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Signal Subspace Estimation in Hyperspectral Data
for Target Detection Applications
2010 IEEE GOLD REMOTE SENSING CONFERENCE2010 IEEE GOLD REMOTE SENSING CONFERENCE
Salvatore RestaSalvatore Resta, Nicola Acito, Marco Diani, Giovanni Corsini
Dipartimento di Ingegneria dell’Informazione, Università di Pisa
via G. Caruso 16, 56122 Pisa, Italy
29, 30 April 2010 29, 30 April 2010
Accademia Navale, Livorno, ItalyAccademia Navale, Livorno, Italy
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Outline
Introduction Dimensionality Reduction (DR) in Target Detection Applications
Analysis and development of DR techniques State of the art Innovative Technique
Performance Evaluation Analysis on a case study Analysis of computational cost
Conclusions Application of the proposed work Further developments
Remote Sensing & Image Processing GroupRemote Sensing & Image Processing Group
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The generic sample, or pixel, of the hyperspectral data can be modeled as the combination of a signal contribution and a noise contribution.
The signal is modeled according to the
Linear Mixture Model (LMM) [Stein,02].
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Hyperspectral sensors are characterized by a very high number of spectral bands and a
very accurate spectral resolution.
Spectral
Dimension
Hyperspectral Data Wavelenght (nm)
Image intensity for a fixed wavelenght
Remote Sensing & Image Processing GroupRemote Sensing & Image Processing Group
Hyperspectral Data Analysis
Spectral Signature of the pixel
Anomaly Detection & Rare Vectors
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Surveillance of strategically sensible areasChange Detection in operative areasMine Detection in terrestrial and sea environmentShipwreck survivor location
Applications
Rare Vectors
Scarcely represented in the observed data
Linearly independent on the abundant vectors which address the background
Rare Vectors are often spectral components of the target of interest
Anomaly Detection (AD)
No a-priori hypothesis about the target is assumedThe goal is to identify those pixels having a spectral signature which is significantly different from the background
Remote Sensing & Image Processing GroupRemote Sensing & Image Processing Group
Dimensionality Reduction (DR)
Determination of the Virtual Dimensionality (VD), which is the minimum number of spectrally distinct signal sources that characterize the hyperspectral data from the perspective view of target detection and classification [Chang,04].
Rank Estimation
Basis Estimation
DR typically includes two distinct steps:
Projection of the original data onto the estimated subspace
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Dimensionality Reduction (DR) goals:
Rare Vectors preservation in Target Detection Applications
Computational complexity reduction
Preservation of major characteristics in the observed data
Remote Sensing & Image Processing GroupRemote Sensing & Image Processing Group
Dimensionality Reduction
Traditional DR Techniques do not perform well in the presence of rare vectors
Optimality criterion oriented to rare vectors preservation [Kuybeda,07].
2
,2minargˆ
XPS
KKK
SLS
K
MX - SVD
IRVE
MOCA
IRVE - SRRE
Basis Estimation Algorithms
DR Algorithms
]|[RA
MMM
Suboptimal Solution
Traditional DR Techniques are based on the analysis of second order statistics
PCAT
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5/10Remote Sensing & Image Processing GroupRemote Sensing & Image Processing Group
Traditional Methods Drawbacks – New Optimality Criterion
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RA
MMM ˆ|ˆˆ
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Rank estimation of the abundant vectors subspace
Singular Value Decomposition
IRVE - SRRE
Subsequently a linear transformation is applied to identify the subspace which address the background.
The original data is first normalized with respect to the estimated covariance matrix of the noise and an estimate of the rank of the abundant vector subspace is obtained.
Finally the IRVE-SRRE algorithm is applied providing the rare vectors subspace rank and components estimation.
rare vectors
background
Remote Sensing & Image Processing GroupRemote Sensing & Image Processing Group
IRVE Algorithm – Statistical Rare Rank Estimator (SRRE)
Rare Vector
NORMA RESIDUA AL QUADRATO - METODO BIC + PCA
20 40 60 80 100 120 140
20
40
60
80
100
120
1407.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
8
8.1
x 104
Original Data Energy
BIC - PCA
0 50100 150 0
50100
150
7
7.2
7.4
7.6
7.8
8
8.2
x 104
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
8
8.1
x 104
RGB image
Indian Pine
DR on a case study
NORMA RESIDUA AL QUADRATO - METODO MOCA
20 40 60 80 100 120 140
20
40
60
80
100
120
1400
50
100
150
200
250
300
MOCA IRVE - SRRE
Residual Energy
NORMA RESIDUA AL QUADRATO - METODO AIRVE-SRRE
20 40 60 80 100 120 140
20
40
60
80
100
120
1400
50
100
150
200
250
300
350
T
KK
T
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1
ˆˆˆˆˆˆˆ
Projection Matrix
BIC - PCA MOCA IRVE - SRRE
80000 329 321K
S ˆˆ
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Maximum Value of residual energy
Remote Sensing & Image Processing GroupRemote Sensing & Image Processing Group
Experiments on a case study
RESIDUAL ENERGY RESIDUAL ENERGY
RESIDUAL ENERGY
0 50 100 150 200 25010
11
12
13
14
15
16
17
18INFORMATION THEORETIC CRITERIA
ORDINE
Log(I
TC)
AICGICMDLAICC
VDAIC = 108
VDMDL = 21
VDGIC = 39
VDIRVE-SRRE = 25
VDMOCA = 23 VD estimation on a case study
Computational load evaluation
)ˆ( 2totCPCAITC NNKC Ο
)ˆ( 22totCMOCA NNKC Ο
)ˆ( 2totCRSRREAIRVE NNKC Ο
Computational load of IRVE – SRRE algorithm is considerably reduced with
respect to MOCA algorithm
Traditional methods show a tendency to overestimate the
subspace rank
ITC – PCA MOCA IRVE - SRRE
154 s 690 s 64 s
Computational load Indian Pine
8/10Remote Sensing & Image Processing GroupRemote Sensing & Image Processing Group
Experiment on a case study & Computational Complexity
Traditional DR methods can reveal some inadequacy to preserve rare vectors representation.
Analysis of DR methods aimed at preserving rare vectors which can be spectral components of the target of interest.
Development of a new method oriented to rare vectors preservation which is very efficient from a
computational point of view
Exaustive performance evaluation introduced by the new
techniques on existing target detection algorithms.
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Open research topic
Remote Sensing & Image Processing GroupRemote Sensing & Image Processing Group
Conclusions
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1. [Ste02] D. W. J. Stein, S. G. Beaven, L. E. Hoff, E. M. Winter, A. P. Schaum, A. D. Stocker, “Anomaly Detection from Hyperspectral Imagery”, IEEE Signal Process. Mag., 19(1), 58-69 (2002).
2. [Ric93] J. A. Richards, X. Jia, Remote Sensing Digital Image Processing, 9, Springer-Verlag, 1993.3. [Aci08] N. Acito, G. Corsini, M. Diani, S. Matteoli, S. Resta, “A novel technique for hyperspectral signal subspace estimation in target detection applications ”,
Accepted for International Conference on Geoscience and remote sensing – IGARSS, 2008.4. [Kuy07] O. Kuybeda, D. Malah and M. Barzohar, ”Rank estimation and redundancy reduction of high dimensional noisy signals with preservation of rare vectors”,
IEEE Signal Processing Magazine, vol. 55, Issue 12, Decemder 2007, pp. 5579-5592.5. [Cha04] C. I. Chang and Q. Du, “Estimation of Number of Spectrally Distinct Signal Sources in Hyperspectral Imagery”, IEEE Transactions on Geoscience and
Remote Sensing, vol. 42, no. 3, March 2004.6. [Sto04] P. Stoica and Y. Selen, “Model order selection: a review of information criterion rules”, IEEE Signal Processing Magazine, vol. 21, Issue 4, July 2004, pp.
36-47.7. [Rog96] R. E. Roger and J. F. Arnold, “Reliably estimating the noise in AVIRIS hyperspectral imagers” Int. J. Remote Sens., vol. 17, no. 10, pp. 1951–1962, 1996.
Thank you for the attention!
Remote Sensing & Image Processing GroupRemote Sensing & Image Processing Group
References