Bilateral Two-Dimensional Matrix Regression Preserving Discriminant Embedding for Corrupted Image Recognition

Nuclear-norm-based matrix regression (NMR) methods have been successfully applied for the recognition of corrupted images. However, most of these methods do not consider the label information and are classified as unsupervised learning methods. In this paper, we propose a new regression-based algorithm, named bilateral two-dimensional matrix regression preserving discriminant embedding (B2DMRPDE). The proposed algorithm constructs the within-reconstruction graph and between-reconstruction graph using NMR. Then, B2DMRPDE aims to seek a subspace in which the within-class reconstructive residual is minimized and the between-class reconstructive residual is maximized based on Fisher's criterion. Hence, B2DMRPDE can capture the potential discriminative information for classification. To enhance the classification effectiveness, we present a new NMR-based classifier to determine the class label of the testing sample. Extensive experiments on face image databases were performed, and the results validate the effectiveness of the proposed method.