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L1-minimization refers to finding the minimum L1-norm solution to anunderdetermined linear system b=Ax. Under certain conditions as described incompressive sensing theory, the minimum L1-norm solution is also the sparsestsolution. In this paper, our study addresses the speed and scalability of itsalgorithms. In particular, we focus on the numerical implementation of asparsity-based classification framework in robust face recognition, wheresparse representation is sought to recover human identities from veryhigh-dimensional facial images that may be corrupted by illumination, facialdisguise, and pose variation. Although the underlying numerical problem is alinear program, traditional algorithms are known to suffer poor scalability forlarge-scale applications. We investigate a new solution based on a classicalconvex optimization framework, known as Augmented Lagrangian Methods (ALM). Thenew convex solvers provide a viable solution to real-world, time-criticalapplications such as face recognition. We conduct extensive experiments tovalidate and compare the performance of the ALM algorithms against severalpopular L1-minimization solvers, including interior-point method, Homotopy,FISTA, SESOP-PCD, approximate message passing (AMP) and TFOCS. To aid peerevaluation, the code for all the algorithms has been made publicly available.

Fast L1-Minimization Algorithms For Robust Face Recognition