New Robust Tensor PCA via Affine Transformations and $L_{\mathrm{2,1}}$ Norms for Exact Tubal Low-Rank Recovery from Highly Corrupted and Correlated Images in Signal Processing

Abstract

In this latest work, the Newly Modified Robust Tensor Principal Component Analysis (New RTPCA) using affine transformation and L 2,1 norms is proposed to remove the outliers and heavy sparse noises in signal processing. This process is done by decomposing the original data matrix as the low-rank heavy sparse noises. The determination of the potential variables is casted as constrained convex optimization problem, and the Alternating Direction Method of Multipliers (ADMM) method is considered to reduce the computational loads in an iterative manner. The simulation results validate the effectiveness of the new method as compared with that of the state-of-the-art methods.