Mathematics – Optimization and Control
Scientific paper
2010-02-24
Mathematics
Optimization and Control
4 pages; submitted
Scientific paper
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.
Bioucas-Dias José M.
Figueiredo Mário A. T.
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