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Terahertz Imaging with Compressed Sensing and Phase Retrieval. Wai Lam Chan Matthew Moravec Daniel Mittleman Richard Baraniuk. Department of Electrical and Computer Engineering Rice University, Houston, Texas, USA. THz Time-domain Imaging. THz Transmitter. - PowerPoint PPT Presentation
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Terahertz Imaging with Compressed Sensing and Phase Retrieval
Wai Lam Chan Matthew Moravec Daniel Mittleman Richard Baraniuk
Department of Electrical and Computer Engineering Rice University, Houston, Texas, USA
THz Time-domain Imaging
Object
THz TransmitterTHz Receiver
THz Time-domain Imaging
Object
THz TransmitterTHz Receiver
Suitcase (weapons) Automobile dashboard (foam layer)
Chocolate bar (food)
(Mittleman, et al., Appl. Phys. B, vol. 68, 1085-1094 (1999))
(Karpowicz, et al., Appl. Phys. Lett. vol. 86, 054105 (2005))
THz Time-domain Imaging
Object
THz TransmitterTHz Receiver
• Pixel-by-pixel scanning
• Limitations: acquisition time vs. resolution
• Faster imaging method
• Reconstruct via nonlinear processing (optimization)
• Take fewer ( ) measurements
High-speed THz Imaging with Compressed Sensing (CS)
Measurements(random projections) Measurement
Matrix (e.g., random Fourier)
(Donoho, IEEE Trans. on Information Theory, 52(4), pp. 1289 - 1306, April 2006)
“sparse” signal / image(K-sparse)
information rate
Compressed Sensing (CS) Example: Single-Pixel Camera
DMD
Random pattern onDMD array
(Baraniuk, Kelly, et al. Proc. of Computational Imaging IV at SPIE Electronic Imaging, Jan 2006)
imagereconstruction
DSP
DMD
THz Fourier Imaging Setup
12cm6cm 12cm 12cm
objectmask
THz transmitter (fiber-coupled PC antenna)
THz receiver
6cm
aperture
automated translation stage
N Fourier samples
THz Fourier Imaging Setup
12cm6cm 12cm 12cm
objectmask
THz transmitter
6cm
Fourier plane
pick only random measurements for
Compressed Sensing
THz Fourier Imaging Setup
automated translation
stage
polyethlene lens
object mask “R”(3.5cm x 3.5cm)
THz receiver
Fourier Imaging Results
Fourier Transform of object (Magnitude)
Inverse Fourier Transform Reconstruction (zoomed-in)
8 cm 6 cm
8
cm6
cm
Resolution: 3mm
Imaging Results with Compressed Sensing (CS)
Inverse Fourier Transform Reconstruction
(6400 measurements)
CS Reconstruction (1000 measurements)
6 cm
6
cm
Imaging Using the Fourier Magnitude
12cm
objectmask
THz transmitterTHz receiver
6cm
aperture
translationstage
variable objectposition
Reconstruction with Phase Retrieval (PR)
• Reconstruct signal from only the magnitude of its Fourier transform
• Iterative algorithm based on prior knowledge of signal:– positivity– real-valued– finite support
• Hybrid Input-Output (HIO) algorithm(Fienup, Appl. Optics., 21(15), pp. 2758 - 2769, August 1982)
Imaging Results with PR
8 cm
8
cm
6.4 cm
6.4
cm
Resolution: 3.2mm
Fourier Transform of object (Magnitude)
PR Reconstruction(6400 measurements)
Compressed Sensing Phase Retrieval (CSPR) Results
• Modified PR algorithm with CS
Fourier Transform of object (Magnitude)
PR Reconstruction (6400 measurements)
CSPR Reconstruction (1000 measurements)
8 cm
8
cm
6.4 cm
6.4
cm
Summary of CSPR Imaging System
• Novel THz imaging method with compressed sensing (CS) and phase retrieval (PR)
• Improved acquisition speed
• Processing time
• Resolution in reconstructed image
Acknowledgements
National Science Foundation
National Aeronautics and Space Administration
Defense Advanced Research Projects Agency
Compressed Sensing (CS) Theory
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
sparsesignal (image)
informationrate
….001010….
Measurement matrix(e.g., random)
Compressed Sensing (CS) Theory
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
sparsesignal (image)
informationrate
measurements
Measurement matrix(e.g., random)
THz Tomography
• Other imaging methods:– Pulsed THz Tomography (S. Wang & X.C.
Zhang)– WART (J. Pearce & D. Mittleman)– Interferometric and synthetic aperture
imaging (A. Bandyopadhyay & J. Federici)
• Limitations in speed and resolution
Future Improvements
• Higher imaging resolution• Higher SNR• Using Broad spectral information• Reconstruction of “complex” objects• CS and CSPR detection
2-D Wavelet Transform (Sparsity)