Low-Rank Reduced Biquaternion Tensor Ring Decomposition and Tensor Completion

2025/01/09 by Luo Hui, Xin Liu, Luo, Hui +5
Mathematics · #Commutative Algebra (math.AC) #FOS: Mathematics #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2501.04948

openalex publication_date 2025/01/09 · openalex created_date 2025/01/11 · openalex updated_date 2026/07/28

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.

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