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Tensor Conjugate Gradient Methods with Automatically Determination of Regularization Parameters for Ill-Posed Problems with t-Product

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Listed:
  • Shi-Wei Wang

    (Geomathematics Key Laboratory of Sichuan, College of Mathematics and Physics, Chengdu University of Technology, Chengdu 610059, China)

  • Guang-Xin Huang

    (College of Computer Science and Cyber Security, Chengdu University of Technology, Chengdu 610059, China)

  • Feng Yin

    (Geomathematics Key Laboratory of Sichuan, College of Mathematics and Physics, Chengdu University of Technology, Chengdu 610059, China)

Abstract

Ill-posed problems arise in many areas of science and engineering. Tikhonov is a usual regularization which replaces the original problem by a minimization problem with a fidelity term and a regularization term. In this paper, a tensor t-production structure preserved Conjugate-Gradient (tCG) method is presented to solve the regularization minimization problem. We provide a truncated version of regularization parameters for the tCG method and a preprocessed version of the tCG method. The discrepancy principle is used to automatically determine the regularization parameter. Several examples on image and video recover are given to show the effectiveness of the proposed methods by comparing them with some previous algorithms.

Suggested Citation

  • Shi-Wei Wang & Guang-Xin Huang & Feng Yin, 2024. "Tensor Conjugate Gradient Methods with Automatically Determination of Regularization Parameters for Ill-Posed Problems with t-Product," Mathematics, MDPI, vol. 12(1), pages 1-20, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:1:p:159-:d:1312781
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    References listed on IDEAS

    as
    1. Quan Yu & Xinzhen Zhang, 2023. "T-product factorization based method for matrix and tensor completion problems," Computational Optimization and Applications, Springer, vol. 84(3), pages 761-788, April.
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