A Fast (l)1-solver and Its Applications to Robust Face Recognition

摘要

This paper applies Wang’s recently proposed Lagrange Dual Method (LDM) to design the Sparse Representation-based Classification (SRC) algorithm for robust face recognition problem and this improves the efficiency of the SRC algorithm. With regard to the high computational cost of the original SRC algorithm, we propose a LDM-SRC variant which tries to tackle the high commotional cost issue for the SRC problem. The proposed algorithm has these advantages: (1) it employs the LDM (l)1-solver to find solution of the (l)1-norm minimization problem, which is much faster than other state-of-the-art (l)1-solvers, e.g. (l)1-magic and l1 ls. (2) The LDM (l)1-solver utilizes a new Lagrange-dual reformulation of the original (l)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, hence it bridges the nonsmooth (l)1-norm minimization problem and so a number of maturely developed smooth optimization algorithms can be used to solve it. (3) The LDM-SRC algorithm maintains robust face recognition performance in terms of the average recognition accuracy and reduces the average computational time. These advantages are illustrated by experimental results on standard benchmark face databases.