A log-based non-convex relaxation regularized regression for robust face recognition

Regression methods are widely employed in face recognition applications. The vector-based norm regression model only represents the pixel by pixel correlation and exhibits poor performance with contiguous occlusion. In contrast, methods based on the nuclear norm describe the low-rank structural information, but it is difficult to achieve satisfactory performance when dealing with complex noise. To address this, a log-based non-convex relaxation regularized regression (log-NCRR) model for robust face recognition is proposed in this paper. We adopt the log-based matrix loss without additional parameters to characterize the low-rank part of error image. Considering sparsity, we design a log-based vector loss to describe the sparse part of the error matrix, which achieves a balance between the l0-norm and l1-norm. Additionally, a weighted non-convex relaxation of l2,1-norm is proposed to ensure the group sparsity of the regression coefficient. The optimization problem is optimized by ADMM, with the corresponding sub-problems easily solved by the generalized singular value shrinkage operator. Finally, experimental results on four public databases for various types of noise validate the effectiveness and robustness of log-NCRR in face recognition.