约束稀疏回归的交替方向算法：应用于高光谱解混
Alternating Direction Algorithms for Constrained Sparse Regression: Application to Hyperspectral Unmixing
AI总结：
提出基于交替方向乘子法的SUnSAL和C-SUnSAL算法，高效求解高光谱解混中的约束稀疏回归问题，在速度和精度上优于现有方法。
摘要：
凸优化问题在高光谱解混中很常见。例如：约束最小二乘（CLS）和完全约束最小二乘（FCLS）问题，用于计算已知光谱线性混合中的丰度；约束基追踪（CBP）问题，用于从大型库中寻找稀疏（即非零项数量少）光谱线性混合；约束基追踪去噪（CBPDN）问题，是BP的推广，允许建模误差。本文基于交替方向乘子法（增广拉格朗日家族的一种方法）引入两种新算法来高效求解这些优化问题。算法称为SUnSAL（通过变量分裂和增广拉格朗日的稀疏解混）和C-SUnSAL（约束SUnSAL）。C-SUnSAL求解CBP和CBPDN问题，而SUnSAL求解CLS和FCLS及其更一般版本——约束稀疏回归（CSR）。实验表明，C-SUnSAL和SUnSAL在速度和精度上优于现成方法。
英文摘要：
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.
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