Robust Nuclear Norm-Based Matrix Regression With Applications to Robust Face Recognition

Face recognition (FR) via regression analysis-based classification has been widely studied in the past several years. Most existing regression analysis methods characterize the pixelwise representation error via l
₁
-norm or l
₂
-norm, which overlook the 2D structure of the error image. Recently, the nuclear norm-based matrix regression model is proposed to characterize low-rank structure of the error image. However, the nuclear norm cannot accurately describe the low-rank structural noise when the incoherence assumptions on the singular values does not hold, since it overpenalizes several much larger singular values. To address this problem, this paper presents the robust nuclear norm to characterize the structural error image and then extends it to deal with the mixed noise. The majorization-minimization (MM) method is applied to derive a iterative scheme for minimization of the robust nuclear norm optimization problem. Then, an efficiently alternating direction method of multipliers (ADMM) method is used to solve the proposed models. We use weighted nuclear norm as classification criterion to obtain the final recognition results. Experiments on several public face databases demonstrate the effectiveness of our models in handling with variations of structural noise (occlusion, illumination, and so on) and mixed noise.