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Fast \ell _{1} -Minimization Algorithms for Robust Face Recognition

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5 Author(s)
Yang, A.Y. ; Dept. of Electr. Eng. & Comput. Sci., Univ. of California, Berkeley, Berkeley, CA, USA ; Zihan Zhou ; Balasubramanian, A.G. ; Sastry, S.S.
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l 1-minimization refers to finding the minimum l1-norm solution to an underdetermined linear system mbib=Ambix. Under certain conditions as described in compressive sensing theory, the minimum l1-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 l1-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.

Published in:

Image Processing, IEEE Transactions on  (Volume:22 ,  Issue: 8 )
Biometrics Compendium, IEEE