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An inertial-type method for solving image restoration problems

  • Optimization
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Abstract

We first establish weak convergence results regarding an inertial Krasnosel’skiĭ-Mann iterative method for approximating common fixed points of countable families of nonexpansive mappings in real Hilbert spaces with no extra assumptions on the considered countable families of nonexpansive mappings. The method of proof and the imposed conditions on the iterative parameters are different from those already available in the literature. We then present some applications to the Douglas–Rachford splitting method and image restoration problems, and compare the performance of our method with that of other popular inertial Krasnosel’skiĭ-Mann methods which can be found in the literature.

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Acknowledgements

The authors are very grateful to the editor and anonymous referees whose insightful comments and suggestions have helped them to substantially improve an earlier version of this paper.

Funding

Simeon Reich was partially supported by the Israel Science Foundation (Grant 820/17), by the Fund for the Promotion of Research at the Technion (Grant 2001893) and by the Technion General Research Fund (Grant 2016723).

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Authors and Affiliations

  1. School of Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg, 2050, South Africa

    Chinedu Izuchukwu

  2. School of Mathematical Sciences, Zhejiang Normal University, Jinhua, 321004, People’s Republic of China

    Yekini Shehu

  3. Department of Mathematics, The Technion – Israel Institute of Technology, 3200003, Haifa, Israel

    Simeon Reich

Authors
  1. Chinedu Izuchukwu
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  2. Yekini Shehu
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  3. Simeon Reich
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All the authors contributed equally to the final version of the manuscript.

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Correspondence to Yekini Shehu.

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Izuchukwu, C., Shehu, Y. & Reich, S. An inertial-type method for solving image restoration problems. Soft Comput 27, 16571–16587 (2023). https://doi.org/10.1007/s00500-023-08921-3

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