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ALTERNATING DIRECTION ALGORITHMS FOR CONSTRAINED SPARSE REGRESSION: APPLICATION TO HYPERSPECTRAL UNMIXING
| Citations: | 32 - 11 self |
BibTeX
@MISC{Bioucas-dias_alternatingdirection,
author = {José M. Bioucas-dias and Mário A. T. Figueiredo},
title = {ALTERNATING DIRECTION ALGORITHMS FOR CONSTRAINED SPARSE REGRESSION: APPLICATION TO HYPERSPECTRAL UNMIXING},
year = {}
}
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Abstract
Convex optimization problems are common in hyperspectral unmixing. Examples are the constrained least squares (CLS) problem used to compute the fractional abundances in a linear mixture of known spectra, the constrained basis pursuit (CBP) to find sparse (i.e., with a small number of terms) linear mixtures of spectra, selected from large libraries, and the constrained basis pursuit denoising (CBPDN), which is a generalization of BP to admit modeling errors. In this paper, we introduce two new algorithms to efficiently solve these optimization problems, based on the alternating direction method of multipliers, a method from the augmented Lagrangian family. The algorithms are termed SUnSAL (sparse unmixing by variable splitting and augmented Lagrangian) and C-SUnSAL (constrained SUnSAL). C-SUnSAL solves the CBP and CBPDN problems, while SUnSAL solves CLS as well as a more general version thereof, called constrained sparse regression (CSR). C-SUnSAL and SUnSAL are shown to outperform off-the-shelf methods in terms of speed and accuracy. 1.
Keyphrases
application hyperspectral unmixing direction algorithm constrained sparse regression augmented lagrangian fractional abundance large library cbpdn problem off-the-shelf method general version thereof constrained basis pursuit augmented lagrangian family constrained basis pursuit denoising direction method sparse unmixing optimization problem sparse regression small number variable splitting hyperspectral unmixing new algorithm modeling error linear mixture convex optimization problem
