l1-minimization refers to finding the minimum l1-norm solution to an underdetermined linear system b=Ax. It has recently received much attention, mainly motivated by the new compressive sensing theory that shows that under quite general conditions the minimum l1-norm solution is also the sparsest solution to the system of linear equations. Although the underlying problem is a linear program, conventional algorithms such as interior-point methods suffer from poor scalability for large-scale real world problems. A number of accelerated algorithms have been recently proposed that take advantage of the special structure of the l1-minimization problem. In this paper, we provide a comprehensive review of five representative approaches, namely, Gradient Projection, Homotopy, Iterative Shrinkage-Thresholding, Proximal Gradient, and Augmented Lagrange Multiplier. The work is intended to fill in a gap in the existing literature to systematically benchmark the performance of these algorithms using a consistent experimental setting. In particular, the paper will focus on a recently proposed face recognition algorithm, where a sparse representation framework has been used to recover human identities from facial images that may be affected by illumination, occlusion, and facial disguise. MATLAB implementations of the algorithms described in this paper have been made publicly available.

本研究探究基于凸优化框架的新解法（即增广拉格朗日方法）以提高L1-minimization在稀疏表示和面部识别方面的速度和可伸缩性。我们进行了大量实验并将算法代码公开以供同行评估。

快速L1最小化算法用于强韧人脸识别