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A New Accelerated Viscosity Iterative Method for an Infinite Family of Nonexpansive Mappings with Applications to Image Restoration Problems

Author

Listed:
  • Jenwit Puangpee

    (PhD Degree Program in 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

The image restoration problem is one of the popular topics in image processing which is extensively studied by many authors because of its applications in various areas of science, engineering and medical image. The main aim of this paper is to introduce a new accelerated fixed algorithm using viscosity approximation technique with inertial effect for finding a common fixed point of an infinite family of nonexpansive mappings in a Hilbert space and prove a strong convergence result of the proposed method under some suitable control conditions. As an application, we apply our algorithm to solving image restoration problem and compare the efficiency of our algorithm with FISTA method which is a popular algorithm for image restoration. By numerical experiments, it is shown that our algorithm has more efficiency than that of FISTA.

Suggested Citation

  • Jenwit Puangpee & Suthep Suantai, 2020. "A New Accelerated Viscosity Iterative Method for an Infinite Family of Nonexpansive Mappings with Applications to Image Restoration Problems," Mathematics, MDPI, vol. 8(4), pages 1-20, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:615-:d:346513
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    References listed on IDEAS

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    1. Genaro López & Victoria Martín-Márquez & Fenghui Wang & Hong-Kun Xu, 2012. "Forward-Backward Splitting Methods for Accretive Operators in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-25, July.
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    Cited by:

    1. Piti Thongsri & Bancha Panyanak & Suthep Suantai, 2023. "A New Accelerated Algorithm Based on Fixed Point Method for Convex Bilevel Optimization Problems with Applications," Mathematics, MDPI, vol. 11(3), pages 1-15, January.

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