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Instituto de Telecomunicações, Instituto Superior Técnico, Technical University of Lisbon , Lisbon

Sparse Regression-based Hyperspectral Unmixing. Marian-Daniel Iordache 1,2. José M. Bioucas-Dias 2. Antonio Plaza 1. 2. 1. Department of Technology of Computers and Communications , University of Extremadura , Caceres Spain.

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Instituto de Telecomunicações, Instituto Superior Técnico, Technical University of Lisbon , Lisbon

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  1. Sparse Regression-based Hyperspectral Unmixing Marian-Daniel Iordache1,2 José M. Bioucas-Dias2 Antonio Plaza1 2 1 Department of Technology of Computers and Communications,University of Extremadura, Caceres Spain Instituto de Telecomunicações,Instituto Superior Técnico,Technical University of Lisbon, Lisbon IGARSS 2011

  2. Hyperspectral imaging concept IGARSS 2011

  3. Outline • Linear mixing model • Spectral unmixing • Sparse regression-based unmixing • Sparsity-inducing regularizers ( ) • Algorithms • Results IGARSS 2011

  4. Incident radiation interacts only with one component (checkerboard type scenes) Hyperspectral linear unmixing Estimate Linear mixing model (LMM) IGARSS 2011

  5. Endmember determination (Identify the columns of ) • Inversion (For each pixel, identify the vector of proportions ) Algorithms for SLU Three step approach • Dimensionality reduction (Identify the subspace spanned by the columns of ) Sparse regression IGARSS 2011

  6. Sparse regression-based SLU • Spectral vectors can be expressed as linear combinations • of a few pure spectral signatures obtained from a • (potentially very large) spectral library 0 0 0 0 0 0 • Unmixing: given y andA, findthesparsestsolutionof • Advantage: sidesteps endmember estimation IGARSS 2011 6

  7. (library, , undetermined system) Problem – P0 Sparse regression-based SLU Very difficult (NP-hard) Approximations to P0: OMP – orthogonal matching pursuit [Pati et al., 2003] BP – basis pursuit [Chen et al., 2003] BPDN – basis pursuit denoising IGARSS 2011 7

  8. CBPDN – Constrained basis pursuit denoising Convex approximations to P0 Equivalent problem Striking result: In given circumstances, related with the coherence of among the columns of matrix A, BP(DN) yields the sparsest solution ([Donoho 06], [Candès et al. 06]). Efficient solvers for CBPDN: SUNSAL, CSUNSAL [Bioucas-Dias, Figueiredo, 2010] IGARSS 2011 8

  9. Application of CBPDN to SLU Extensively studied in [Iordache et al.,10,11] • Sixlibraries (A1, …, A6 ) • Simulated data • Endmembers random selected from the libraries • Fractional abundances uniformely distributed • over the simplex • Real data • AVIRIS Cuprite • Library: calibratedversionof USGS (A1) IGARSS 2011

  10. Hyperspectral libraries Bad news: hiperspectral libraries exhibits high mutual coherence Good news: hiperspectral mixtures are sparse (k· 5 very often) IGARSS 2011

  11. Reconstruction errors (SNR = 30 dB) ISMA [Rogge et al, 2006] IGARSS 2011

  12. Real data – AVIRIS Cuprite IGARSS 2011

  13. Real data – AVIRIS Cuprite IGARSS 2011

  14. Beyond l1 regularization Rationale: introduce new sparsity-inducing regularizers to counter the sparse regression limits imposed by the high coherence of the hyperspectral libraries. New regularizers: Total variation (TV ) and group lasso (GL) Matrix with all vectors of fractions TV regularizer l1regularizer GL regularizer IGARSS 2011

  15. Total variation and group lasso regularizers i-th image band i-th pixel promotes similarity between neighboring fractions promotesgroupsofatomsofA (groupsparsity) IGARSS 2011

  16. GLTV_SUnSAL for hyperspectral unmixing Criterion: GLTV_SUnSAL algorithm: based on CSALSA [Afonso et al., 11]. Applies the augmented Lagrangian method and alternating optimization to decompose the initial problem into a sequence of simper optimizations IGARSS 2011

  17. GLTV_SUnSAL results: l1 and GL regularizers LibraryA2 2 groups active GLTV_SUnSAL (l1+GL) GLTV_SUnSAL (l1) SRE = 5.2 dB SRE = 15.4 dB MC runs = 20 SNR = 1 IGARSS 2011

  18. GLTV_SUnSAL results: l1 and GL regularizers Library SNR = 20 dB, l1+TV SNR = 20 dB, l1 Endmember #5 SNR = 30 dB, l1 SNR = 30 dB, l1+TV IGARSS 2011

  19. Real data – AVIRIS Cuprite IGARSS 2011

  20. Concluding remarks • Shown that the sparse regression framework • has a strong potential for linear hyperspectral unmixing • Tailored new regression criteria to cope with • the high coherence of hyperspectral libraries • Developed optimization algorithms for the above • criteria • To be done: reseach ditionary learning techniques IGARSS 2011

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