Weighted Mixed-Norm Regularized Regression for Robust Face Identification

Face identification (FI) via regression-based classification has been extensively studied during the recent years. Most vector-based methods achieve appealing performance in handing the noncontiguous pixelwise noises, while some matrix-based regression methods show great potential in dealing with contiguous imagewise noises. However, there is a lack of consideration of the mixture noises case, where both contiguous and noncontiguous noises are jointly contained. In this paper, we propose a weighted mixed-norm regression (WMNR) method to cope with the mixture image corruption. WMNR reveals certain essential characteristics of FI problems and bridges the vector- and matrix-based methods. Particularly, WMNR provides two advantages for both theoretical analysis and practical implementation. First, it generalizes possible distributions of the residuals into a unified feature weighted loss function. Second, it constrains the residual image as low-rank structure that can be quantified with general nonconvex functions and a weight factor. Moreover, a new reweighted alternating direction method of multipliers algorithm is derived for the proposed WMNR model. The algorithm exhibits great computational efficiency since it divides the original optimization problem into certain subproblems with analytical solution or can be implemented in a parallel manner. Extensive experiments on several public face databases demonstrate the advantages of WMNR over the state-of-the-art regression-based approaches. More specifically, the WMNR achieves an appealing tradeoff between identification accuracy and computational efficiency. Compared with the pure vector-based methods, our approach achieves more than 10% performance improvement and saves more than 70% of runtime, especially in severe corruption scenarios. Compared with the pure matrix-based methods, although it requires slightly more computation time, the performance benefits are even larger; up to 20% improvement can be obtained.