Instituto de Telecomunica

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

• Linear mixing model

• Spectral unmixing

• Sparse regression-based unmixing

• Algorithms

• Results

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Linear mixing model (LMM)
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Algorithms for SLU
Three step approach
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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

• Advantage sidesteps endmember estimation

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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
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Convex approximations to P0
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
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Application of CBPDN to SLU
Extensively studied in Iordache et al.,10,11

• Six libraries (A1, , A6 )

• Simulated data
• Endmembers random selected from the libraries
• Fractional abundances uniformely distributed
• over the simplex

• Real data
• AVIRIS Cuprite
• Library calibrated version of USGS (A1)

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Hyperspectral libraries
Bad news hiperspectral libraries exhibits high
mutual coherence
Good news hiperspectral mixtures are sparse (k
5 very often)
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Reconstruction errors (SNR 30 dB)
ISMA Rogge et al, 2006
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Real data AVIRIS Cuprite
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Real data AVIRIS Cuprite
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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)
TV regularizer
l1 regularizer
GL regularizer
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Total variation and group lasso regularizers
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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
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GLTV_SUnSAL results l1 and GL regularizers
k (no. act. groups) no. endmembers SRE (l1) dB SRE (l1GL) 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
MC runs 20 SNR 1
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GLTV_SUnSAL results l1 and GL regularizers
Library
SNR 20 dB, l1TV
SNR 20 dB, l1
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Real data AVIRIS Cuprite
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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

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