Fast 퓁 1 -Minimization Algorithms for Robust Face Recognition

Allen Y. Yang, Zihan Zhou, A. G. Balasubramanian, S. Shankar Sastry, Yi Ma

2013 (modified: 25 Apr 2023)IEEE Trans. Image Process. 2013Readers: Everyone

Abstract: i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l 1 -minimization refers to finding the minimum l 1 -norm solution to an underdetermined linear system \mbi b = A \mbi x . Under certain conditions as described in compressive sensing theory, the minimum l 1 -norm solution is also the sparsest solution. In this paper, we study the speed and scalability of its algorithms. In particular, we focus on the numerical implementation of a sparsity-based classification framework in robust face recognition, where sparse representation is sought to recover human identities from high-dimensional facial images that may be corrupted by illumination, facial disguise, and pose variation. Although the underlying numerical problem is a linear program, traditional algorithms are known to suffer poor scalability for large-scale applications. We investigate a new solution based on a classical convex optimization framework, known as augmented Lagrangian methods. We conduct extensive experiments to validate and compare its performance against several popular l 1 -minimization solvers, including interior-point method, Homotopy, FISTA, SESOP-PCD, approximate message passing, and TFOCS. To aid peer evaluation, the code for all the algorithms has been made publicly available.

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