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Modified inertial algorithms for inclusion problems with numerical experiments and application to image restoration

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Abstract

In this paper, we introduce two modified algorithms based on the inertial forward–backward method to find the common solution of an inclusion problem and a fixed point problem of a nonexpansive mapping in real Hilbert space. We prove some weak and strong convergence theorems of the modified inertial algorithms under standard conditions. We also give some numerical examples in both finite and infinite real Hilbert spaces to demonstrate the computational performance and advantage of our modified algorithms over other related works. In addition, we apply our algorithms to solve the image restoration problems and we present the quality of image recovery by structural similarity index to show efficiency of our proposed algorithms in comparison with other related ones.

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Acknowledgements

This research was supported by Kasetsart University Research and Development Institute, KURDI with Contract no. YF(KU)7.65. The third author would like to thank Kasetsart University Research and Development Institute, KURDI, and Department of Mathematics, Statistics, and Computer, Faculty of Liberal Arts and Science, Kasetsart University, Kampaeng Saen for their financial support that facilitated the success of this research.

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Authors and Affiliations

  1. Department of Science, Faculty of Science and Agriculture, Rajamangala University of Technology Lanna, Chiangrai Campus, Chiangrai, 57120, Thailand

    Thanyarat Jitpeera

  2. Department of Computational Science and Digital Technology, Faculty of Liberal Arts and Sciences, Kasetsart University, Kamphaeng-Saen Campus, Nakhonpathom, 73140, Thailand

    Chirasak Mongkolkeha & Thanittha Kowan

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  1. Thanyarat Jitpeera
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  2. Chirasak Mongkolkeha
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  3. Thanittha Kowan
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Correspondence to Chirasak Mongkolkeha or Thanittha Kowan.

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Jitpeera, T., Mongkolkeha, C. & Kowan, T. Modified inertial algorithms for inclusion problems with numerical experiments and application to image restoration. Comp. Appl. Math. 42, 325 (2023). https://doi.org/10.1007/s40314-023-02469-6

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  • DOI: https://doi.org/10.1007/s40314-023-02469-6

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