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A Fast Image Restoration Algorithm Based on a Fixed Point and Optimization Method

Author

Listed:
  • Adisak Hanjing

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

  • Suthep Suantai

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

Abstract

In this paper, a new accelerated fixed point algorithm for solving a common fixed point of a family of nonexpansive operators is introduced and studied, and then a weak convergence result and the convergence behavior of the proposed method is proven and discussed. Using our main result, we obtain a new accelerated image restoration algorithm, called the forward-backward modified W-algorithm (FBMWA), for solving a minimization problem in the form of the sum of two proper lower semi-continuous and convex functions. As applications, we apply the FBMWA algorithm to solving image restoration problems. We analyze and compare convergence behavior of our method with the others for deblurring the image. We found that our algorithm has a higher efficiency than the others in the literature.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:378-:d:329953
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    References listed on IDEAS

    as
    1. Suthep Suantai & Suparat Kesornprom & Prasit Cholamjiak, 2019. "Modified Proximal Algorithms for Finding Solutions of the Split Variational Inclusions," Mathematics, MDPI, vol. 7(8), pages 1-17, August.
    2. Suthep Suantai & Nontawat Eiamniran & Nattawut Pholasa & Prasit Cholamjiak, 2019. "Three-Step Projective Methods for Solving the Split Feasibility Problems," Mathematics, MDPI, vol. 7(8), pages 1-15, August.
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    Citations

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    Cited by:

    1. Nattakarn Kaewyong & Kanokwan Sitthithakerngkiet, 2021. "Modified Tseng’s Method with Inertial Viscosity Type for Solving Inclusion Problems and Its Application to Image Restoration Problems," Mathematics, MDPI, vol. 9(10), pages 1-15, May.
    2. 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.
    3. Suthep Suantai & Suparat Kesornprom & Watcharaporn Cholamjiak & Prasit Cholamjiak, 2022. "Modified Projection Method with Inertial Technique and Hybrid Stepsize for the Split Feasibility Problem," Mathematics, MDPI, vol. 10(6), pages 1-12, March.
    4. Panadda Thongpaen & Rattanakorn Wattanataweekul, 2021. "A Fast Fixed-Point Algorithm for Convex Minimization Problems and Its Application in Image Restoration Problems," Mathematics, MDPI, vol. 9(20), pages 1-13, October.
    5. Dawan Chumpungam & Panitarn Sarnmeta & Suthep Suantai, 2022. "An Accelerated Convex Optimization Algorithm with Line Search and Applications in Machine Learning," Mathematics, MDPI, vol. 10(9), pages 1-20, April.
    6. Dawan Chumpungam & Panitarn Sarnmeta & Suthep Suantai, 2021. "A New Forward–Backward Algorithm with Line Searchand Inertial Techniques for Convex Minimization Problems with Applications," Mathematics, MDPI, vol. 9(13), pages 1-20, July.

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