Tensor Nuclear Norm-Based Multi-Channel Atomic Representation for Robust Face Recognition

Abstract

Numerous representation-based classification (RC) methods have been developed for face recognition due to their decent model interpretability and robustness against noise. Most existing RC methods primarily characterize the gray-scale reconstruction error image (single-channel data) in two ways: the one-dimensional (1D) pixel-based error model and the two-dimensional (2D) gray-scale image-matrix-based error model. The former measures the reconstruction error pixel by pixel, while the latter leverages 2D structural information of the gray-scale error image, such as the low-rank property. However, when applying these methods to different color channels of a test color face image (multi-channel data) separately and independently, they neglect the three-dimensional (3D) structural correlations among distinct color channels. In real-world scenarios, face images are often contaminated with complex noise, including contiguous occlusion and random pixel corruption, which pose significant challenges to these approaches and can lead to a decline in performance. In this paper, we propose a Tensor Nuclear Norm based Robust Multi-channel Atomic Representation (TNN-RMAR) framework with application to color face recognition. The proposed method has the following three critical ingredients: 1) We propose a 3D color image-tensor-based error model, which can take full advantage of the 3D structural information of the color error image. 2) To leverage the 3D structural information of the color error image, we model it as a 3-order tensor ${\mathcal {E}}$ and exploit its low-rank property with the tensor nuclear norm. Given that multiple color channels in a color image are generally corrupted at the same positions, we design a tube-wise tailored loss function to further leverage its tube-wise structure. 3) We devise the multi-channel atomic norm (MAN) regularization for the representation coefficient matrix, which allows us to jointly harness the correlation information of coefficients in different color channels. In addition, we also devise an efficient algorithm to solve the TNN-RMAR framework based on the alternating direction method of multipliers (ADMM) framework. By leveraging TNN-RMAR as a general platform, we also develop several novel robust multi-channel RC methods. Experimental results on benchmark real-world databases validate the effectiveness and robustness of the proposed framework for robust color face recognition.