A fast ℓ1-solver and its applications to robust face recognition

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 ℓ1-solver to find solution of theℓ1-norm minimization problem, which is much faster than other state-of-the-art ℓ1-solvers, e.g. ℓ1-magic and ℓ1−ℓs . (2) The LDM ℓ1-solver utilizes a new Lagrange-dual reformulation of the original ℓ1-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 ℓ1-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.