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An Accelerated Tensorial Double Proximal Gradient Method for Total Variation Regularization Problem

Author

Listed:
  • Oumaima Benchettou

    (University Cadi Ayyad
    University Littoral, Côte d’Opale)

  • Abdeslem Hafid Bentbib

    (University Cadi Ayyad)

  • Abderrahman Bouhamidi

    (University Littoral, Côte d’Opale)

Abstract

We consider the constrained tensorial total variation minimization problem for regularizing ill-posed multidimensional problems arising in many fields, such as image and video processing and multidimensional data completion. The nonlinearity and the non-differentiability of the total variation minimization problem make the resolution directly more complex. The aim of the present paper is to bring together the resolution of this problem using an iterative tensorial double proximal gradient algorithm and the acceleration of the convergence rate by updating some efficient extrapolation techniques in the tensor form. The general structure of the proposed method expands its fields of application. We will restrict our numerical application to the multidimensional data completion which illustrates the effectiveness of the proposed algorithm.

Suggested Citation

  • Oumaima Benchettou & Abdeslem Hafid Bentbib & Abderrahman Bouhamidi, 2023. "An Accelerated Tensorial Double Proximal Gradient Method for Total Variation Regularization Problem," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 111-134, July.
    • Handle: RePEc:spr:joptap:v:198:y:2023:i:1:d:10.1007_s10957-023-02234-z
    DOI: 10.1007/s10957-023-02234-z
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    References listed on IDEAS

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    1. Abderrahman Bouhamidi & Mohammed Bellalij & Rentsen Enkhbat & Khalid Jbilou & Marcos Raydan, 2018. "Conditional Gradient Method for Double-Convex Fractional Programming Matrix Problems," Journal of Optimization Theory and Applications, Springer, vol. 176(1), pages 163-177, January.
    2. Alaa El Ichi & Khalide Jbilou & Rachid Sadaka, 2020. "Tensor Global Extrapolation Methods Using the n-Mode and the Einstein Products," Mathematics, MDPI, vol. 8(8), pages 1-14, August.
    3. Patrick L. Combettes & Jean-Christophe Pesquet, 2011. "Proximal Splitting Methods in Signal Processing," Springer Optimization and Its Applications, in: Heinz H. Bauschke & Regina S. Burachik & Patrick L. Combettes & Veit Elser & D. Russell Luke & Henry (ed.), Fixed-Point Algorithms for Inverse Problems in Science and Engineering, chapter 0, pages 185-212, Springer.
    4. NESTEROV, Yurii, 2013. "Gradient methods for minimizing composite functions," LIDAM Reprints CORE 2510, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Williams López & Marcos Raydan, 2016. "An acceleration scheme for Dykstra’s algorithm," Computational Optimization and Applications, Springer, vol. 63(1), pages 29-44, January.
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