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A Projected Forward-Backward Algorithm for Constrained Minimization with Applications to Image Inpainting

Author

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  • Suthep Suantai

    (Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Kunrada Kankam

    (School of Science, University of Phayao, Phayao 56000, Thailand)

  • Prasit Cholamjiak

    (School of Science, University of Phayao, Phayao 56000, Thailand)

Abstract

In this research, we study the convex minimization problem in the form of the sum of two proper, lower-semicontinuous, and convex functions. We introduce a new projected forward-backward algorithm using linesearch and inertial techniques. We then establish a weak convergence theorem under mild conditions. It is known that image processing such as inpainting problems can be modeled as the constrained minimization problem of the sum of convex functions. In this connection, we aim to apply the suggested method for solving image inpainting. We also give some comparisons to other methods in the literature. It is shown that the proposed algorithm outperforms others in terms of iterations. Finally, we give an analysis on parameters that are assumed in our hypothesis.

Suggested Citation

  • Suthep Suantai & Kunrada Kankam & Prasit Cholamjiak, 2021. "A Projected Forward-Backward Algorithm for Constrained Minimization with Applications to Image Inpainting," Mathematics, MDPI, vol. 9(8), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:8:p:890-:d:537799
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    References listed on IDEAS

    as
    1. Hong-Kun Xu, 2011. "Averaged Mappings and the Gradient-Projection Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 360-378, August.
    2. Alfredo N. Iusem & B. F. Svaiter & Marc Teboulle, 1994. "Entropy-Like Proximal Methods in Convex Programming," Mathematics of Operations Research, INFORMS, vol. 19(4), pages 790-814, November.
    3. Adisak Hanjing & Suthep Suantai, 2020. "A Fast Image Restoration Algorithm Based on a Fixed Point and Optimization Method," Mathematics, MDPI, vol. 8(3), pages 1-13, March.
    4. Regina S. Burachik & Alfredo N. Iusem, 2008. "Enlargements of Monotone Operators," Springer Optimization and Its Applications, in: Set-Valued Mappings and Enlargements of Monotone Operators, chapter 0, pages 161-220, Springer.
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