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A Tensor Regularized Nuclear Norm Method for Image and Video Completion

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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.

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Acknowledgements

The authors would like to thank the editor and anonymous referees for their valuable suggestions and constructive comments which improved the quality of the paper.

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Authors and Affiliations

  1. Faculté des Sciences et Techniques-Gueliz, Laboratoire de Mathématiques Appliquées, Marrakech, Morocco

    A. H. Bentbib

  2. Laboratory MSDA, Mohammed VI Polytechnic University, Green City, Morocco

    A. El Hachimi, K. Jbilou & A. Ratnani

  3. LMPA, Université du Littoral Cote d’Opale, 50 Rue F. Buisson, 62228, Calais-Cedex, France

    K. Jbilou

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  1. A. H. Bentbib
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  2. A. El Hachimi
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  3. K. Jbilou
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Correspondence to K. Jbilou.

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Communicated by Xiaojun Chen.

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Bentbib, A.H., Hachimi, A.E., Jbilou, K. et al. A Tensor Regularized Nuclear Norm Method for Image and Video Completion. J Optim Theory Appl 192, 401–425 (2022). https://doi.org/10.1007/s10957-021-01947-3

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  • DOI: https://doi.org/10.1007/s10957-021-01947-3

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