A fast $\ell_1$-solver and its applications to robust face recognition

Huining Qiu; Xiaoming Chen; Wanquan Liu; Guanglu Zhou; Yiju Wang; Jianhuang Lai

doi:10.3934/jimo.2012.8.163

Article Contents

2012, Volume 8, Issue 1: 163-178. Doi: 10.3934/jimo.2012.8.163

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A fast $\ell_1$-solver and its applications to robust face recognition

1.
Sun Yat-sen Univeristy, NO.135 Xiguangxi Road, Guangzhou 510275
2.
Curtin University, GPO Box U1987, Perth, WA 6845
3.
Qufu Normal University, Rizhao 276800, Shandong

Received: January 31, 2011

Revised: June 30, 2011

Published: December 2011

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Abstract

In this paper we apply a recently proposed Lagrange Dual Method (LDM) to design a new Sparse Representation-based Classification (LDM-SRC) algorithm for robust face recognition problem. The proposed approach improves the efficiency of the SRC algorithm significantly. The proposed algorithm has the following advantages: (1) it employs the LDM $\ell_1$-solver to find solution of the $\ell_1$-norm minimization problem, which is much faster than other state-of-the-art $\ell_1$-solvers, e.g. $\ell_1$-magic and $\ell_1-\ell_2$. (2) The LDM $\ell_1$-solver utilizes a new Lagrange-dual reformulation of the original $\ell_1$-norm minimization problem, not only reducing the problem size when the dimension of training image data is much less than the number of training samples, but also making the dual problem become smooth and convex. Therefore it converts the non-smooth $\ell_1$-norm minimization problem into a sequence of smooth optimization problems. (3) The LDM-SRC algorithm can maintain good recognition accuracy whilst reducing the computational time dramatically. Experimental results are presented on some benchmark face databases.

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Mathematics Subject Classification: Primary: 65D18, 68U10; Secondary: 65K05.

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