低秩约简双四元数张量环分解与张量补全

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation Pub Date : 2025-05-09 DOI:10.1016/j.amc.2025.129504

Hui Luo , Xin Liu , Wei Liu , Yang Zhang

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引用次数: 0

摘要

定义了简化双四元数张量环分解（RBTR），并详细阐述了相应的RBTR- svd算法。利用RBTR分解，提出了一种新颖的低秩张量补全算法RBTR-TV，该算法将RBTR秩与总变分（TV）正则化相结合，对过程进行优化。对彩色图像和视频补全任务的数值实验表明了该方法的优越性。

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Low-rank reduced biquaternion tensor ring decomposition and tensor completion

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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来源期刊

Applied Mathematics and Computation 数学-应用数学

CiteScore

7.90

自引率

10.00%

发文量

755

审稿时长

36 days

期刊介绍： Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results. In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.