Two New Low Rank Tensor Completion Methods Based on Sum Nuclear Norm

TL;DR

This paper introduces two novel low rank tensor completion methods based on sum nuclear norm and total variation regularization, demonstrating superior performance in image recovery tasks, especially at low sampling rates.

Contribution

The paper proposes two convex tensor completion models incorporating sum nuclear norm and total variation, with efficient ADMM solutions, advancing high-quality image recovery techniques.

Findings

Methods converge reliably and outperform existing approaches.

Significant improvement at low sampling rates, e.g., 2.5%.

Effective utilization of local image prior information.

Abstract

The low rank tensor completion (LRTC) problem has attracted great attention in computer vision and signal processing. How to acquire high quality image recovery effect is still an urgent task to be solved at present. This paper proposes a new tensor $L_{2,1}$ norm minimization model (TLNM) that integrates sum nuclear norm (SNN) method, differing from the classical tensor nuclear norm (TNN)-based tensor completion method, with $L_{2,1}$ norm and Qatar Riyal decomposition for solving the LRTC problem. To improve the utilization rate of the local prior information of the image, a total variation (TV) regularization term is introduced, resulting in a new class of tensor $L_{2,1}$ norm minimization with total variation model (TLNMTV). Both proposed models are convex and therefore have global optimal solutions. Moreover, we adopt the Alternating Direction Multiplier Method (ADMM) to obtain the closed-form solution of each variable, thus ensuring the feasibility of the algorithm. Numerical experiments show that the two proposed algorithms are convergent and outperform compared methods. In particular, our method significantly outperforms the contrastive methods when the sampling rate of hyperspectral images is 2.5\%.