ieee gold 2010 resta

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].

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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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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

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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

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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

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50

100

150

200

250

300

350

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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

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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