Convex optimization problems are common in hyperspectral unmixing. Examples
include: the constrained least squares (CLS) and the fully constrained least
squares (FCLS) problems, which are used to compute the fractional abundances in
linear mixtures of known spectra; the constrained basis pursuit (CBP) problem,
which is used to find sparse (i.e., with a small number of non-zero terms)
linear mixtures of spectra from large libraries; the constrained basis pursuit
denoising (CBPDN) problem, which is a generalization of BP that admits 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 and FCLS, 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.

本文介绍了两种新算法（SUnSAL 和 C-SUnSAL），用于解决凸优化问题，特别是在高光谱分离中使用的问题。这些算法基于交替方向乘子方法，可用于解决 CBP 和 CBPDN 问题以及 CLS 和 FCLS 问题。实验结果表明，这些算法在速度和准确性方面优于现有的方法。