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.
@article{arxiv.2501.04948,
title = {Low-Rank Reduced Biquaternion Tensor Ring Decomposition and Tensor Completion},
author = {Hui Luo and Xin Liu and Wei Liu and Yang Zhang},
journal= {arXiv preprint arXiv:2501.04948},
year = {2025}
}