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A Tensor Regularized Nuclear Norm Method for Image and Video Completion

Author

Listed:
  • A. H. Bentbib

    (Laboratoire de Mathématiques Appliquées)

  • A. El Hachimi

    (Mohammed VI Polytechnic University)

  • K. Jbilou

    (Mohammed VI Polytechnic University
    Université du Littoral Cote d’Opale)

  • A. Ratnani

    (Mohammed VI Polytechnic University)

Abstract

In the present paper, we propose two new methods for tensor completion of third-order tensors. The proposed methods consist in minimizing the average rank of the underlying tensor using its approximate function, namely the tensor nuclear norm. The recovered data will be obtained by combining the minimization process with the total variation regularization technique. We will adopt the alternating direction method of multipliers, using the tensor T-product, to solve the main optimization problems associated with the two proposed algorithms. In the last section, we present some numerical experiments and comparisons with the most known image video completion methods.

Suggested Citation

  • A. H. Bentbib & A. El Hachimi & K. Jbilou & A. Ratnani, 2022. "A Tensor Regularized Nuclear Norm Method for Image and Video Completion," Journal of Optimization Theory and Applications, Springer, vol. 192(2), pages 401-425, February.
    • Handle: RePEc:spr:joptap:v:192:y:2022:i:2:d:10.1007_s10957-021-01947-3
    DOI: 10.1007/s10957-021-01947-3
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    References listed on IDEAS

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    1. Jushan Bai & Junlong Feng, 2019. "Robust Principal Component Analysis with Non-Sparse Errors," Papers 1902.08735, arXiv.org, revised Nov 2019.
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    Cited by:

    1. Feiyang Han & Yimin Wei & Pengpeng Xie, 2024. "Regularized and Structured Tensor Total Least Squares Methods with Applications," Journal of Optimization Theory and Applications, Springer, vol. 202(3), pages 1101-1136, September.

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