Low-Rank Reduced Biquaternion Tensor Ring Decomposition and Tensor Completion

TL;DR

This paper introduces a new low-rank tensor decomposition method called RBTR, along with an algorithm RBTR-SVD, and applies it to tensor completion tasks like color image and video recovery.

Contribution

The paper proposes the reduced biquaternion tensor ring (RBTR) decomposition and a novel tensor completion algorithm RBTR-TV that combines RBTR ranks with TV regularization.

Findings

Effective in color image completion

Superior video recovery performance

Advantages demonstrated through numerical experiments

Abstract

We define the reduced biquaternion tensor ring (RBTR) decomposition and provide a detailed exposition of the corresponding algorithm RBTR-SVD. Leveraging RBTR decomposition, we propose a novel low-rank tensor completion algorithm RBTR-TV integrating RBTR ranks with total variation (TV) regularization to optimize the process. Numerical experiments on color image and video completion tasks indicate the advantages of our method.