Jose_TH1_T09_5.ppt

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Jose_TH1_T09_5.ppt

  1. 1. Instituto de Telecomunicações, Instituto Superior Técnico, Technical University of Lisbon , Lisbon Sparse Regression-based Hyperspectral Unmixing IGARSS 2011 Antonio Plaza 1 Marian-Daniel Iordache 1,2 Department of Technology of Computers and Communications , University of Extremadura , Caceres Spain José M. Bioucas-Dias 2 1 2
  2. 2. Hyperspectral imaging concept IGARSS 2011
  3. 3. 3 Outline <ul><li>Sparse regression-based unmixing </li></ul><ul><li>Linear mixing model </li></ul>IGARSS 2011 <ul><li>Spectral unmixing </li></ul><ul><li>Algorithms </li></ul><ul><li>Results </li></ul><ul><li>Sparsity-inducing regularizers ( ) </li></ul>
  4. 4. 4 Linear mixing model (LMM) IGARSS 2011 Incident radiation interacts only with one component (checkerboard type scenes) Hyperspectral linear unmixing Estimate
  5. 5. IGARSS 2011 5 Algorithms for SLU Three step approach <ul><li>Endmember determination </li></ul>(Identify the columns of ) <ul><ul><li>Inversion </li></ul></ul>(For each pixel, identify the vector of proportions ) <ul><ul><li>Dimensionality reduction </li></ul></ul>(Identify the subspace spanned by the columns of ) Sparse regression
  6. 6. Sparse regression-based SLU <ul><li>Spectral vectors can be expressed as linear combinations </li></ul><ul><li>of a few pure spectral signatures obtained from a </li></ul><ul><li>(potentially very large) spectral library </li></ul>6 IGARSS 2011 <ul><li>Advantage : sidesteps endmember estimation </li></ul>0 0 0 0 0 0 <ul><li>Unmixing : given y and A , find the sparsest solution of </li></ul>
  7. 7. 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 Sparse regression-based SLU Problem – P0 (library, , undetermined system)
  8. 8. 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]). Convex approximations to P0 8 IGARSS 2011 Efficient solvers for CBPDN: SUNSAL, CSUNSAL [Bioucas-Dias, Figueiredo, 2010] CBPDN – Constrained basis pursuit denoising Equivalent problem
  9. 9. Application of CBPDN to SLU Extensively studied in [Iordache et al .,10,11] <ul><li>Six libraries ( A 1 , …, A 6 ) </li></ul><ul><li>Simulated data </li></ul><ul><ul><li>Endmembers random selected from the libraries </li></ul></ul><ul><ul><li>Fractional abundances uniformely distributed </li></ul></ul><ul><ul><li>over the simplex </li></ul></ul><ul><li>Real data </li></ul><ul><ul><li>AVIRIS Cuprite </li></ul></ul><ul><ul><li>Library: calibrated version of USGS ( A 1 ) </li></ul></ul>IGARSS 2011
  10. 10. Bad news: hiperspectral libraries exhibits high mutual coherence Good news: hiperspectral mixtures are sparse (k · 5 very often) Hyperspectral libraries IGARSS 2011
  11. 11. Reconstruction errors (SNR = 30 dB) ISMA [Rogge et al , 2006] IGARSS 2011
  12. 12. Real data – AVIRIS Cuprite IGARSS 2011
  13. 13. Real data – AVIRIS Cuprite IGARSS 2011
  14. 14. Beyond l 1 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) l 1 regularizer GL regularizer TV regularizer IGARSS 2011 Matrix with all vectors of fractions
  15. 15. Total variation and group lasso regularizers IGARSS 2011 i- th image band promotes similarity between neighboring fractions i- th pixel promotes groups of atoms of A (group sparsity)
  16. 16. GLTV_SUnSAL for hyperspectral unmixing 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 Criterion: IGARSS 2011
  17. 17. GLTV_SUnSAL results: l 1 and GL regularizers MC runs = 20 SNR = 1 IGARSS 2011 GLTV_SUnSAL (l 1 ) Library A 2 2 groups active SRE = 5.2 dB GLTV_SUnSAL (l 1 +GL) SRE = 15.4 dB k (no. act. groups) no. endmembers SRE (l1) dB SRE (l1+GL) dB 1 3 9.7 16.3 2 6 7.8 14.5 3 9 6.7 14.0 4 12 4.8 12.3
  18. 18. SNR = 20 dB, l1 GLTV_SUnSAL results: l 1 and GL regularizers SNR = 20 dB, l1+TV Library IGARSS 2011 SNR = 30 dB, l1 SNR = 30 dB, l1+TV Endmember #5
  19. 19. Real data – AVIRIS Cuprite IGARSS 2011
  20. 20. Concluding remarks <ul><li>Shown that the sparse regression framework </li></ul><ul><li>has a strong potential for linear hyperspectral unmixing </li></ul><ul><li>Tailored new regression criteria to cope with </li></ul><ul><li>the high coherence of hyperspectral libraries </li></ul><ul><li>Developed optimization algorithms for the above </li></ul><ul><li>criteria </li></ul><ul><li>To be done: reseach ditionary learning techniques </li></ul>IGARSS 2011

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