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Quaternion Matrix Factorization for Low-Rank Quaternion Matrix Completion

Author

Listed:
  • Jiang-Feng Chen

    (Department of Mathematics, Shanghai University, Shanghai 200444, China)

  • Qing-Wen Wang

    (Department of Mathematics, Shanghai University, Shanghai 200444, China)

  • Guang-Jing Song

    (School of Mathematics and Information Sciences, Weifang University, Weifang 261061, China)

  • Tao Li

    (Key Laboratory of Engineering Modeling and Statistical Computation of Hainan Province, Department of Mathematics, Hainan University, Haikou 570228, China)

Abstract

The main aim of this paper is to study quaternion matrix factorization for low-rank quaternion matrix completion and its applications in color image processing. For the real-world color images, we proposed a novel model called low-rank quaternion matrix completion (LRQC), which adds total variation and Tikhonov regularization to the factor quaternion matrices to preserve the spatial/temporal smoothness. Moreover, a proximal alternating minimization (PAM) algorithm was proposed to tackle the corresponding optimal problem. Numerical results on color images indicate the advantages of our method.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2144-:d:1138593
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    Cited by:

    1. Wei Yuan & Han Liu & Lili Liang & Wenqing Wang, 2024. "Learning the Hybrid Nonlocal Self-Similarity Prior for Image Restoration," Mathematics, MDPI, vol. 12(9), pages 1-18, May.

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