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Low-rank reduced biquaternion tensor ring decomposition and tensor completion

Author

Listed:
  • Luo, Hui
  • Liu, Xin
  • Liu, Wei
  • Zhang, Yang

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.

Suggested Citation

  • Luo, Hui & Liu, Xin & Liu, Wei & Zhang, Yang, 2025. "Low-rank reduced biquaternion tensor ring decomposition and tensor completion," Applied Mathematics and Computation, Elsevier, vol. 504(C).
    • Handle: RePEc:eee:apmaco:v:504:y:2025:i:c:s0096300325002309
    DOI: 10.1016/j.amc.2025.129504
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    References listed on IDEAS

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    1. Jiang-Feng Chen & Qing-Wen Wang & Guang-Jing Song & Tao Li, 2023. "Quaternion Matrix Factorization for Low-Rank Quaternion Matrix Completion," Mathematics, MDPI, vol. 11(9), pages 1-13, May.
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