Low-rank tensor recovery via jointing the non-convex regularization and deep prior

This paper addresses the low-rank tensor completion (LRTC) and tensor robust principal component analysis (TRPCA), which have broad applications in the recovery of real-world multi-dimensional data. To enhance recovery performance, we propose novel non-convex tensor recovery models for both LRTC and TRPCA by combining low-rank priors with data-driven deep priors. Specifically, we use the tensor ${\ell }_r^p$ pseudo-norm to effectively capture the low-rank structure of the tensor, providing a more accurate approximation of its rank. In addition, a convolutional neural network (CNN) denoiser is incorporated to learn deep prior information, further improving recovery accuracy. We also develop efficient iterative algorithms for solving the proposed models based on the alternating direction method of multipliers (ADMM). Experimental results show that the proposed methods outperform state-of-the-art techniques in terms of recovery accuracy for both LRTC and TRPCA.