A Robust Group-Sparse Representation Variational Method With Applications to Face Recognition

In this paper, we propose a Group-Sparse Representation-based method with applications to Face Recognition (GSR-FR). The novel sparse representation variational model includes a non-convex sparsity-inducing penalty and a robust non-convex loss function. The penalty encourages group sparsity by using an approximation of the $\ell _{0}$ -quasinorm, and the loss function is chosen to make the algorithm robust to noise, occlusions, and disguises. The solution of the non-trivial non-convex optimization problem is efficiently obtained by a majorization-minimization strategy combined with forward-backward splitting, which, in particular, reduces the solution to a sequence of easier convex optimization sub-problems. Extensive experiments on widely used face databases show the potentiality of the proposed model and demonstrate that the GSR-FR algorithm is competitive with the state-of-the-art methods based on sparse representation, especially for very low dimensional feature spaces.