Jose_TH1_T09_5.ppt

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  • 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. Hyperspectral imaging concept IGARSS 2011
  • 3. 3 Outline
    • Sparse regression-based unmixing
    • Linear mixing model
    IGARSS 2011
    • Spectral unmixing
    • Algorithms
    • Results
    • Sparsity-inducing regularizers ( )
  • 4. 4 Linear mixing model (LMM) IGARSS 2011 Incident radiation interacts only with one component (checkerboard type scenes) Hyperspectral linear unmixing Estimate
  • 5. IGARSS 2011 5 Algorithms for SLU Three step approach
    • Endmember determination
    (Identify the columns of )
      • Inversion
    (For each pixel, identify the vector of proportions )
      • Dimensionality reduction
    (Identify the subspace spanned by the columns of ) Sparse regression
  • 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
    6 IGARSS 2011
    • Advantage : sidesteps endmember estimation
    0 0 0 0 0 0
    • Unmixing : given y and A , find the sparsest solution of
  • 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. 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. Application of CBPDN to SLU Extensively studied in [Iordache et al .,10,11]
    • Six libraries ( A 1 , …, A 6 )
    • Simulated data
      • Endmembers random selected from the libraries
      • Fractional abundances uniformely distributed
      • over the simplex
    • Real data
      • AVIRIS Cuprite
      • Library: calibrated version of USGS ( A 1 )
    IGARSS 2011
  • 10. Bad news: hiperspectral libraries exhibits high mutual coherence Good news: hiperspectral mixtures are sparse (k · 5 very often) Hyperspectral libraries 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 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. 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. 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. 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. 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. 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