4145ndash4156 2012

[19] Y Zhang J Sun P Lei and W Hong ldquoSAR-based pairedecho focusing and suppression of vibrating targetsrdquo IEEETransactions on Geoscience and Remote Sensing vol 52 no 12pp 7593ndash7605 2014

[20] Y Qin B Deng Z Huang and W Su ldquoHybrid micromotion-scattering center model for synthetic aperture radar micro-motion target imagingrdquo Journal of Systems Engineering andElectronics vol 24 no 6 pp 931ndash937 2013

[21] H B Wallace ldquoVideo synthetic aperture radar (ViSAR)rdquoDARPA 2012

[22] R G Wiley The Interception and Analysis of Radar SignalsArtch House Bristol UK 2006

[23] J Ender ldquoA brief review of compressive sensing applied toradarrdquo in Proceedings of the 14th International Radar Symposium(IRS rsquo13) pp 3ndash16 Dresden Germany June 2013

[24] K Qiu and A Dogandzic ldquoVariance-component based sparsesignal reconstruction and model selectionrdquo IEEE Transactionson Signal Processing vol 58 no 6 pp 2935ndash2952 2010

[25] W G Su H Q Wang B Deng and R J Wang ldquoSparseBayesian SAR imaging of moving target via the excov methodrdquoin Proceedings of the IEEE Workshop on Statistical SignalProcessing pp 448ndash451 June-July 2014

[26] B Deng Y Qin Y Li H Wang and X Li ldquoFast simulation ofraw signals from natural scenes for squint stripmap SARrdquo inProceedings of the Asia-Pacific Conference on Synthetic ApertureRadar (APSAR rsquo09) pp 235ndash238 IEEE Xian China October2009

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Antennas and Propagation 7

minus04minus0200204 minus04minus0200204 minus04minus0200204 minus04minus0200204

minus04minus0200204 minus04minus0200204 minus04minus0200204 minus04minus0200204

Rang

e (m

)Ra

nge (

m)

Rang

e (m

)Ra

nge (

m)

minus04minus0200204 minus04minus0200204 minus04minus0200204 minus04minus0200204

minus04minus0200204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

Azimuth (m)Azimuth (m)Azimuth (m)Azimuth (m)minus04minus0200204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus0200204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus0200204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

minus04minus02

00204

1

2

3

fm = 27Hzfm = 26Hzfm = 25Hzfm = 0Hz

r=

0m

r=

000

5m

r=

000

6m

r=

000

7m

Figure 6 THz-SAR image of point targets in Table 2 under minus10 dB SNR refocused via correlation imaging

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

Rang

e (m

)Ra

nge (

m)

Rang

e (m

)Ra

nge (

m)

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

minus04minus0200204minus04minus02

00204

Azimuth (m) Azimuth (m) Azimuth (m) Azimuth (m)

1

2

3

fm = 0Hz fm = 25Hz fm = 26Hz fm = 27Hz

r=

0m

r=

000

5m

r=

000

6m

r=

000

7m

Figure 7 THz-SAR image of point targets in Table 2 under minus10 dB SNR refocused via ExCoV imaging

vibration frequency 119891119898 and amplitude 119903 are shown in Figures6 and 7 Clearly the ExCoV method provides better imagingresults while the image by the correlation method showshigh sidelobes and generates some artifacts for the stationarytarget From the location of the focused image slices inFigure 7 one can readily estimate the vibration parameters

We define the root MSE (RMSE) between the recon-structed scattering coefficient and the true values that isRMSE = a minus aa where a denotes the true valuesto test the algorithm performance 100 times Monte Carlosimulations are conducted for each SNR value to obtainFigure 8 indicating that RMSE drops sharply with SNR

Excellent performance can be realized in low SNR andFigure 7 is an example of minus10 dB SNR

523 Vibrating Tank Model Imaging A real SAR imagearound the Isleta Lake in New Mexico (Figure 9(b)) isdownloaded from the Sandia Cooperation website and isused to generate the scene echoes [26] Then a simulatedvibrating tank model (Figure 9(a)) is fed into the scenewith the size 037m times 02m times 018m (length by widthby height) and with the vibration frequency 25Hz andamplitude 0005m Its images when stationary and vibratingare shown in Figures 9(c) and 9(d)The refocused image slice

8 International Journal of Antennas and Propagation

minus20 minus10 0 10

025

03

035

04

045

05

SNR (dB)

RMSE

Figure 8 The RMSE versus SNR for the ExCoV method

(a) (b)

Azimuth (m)

Rang

e (m

)

minus05005

minus08

minus06

minus04

minus02

0

02

04

06

08

(c)

Azimuth (m)

Rang

e (m

)

minus05005

minus08

minus06

minus04

minus02

0

02

04

06

08

(d)

Figure 9 Simulated THz-SAR images of the tank model when stationary and vibrating respectively (a) Tank model (b) Isleta Lake in NewMexico used as the background (c) image of stationary tank model (d) image of vibrating tank model

Table 2 Point target parameters

Target number Azimuth Range Vibration frequency Vibration amplitude1 (stationary) 02m minus02m 0 02 (vibrating) 0 0 25Hz 0006m3 (vibrating) minus02m 02m 26Hz 0007m

International Journal of Antennas and Propagation 9

Azimuth (m)

Rang

e (m

)

minus04minus0200204minus04

minus03

minus02

minus01

0

01

02

03

04

Figure 10 THz-SAR image slice of the vibrating tank model on theIsleta Lake background refocused by the ExCoV method

is displayed in Figure 10 and the location of the slice indicatesthe correct vibration frequency and amplitude In reality thevibrating parameters will take on estimation error due toparameter grid mismatch which remains to be explored infuture investigations

6 Conclusion

Terahertz has significant advantages of remote vibration sens-ing over microwave bands In this paper the THz-SAR echomodel of vibrating targets has been establishedTheir imagingcharacteristics with THz-SAR are analyzed and the mainfeatures of vibrating point targets are segments consistingof unresolvable ghosts An improved algorithm based onExCoV withmore robust and efficient initialization has beenproposed in the sparse Bayesian framework for reconstruct-ing scattering coefficients Data of vibrating targets and a tankmodel in a real background has been simulated at 220GHzand the reconstructed images show good performance atlow SNR The algorithm proposed can also overcome thedeficiencies of sidelobes and artifacts arising from traditionalcorrelation (or back projection) imaging method as com-pared in Figures 6 and 7 In fact the algorithm begins withcorrelation and can be treated as combination of ExCoVand correlation Terahertz together with the sparse Bayesiantheory shows a viable and most promising alternative toremote sensing of minor vibrations in particular with rapidlyevolving of solid-state and high-power electric-vacuum tera-hertz devices Although the Bayesian method provides a finesolution to vibrating target imaging algorithms with higherefficiency to realize video-rate THz-SAR imaging are stillto be studied in future especially when multiple vibrationcomponents are taken into account

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The paper is supported by the National Natural ScienceFoundation for Young Scientists of China under Grants61302148 and 61571011

References

[1] S Baumgartner G Krieger K Bethke and S Zuev ldquoTrafficmonitoring with SAR implications of target accelerationrdquo inProceedings of the European Conference on Synthetic ApertureRadar (EUSAR rsquo06) May 2006

[2] X Li B Deng Y Qin H Wang and Y Li ldquoThe influence oftarget micromotion on SAR and GMTIrdquo IEEE Transactions onGeoscience and Remote Sensing vol 49 no 7 pp 2738ndash27512011

[3] E F Stockburger and D N Held ldquoInterferometric movingground target imagingrdquo in Proceedings of the IEEE 1995 Inter-national Radar Conference pp 438ndash443 Alexandria Va USA1995

[4] B Deng G Wu Y Qin H Wang and X Li ldquoSARMMTIAn extension to conventional SARGMTI and a combinationof SAR and micromotion techniquesrdquo in Proceedings of the IETInternational Radar Conference pp 42ndash45 Guilin China April2009

[5] B Deng Y Qin H Wang and Y Li ldquoAngular extent effect ofmicromotion target in SAR image by polar format algorithmrdquoJournal of Systems Engineering and Electronics vol 25 no 3Article ID 6850221 pp 428ndash433 2014

[6] B Deng H-Q Wang Y-L Qin S Zhu and X Li ldquoRotatingparabolic-reflector antenna target in SAR data model char-acteristics and parameter estimationrdquo International Journal ofAntennas and Propagation vol 2013 Article ID 583865 13pages 2013

[7] D B Andre D Blacknell D G Muff and M R NottinghamldquoThe physics of vibrating scatterers in SAR imageryrdquo in SPIEProceedings of the Algorithms for Synthetic Aperture RadarImagery XVIII SPIE Orlando Fla USA April 2011

[8] B Deng H-Q Wang X Li Y-L Qin and J-T WangldquoGeneralised likelihood ratio test detector for micro-motiontargets in synthetic aperture radar raw signalsrdquo IET RadarSonar and Navigation vol 5 no 5 pp 528ndash535 2011

[9] W G Carrara R S Goodman and R M Majewski SpotlightSynthetic Aperture Radar Signal Processing Algorithms ArtechHouse Norwood Mass USA 1995

[10] N S Subotic B J Thelen and D A Carrara ldquoCyclostationarysignalmodels for the detection and characterization of vibratingobjects in SAR datardquo in Proceedings of the Conference Record ofthe 32nd Asilomar Conference on Signals Systems amp Computers(ACSSC rsquo98) vol 2 pp 1304ndash1308 November 1998

[11] Y Chen B Deng H Wang Y Qin and J Ding ldquoVibrationtarget detection and vibration parameters estimation based onthe DPCA technique in dual-channel SARrdquo Science ChinaInformation Sciences vol 55 no 10 pp 2281ndash2291 2012

[12] M Ruegg E Meier and D Nuesch ldquoVibration and rotationin millimeter-wave SARrdquo IEEE Transactions on Geoscience andRemote Sensing vol 45 no 2 pp 293ndash304 2007

[13] W Zhang C Tong Q Zhang Y Zhang and X ZhangldquoExtraction of vibrating features with dual-channel fixed-receiver bistatic SARrdquo IEEE Geoscience and Remote SensingLetters vol 9 no 3 pp 507ndash511 2012

10 International Journal of Antennas and Propagation

[14] W Zhang C Tong L Ren X Chen and X Zhang ldquoBistaticmicro-Doppler radar signatures of vibrating targets with along-track interferometryrdquo in Proceedings of the 4th IEEE Interna-tional Symposium on Microwave Antenna Propagation andEMC Technologies for Wireless Communications (MAPE rsquo11) pp505ndash508 Beijing China November 2011

[15] Q Wang M Pepin A Wright et al ldquoReduction of vibration-induced artifacts in synthetic aperture radar imageryrdquo IEEETransactions on Geoscience and Remote Sensing vol 52 no 6pp 3063ndash3073 2014

[16] B Deng Y-L Qin H-Q Wang X Li and H Li ldquoPulse-repetition-interval transform-based vibrating target detectionand estimation in synthetic aperture radarrdquo IET Signal Process-ing vol 6 no 6 pp 551ndash558 2012

[17] T Sparr and B Krane ldquoMicro-Doppler analysis of vibratingtargets in SARrdquo IEE ProceedingsmdashRadar Sonar and Navigationvol 150 no 4 pp 277ndash283 2003

[18] Q Wang M Pepin R J Beach et al ldquoSAR-based vibrationestimation using the discrete fractional Fourier transformrdquoIEEE Transactions on Geoscience and Remote Sensing vol 50no 10 pp 4145ndash4156 2012

[19] Y Zhang J Sun P Lei and W Hong ldquoSAR-based pairedecho focusing and suppression of vibrating targetsrdquo IEEETransactions on Geoscience and Remote Sensing vol 52 no 12pp 7593ndash7605 2014

[20] Y Qin B Deng Z Huang and W Su ldquoHybrid micromotion-scattering center model for synthetic aperture radar micro-motion target imagingrdquo Journal of Systems Engineering andElectronics vol 24 no 6 pp 931ndash937 2013

[21] H B Wallace ldquoVideo synthetic aperture radar (ViSAR)rdquoDARPA 2012

[22] R G Wiley The Interception and Analysis of Radar SignalsArtch House Bristol UK 2006

[23] J Ender ldquoA brief review of compressive sensing applied toradarrdquo in Proceedings of the 14th International Radar Symposium(IRS rsquo13) pp 3ndash16 Dresden Germany June 2013

[24] K Qiu and A Dogandzic ldquoVariance-component based sparsesignal reconstruction and model selectionrdquo IEEE Transactionson Signal Processing vol 58 no 6 pp 2935ndash2952 2010

[25] W G Su H Q Wang B Deng and R J Wang ldquoSparseBayesian SAR imaging of moving target via the excov methodrdquoin Proceedings of the IEEE Workshop on Statistical SignalProcessing pp 448ndash451 June-July 2014

[26] B Deng Y Qin Y Li H Wang and X Li ldquoFast simulation ofraw signals from natural scenes for squint stripmap SARrdquo inProceedings of the Asia-Pacific Conference on Synthetic ApertureRadar (APSAR rsquo09) pp 235ndash238 IEEE Xian China October2009

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 International Journal of Antennas and Propagation

minus20 minus10 0 10

025

03

035

04

045

05

SNR (dB)

RMSE

Figure 8 The RMSE versus SNR for the ExCoV method

(a) (b)

Azimuth (m)

Rang

e (m

)

minus05005

minus08

minus06

minus04

minus02

0

02

04

06

08

(c)

Azimuth (m)

Rang

e (m

)

minus05005

minus08

minus06

minus04

minus02

0

02

04

06

08

(d)

Figure 9 Simulated THz-SAR images of the tank model when stationary and vibrating respectively (a) Tank model (b) Isleta Lake in NewMexico used as the background (c) image of stationary tank model (d) image of vibrating tank model

Table 2 Point target parameters

Target number Azimuth Range Vibration frequency Vibration amplitude1 (stationary) 02m minus02m 0 02 (vibrating) 0 0 25Hz 0006m3 (vibrating) minus02m 02m 26Hz 0007m

International Journal of Antennas and Propagation 9

Azimuth (m)

Rang

e (m

)

minus04minus0200204minus04

minus03

minus02

minus01

0

01

02

03

04

Figure 10 THz-SAR image slice of the vibrating tank model on theIsleta Lake background refocused by the ExCoV method

is displayed in Figure 10 and the location of the slice indicatesthe correct vibration frequency and amplitude In reality thevibrating parameters will take on estimation error due toparameter grid mismatch which remains to be explored infuture investigations

6 Conclusion

Terahertz has significant advantages of remote vibration sens-ing over microwave bands In this paper the THz-SAR echomodel of vibrating targets has been establishedTheir imagingcharacteristics with THz-SAR are analyzed and the mainfeatures of vibrating point targets are segments consistingof unresolvable ghosts An improved algorithm based onExCoV withmore robust and efficient initialization has beenproposed in the sparse Bayesian framework for reconstruct-ing scattering coefficients Data of vibrating targets and a tankmodel in a real background has been simulated at 220GHzand the reconstructed images show good performance atlow SNR The algorithm proposed can also overcome thedeficiencies of sidelobes and artifacts arising from traditionalcorrelation (or back projection) imaging method as com-pared in Figures 6 and 7 In fact the algorithm begins withcorrelation and can be treated as combination of ExCoVand correlation Terahertz together with the sparse Bayesiantheory shows a viable and most promising alternative toremote sensing of minor vibrations in particular with rapidlyevolving of solid-state and high-power electric-vacuum tera-hertz devices Although the Bayesian method provides a finesolution to vibrating target imaging algorithms with higherefficiency to realize video-rate THz-SAR imaging are stillto be studied in future especially when multiple vibrationcomponents are taken into account

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The paper is supported by the National Natural ScienceFoundation for Young Scientists of China under Grants61302148 and 61571011

References

[1] S Baumgartner G Krieger K Bethke and S Zuev ldquoTrafficmonitoring with SAR implications of target accelerationrdquo inProceedings of the European Conference on Synthetic ApertureRadar (EUSAR rsquo06) May 2006

[2] X Li B Deng Y Qin H Wang and Y Li ldquoThe influence oftarget micromotion on SAR and GMTIrdquo IEEE Transactions onGeoscience and Remote Sensing vol 49 no 7 pp 2738ndash27512011

[3] E F Stockburger and D N Held ldquoInterferometric movingground target imagingrdquo in Proceedings of the IEEE 1995 Inter-national Radar Conference pp 438ndash443 Alexandria Va USA1995

[4] B Deng G Wu Y Qin H Wang and X Li ldquoSARMMTIAn extension to conventional SARGMTI and a combinationof SAR and micromotion techniquesrdquo in Proceedings of the IETInternational Radar Conference pp 42ndash45 Guilin China April2009

[5] B Deng Y Qin H Wang and Y Li ldquoAngular extent effect ofmicromotion target in SAR image by polar format algorithmrdquoJournal of Systems Engineering and Electronics vol 25 no 3Article ID 6850221 pp 428ndash433 2014

[6] B Deng H-Q Wang Y-L Qin S Zhu and X Li ldquoRotatingparabolic-reflector antenna target in SAR data model char-acteristics and parameter estimationrdquo International Journal ofAntennas and Propagation vol 2013 Article ID 583865 13pages 2013

[7] D B Andre D Blacknell D G Muff and M R NottinghamldquoThe physics of vibrating scatterers in SAR imageryrdquo in SPIEProceedings of the Algorithms for Synthetic Aperture RadarImagery XVIII SPIE Orlando Fla USA April 2011

[8] B Deng H-Q Wang X Li Y-L Qin and J-T WangldquoGeneralised likelihood ratio test detector for micro-motiontargets in synthetic aperture radar raw signalsrdquo IET RadarSonar and Navigation vol 5 no 5 pp 528ndash535 2011

[9] W G Carrara R S Goodman and R M Majewski SpotlightSynthetic Aperture Radar Signal Processing Algorithms ArtechHouse Norwood Mass USA 1995

[10] N S Subotic B J Thelen and D A Carrara ldquoCyclostationarysignalmodels for the detection and characterization of vibratingobjects in SAR datardquo in Proceedings of the Conference Record ofthe 32nd Asilomar Conference on Signals Systems amp Computers(ACSSC rsquo98) vol 2 pp 1304ndash1308 November 1998

[11] Y Chen B Deng H Wang Y Qin and J Ding ldquoVibrationtarget detection and vibration parameters estimation based onthe DPCA technique in dual-channel SARrdquo Science ChinaInformation Sciences vol 55 no 10 pp 2281ndash2291 2012

[12] M Ruegg E Meier and D Nuesch ldquoVibration and rotationin millimeter-wave SARrdquo IEEE Transactions on Geoscience andRemote Sensing vol 45 no 2 pp 293ndash304 2007

[13] W Zhang C Tong Q Zhang Y Zhang and X ZhangldquoExtraction of vibrating features with dual-channel fixed-receiver bistatic SARrdquo IEEE Geoscience and Remote SensingLetters vol 9 no 3 pp 507ndash511 2012

10 International Journal of Antennas and Propagation

[14] W Zhang C Tong L Ren X Chen and X Zhang ldquoBistaticmicro-Doppler radar signatures of vibrating targets with along-track interferometryrdquo in Proceedings of the 4th IEEE Interna-tional Symposium on Microwave Antenna Propagation andEMC Technologies for Wireless Communications (MAPE rsquo11) pp505ndash508 Beijing China November 2011

[15] Q Wang M Pepin A Wright et al ldquoReduction of vibration-induced artifacts in synthetic aperture radar imageryrdquo IEEETransactions on Geoscience and Remote Sensing vol 52 no 6pp 3063ndash3073 2014

[16] B Deng Y-L Qin H-Q Wang X Li and H Li ldquoPulse-repetition-interval transform-based vibrating target detectionand estimation in synthetic aperture radarrdquo IET Signal Process-ing vol 6 no 6 pp 551ndash558 2012

[17] T Sparr and B Krane ldquoMicro-Doppler analysis of vibratingtargets in SARrdquo IEE ProceedingsmdashRadar Sonar and Navigationvol 150 no 4 pp 277ndash283 2003

[18] Q Wang M Pepin R J Beach et al ldquoSAR-based vibrationestimation using the discrete fractional Fourier transformrdquoIEEE Transactions on Geoscience and Remote Sensing vol 50no 10 pp 4145ndash4156 2012

[19] Y Zhang J Sun P Lei and W Hong ldquoSAR-based pairedecho focusing and suppression of vibrating targetsrdquo IEEETransactions on Geoscience and Remote Sensing vol 52 no 12pp 7593ndash7605 2014

[20] Y Qin B Deng Z Huang and W Su ldquoHybrid micromotion-scattering center model for synthetic aperture radar micro-motion target imagingrdquo Journal of Systems Engineering andElectronics vol 24 no 6 pp 931ndash937 2013

[21] H B Wallace ldquoVideo synthetic aperture radar (ViSAR)rdquoDARPA 2012

[22] R G Wiley The Interception and Analysis of Radar SignalsArtch House Bristol UK 2006

[23] J Ender ldquoA brief review of compressive sensing applied toradarrdquo in Proceedings of the 14th International Radar Symposium(IRS rsquo13) pp 3ndash16 Dresden Germany June 2013

[24] K Qiu and A Dogandzic ldquoVariance-component based sparsesignal reconstruction and model selectionrdquo IEEE Transactionson Signal Processing vol 58 no 6 pp 2935ndash2952 2010

[25] W G Su H Q Wang B Deng and R J Wang ldquoSparseBayesian SAR imaging of moving target via the excov methodrdquoin Proceedings of the IEEE Workshop on Statistical SignalProcessing pp 448ndash451 June-July 2014

[26] B Deng Y Qin Y Li H Wang and X Li ldquoFast simulation ofraw signals from natural scenes for squint stripmap SARrdquo inProceedings of the Asia-Pacific Conference on Synthetic ApertureRadar (APSAR rsquo09) pp 235ndash238 IEEE Xian China October2009

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Antennas and Propagation 9

Azimuth (m)

Rang

e (m

)

minus04minus0200204minus04

minus03

minus02

minus01

0

01

02

03

04

Figure 10 THz-SAR image slice of the vibrating tank model on theIsleta Lake background refocused by the ExCoV method

is displayed in Figure 10 and the location of the slice indicatesthe correct vibration frequency and amplitude In reality thevibrating parameters will take on estimation error due toparameter grid mismatch which remains to be explored infuture investigations

6 Conclusion

Terahertz has significant advantages of remote vibration sens-ing over microwave bands In this paper the THz-SAR echomodel of vibrating targets has been establishedTheir imagingcharacteristics with THz-SAR are analyzed and the mainfeatures of vibrating point targets are segments consistingof unresolvable ghosts An improved algorithm based onExCoV withmore robust and efficient initialization has beenproposed in the sparse Bayesian framework for reconstruct-ing scattering coefficients Data of vibrating targets and a tankmodel in a real background has been simulated at 220GHzand the reconstructed images show good performance atlow SNR The algorithm proposed can also overcome thedeficiencies of sidelobes and artifacts arising from traditionalcorrelation (or back projection) imaging method as com-pared in Figures 6 and 7 In fact the algorithm begins withcorrelation and can be treated as combination of ExCoVand correlation Terahertz together with the sparse Bayesiantheory shows a viable and most promising alternative toremote sensing of minor vibrations in particular with rapidlyevolving of solid-state and high-power electric-vacuum tera-hertz devices Although the Bayesian method provides a finesolution to vibrating target imaging algorithms with higherefficiency to realize video-rate THz-SAR imaging are stillto be studied in future especially when multiple vibrationcomponents are taken into account

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The paper is supported by the National Natural ScienceFoundation for Young Scientists of China under Grants61302148 and 61571011

References

[1] S Baumgartner G Krieger K Bethke and S Zuev ldquoTrafficmonitoring with SAR implications of target accelerationrdquo inProceedings of the European Conference on Synthetic ApertureRadar (EUSAR rsquo06) May 2006

[2] X Li B Deng Y Qin H Wang and Y Li ldquoThe influence oftarget micromotion on SAR and GMTIrdquo IEEE Transactions onGeoscience and Remote Sensing vol 49 no 7 pp 2738ndash27512011

[3] E F Stockburger and D N Held ldquoInterferometric movingground target imagingrdquo in Proceedings of the IEEE 1995 Inter-national Radar Conference pp 438ndash443 Alexandria Va USA1995

[4] B Deng G Wu Y Qin H Wang and X Li ldquoSARMMTIAn extension to conventional SARGMTI and a combinationof SAR and micromotion techniquesrdquo in Proceedings of the IETInternational Radar Conference pp 42ndash45 Guilin China April2009

[5] B Deng Y Qin H Wang and Y Li ldquoAngular extent effect ofmicromotion target in SAR image by polar format algorithmrdquoJournal of Systems Engineering and Electronics vol 25 no 3Article ID 6850221 pp 428ndash433 2014

[6] B Deng H-Q Wang Y-L Qin S Zhu and X Li ldquoRotatingparabolic-reflector antenna target in SAR data model char-acteristics and parameter estimationrdquo International Journal ofAntennas and Propagation vol 2013 Article ID 583865 13pages 2013

[7] D B Andre D Blacknell D G Muff and M R NottinghamldquoThe physics of vibrating scatterers in SAR imageryrdquo in SPIEProceedings of the Algorithms for Synthetic Aperture RadarImagery XVIII SPIE Orlando Fla USA April 2011

[8] B Deng H-Q Wang X Li Y-L Qin and J-T WangldquoGeneralised likelihood ratio test detector for micro-motiontargets in synthetic aperture radar raw signalsrdquo IET RadarSonar and Navigation vol 5 no 5 pp 528ndash535 2011

[9] W G Carrara R S Goodman and R M Majewski SpotlightSynthetic Aperture Radar Signal Processing Algorithms ArtechHouse Norwood Mass USA 1995

[10] N S Subotic B J Thelen and D A Carrara ldquoCyclostationarysignalmodels for the detection and characterization of vibratingobjects in SAR datardquo in Proceedings of the Conference Record ofthe 32nd Asilomar Conference on Signals Systems amp Computers(ACSSC rsquo98) vol 2 pp 1304ndash1308 November 1998

[11] Y Chen B Deng H Wang Y Qin and J Ding ldquoVibrationtarget detection and vibration parameters estimation based onthe DPCA technique in dual-channel SARrdquo Science ChinaInformation Sciences vol 55 no 10 pp 2281ndash2291 2012

[12] M Ruegg E Meier and D Nuesch ldquoVibration and rotationin millimeter-wave SARrdquo IEEE Transactions on Geoscience andRemote Sensing vol 45 no 2 pp 293ndash304 2007

[13] W Zhang C Tong Q Zhang Y Zhang and X ZhangldquoExtraction of vibrating features with dual-channel fixed-receiver bistatic SARrdquo IEEE Geoscience and Remote SensingLetters vol 9 no 3 pp 507ndash511 2012

10 International Journal of Antennas and Propagation

[14] W Zhang C Tong L Ren X Chen and X Zhang ldquoBistaticmicro-Doppler radar signatures of vibrating targets with along-track interferometryrdquo in Proceedings of the 4th IEEE Interna-tional Symposium on Microwave Antenna Propagation andEMC Technologies for Wireless Communications (MAPE rsquo11) pp505ndash508 Beijing China November 2011

[15] Q Wang M Pepin A Wright et al ldquoReduction of vibration-induced artifacts in synthetic aperture radar imageryrdquo IEEETransactions on Geoscience and Remote Sensing vol 52 no 6pp 3063ndash3073 2014

[16] B Deng Y-L Qin H-Q Wang X Li and H Li ldquoPulse-repetition-interval transform-based vibrating target detectionand estimation in synthetic aperture radarrdquo IET Signal Process-ing vol 6 no 6 pp 551ndash558 2012

[17] T Sparr and B Krane ldquoMicro-Doppler analysis of vibratingtargets in SARrdquo IEE ProceedingsmdashRadar Sonar and Navigationvol 150 no 4 pp 277ndash283 2003

[18] Q Wang M Pepin R J Beach et al ldquoSAR-based vibrationestimation using the discrete fractional Fourier transformrdquoIEEE Transactions on Geoscience and Remote Sensing vol 50no 10 pp 4145ndash4156 2012

[19] Y Zhang J Sun P Lei and W Hong ldquoSAR-based pairedecho focusing and suppression of vibrating targetsrdquo IEEETransactions on Geoscience and Remote Sensing vol 52 no 12pp 7593ndash7605 2014

[20] Y Qin B Deng Z Huang and W Su ldquoHybrid micromotion-scattering center model for synthetic aperture radar micro-motion target imagingrdquo Journal of Systems Engineering andElectronics vol 24 no 6 pp 931ndash937 2013

[21] H B Wallace ldquoVideo synthetic aperture radar (ViSAR)rdquoDARPA 2012

[22] R G Wiley The Interception and Analysis of Radar SignalsArtch House Bristol UK 2006

[23] J Ender ldquoA brief review of compressive sensing applied toradarrdquo in Proceedings of the 14th International Radar Symposium(IRS rsquo13) pp 3ndash16 Dresden Germany June 2013

[24] K Qiu and A Dogandzic ldquoVariance-component based sparsesignal reconstruction and model selectionrdquo IEEE Transactionson Signal Processing vol 58 no 6 pp 2935ndash2952 2010

[25] W G Su H Q Wang B Deng and R J Wang ldquoSparseBayesian SAR imaging of moving target via the excov methodrdquoin Proceedings of the IEEE Workshop on Statistical SignalProcessing pp 448ndash451 June-July 2014

[26] B Deng Y Qin Y Li H Wang and X Li ldquoFast simulation ofraw signals from natural scenes for squint stripmap SARrdquo inProceedings of the Asia-Pacific Conference on Synthetic ApertureRadar (APSAR rsquo09) pp 235ndash238 IEEE Xian China October2009

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 International Journal of Antennas and Propagation

[14] W Zhang C Tong L Ren X Chen and X Zhang ldquoBistaticmicro-Doppler radar signatures of vibrating targets with along-track interferometryrdquo in Proceedings of the 4th IEEE Interna-tional Symposium on Microwave Antenna Propagation andEMC Technologies for Wireless Communications (MAPE rsquo11) pp505ndash508 Beijing China November 2011

[15] Q Wang M Pepin A Wright et al ldquoReduction of vibration-induced artifacts in synthetic aperture radar imageryrdquo IEEETransactions on Geoscience and Remote Sensing vol 52 no 6pp 3063ndash3073 2014

[16] B Deng Y-L Qin H-Q Wang X Li and H Li ldquoPulse-repetition-interval transform-based vibrating target detectionand estimation in synthetic aperture radarrdquo IET Signal Process-ing vol 6 no 6 pp 551ndash558 2012

[17] T Sparr and B Krane ldquoMicro-Doppler analysis of vibratingtargets in SARrdquo IEE ProceedingsmdashRadar Sonar and Navigationvol 150 no 4 pp 277ndash283 2003

[18] Q Wang M Pepin R J Beach et al ldquoSAR-based vibrationestimation using the discrete fractional Fourier transformrdquoIEEE Transactions on Geoscience and Remote Sensing vol 50no 10 pp 4145ndash4156 2012

[19] Y Zhang J Sun P Lei and W Hong ldquoSAR-based pairedecho focusing and suppression of vibrating targetsrdquo IEEETransactions on Geoscience and Remote Sensing vol 52 no 12pp 7593ndash7605 2014

[20] Y Qin B Deng Z Huang and W Su ldquoHybrid micromotion-scattering center model for synthetic aperture radar micro-motion target imagingrdquo Journal of Systems Engineering andElectronics vol 24 no 6 pp 931ndash937 2013

[21] H B Wallace ldquoVideo synthetic aperture radar (ViSAR)rdquoDARPA 2012

[22] R G Wiley The Interception and Analysis of Radar SignalsArtch House Bristol UK 2006

[23] J Ender ldquoA brief review of compressive sensing applied toradarrdquo in Proceedings of the 14th International Radar Symposium(IRS rsquo13) pp 3ndash16 Dresden Germany June 2013

[24] K Qiu and A Dogandzic ldquoVariance-component based sparsesignal reconstruction and model selectionrdquo IEEE Transactionson Signal Processing vol 58 no 6 pp 2935ndash2952 2010

[25] W G Su H Q Wang B Deng and R J Wang ldquoSparseBayesian SAR imaging of moving target via the excov methodrdquoin Proceedings of the IEEE Workshop on Statistical SignalProcessing pp 448ndash451 June-July 2014

[26] B Deng Y Qin Y Li H Wang and X Li ldquoFast simulation ofraw signals from natural scenes for squint stripmap SARrdquo inProceedings of the Asia-Pacific Conference on Synthetic ApertureRadar (APSAR rsquo09) pp 235ndash238 IEEE Xian China October2009

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of