Nonconvex regularizer and latent pattern based robust regression for face recognition

Abstract

Nuclear norm based matrix regression (NMR) approaches have yielded encouraging recognition results in the presence of image-level noise. However, NMR methods have two shortcomings. One is that test samples are directly used in the reconstruction process, and this may degrade recognition performance, especially when the samples are severely corrupted by noise. The other is that these methods exploit the nuclear norm to characterize low-rank structural information of residual images, which may lead to suboptimal solutions. To overcome these two deficiencies, we present a robust regression model that coalesces a nonconvex regularizer with a latent pattern (NRLPR). The latent pattern is essentially obtained by removing noise from a test sample, and therefore it can be closer to the reconstructed sample than the test sample. Furthermore, the nonconvex regularizer penalizes larger values less while penalizing smaller values more, accordingly, it can efficiently approximate the rank function. Additionally, we integrate the iteratively reweighted least squares method and the alternating direction method of multipliers to devise an efficient iterative algorithm (IR-ADMM) for NRLPR. Meanwhile, a nonconvex function is used for the design of the classifier. Finally, numerous experiments demonstrate the superiority of the proposed methods over state-of-the-art approaches for handling structural and mixed noise.