Robust block tensor principal component analysis

Abstract

Robust tensor principal component analysis based on tensor singular value decomposition (t-SVD) is a very effective tool to extract the low rank and sparse components in multi-way signals. In this paper, instead of the tensor nuclear norm (TNN) based on t-SVD for the whole tensor, we propose using the sum of TNN for its small blocks in the same size aiming to do the extraction in a more appropriate scale. The alternating direction method of multipliers can divide the optimization model into two sub-problems, i.e. low rank tensor approximation and sparse component approximation. The iterative block tensor singular value soft thresholding and iterative soft thresholding are used to solve these two sub-problems, respectively. In numerical experiments, the results demonstrate the performance improvement of the proposal method in face image denoising, color image denoising, and illumination normalization for face images.