On the tensor nuclear norm and the total variation regularization for image and video completion

TL;DR

This paper introduces two novel tensor completion algorithms combining tensor nuclear norm minimization with total variation regularization, solved via ADM with tensor T-product, demonstrating improved image and video recovery performance.

Contribution

The paper proposes new tensor completion algorithms that integrate tensor nuclear norm and total variation regularization, solved using ADM with tensor T-product, advancing image and video recovery methods.

Findings

Algorithms outperform existing methods in image/video completion tasks.

Numerical experiments validate the effectiveness of the proposed methods.

Comparisons show improved accuracy and efficiency over known techniques.

Abstract

In the present paper we propose two new algorithms of tensor completion for three-order tensors. The proposed methods consist in minimizing the average rank of the underlying tensor using its approximate function namely the tensor nuclear norm and then the recovered data will be obtained by using the total variation regularisation technique. We will adopt the Alternating Direction Method of Multipliers (ADM), using the tensor T-product, to solve the main optimization problems associated to the two algorithms. In the last section, we present some numerical experiments and comparisons with the most known image completion methods.