An inertial-type method for solving image restoration problems
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....
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| Veröffentlicht in: | Soft computing (Berlin, Germany) Jg. 27; H. 22; S. 16571 - 16587 |
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| Sprache: | Englisch |
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01.11.2023
Springer Nature B.V |
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| ISSN: | 1432-7643, 1433-7479 |
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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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| AbstractList | 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. |
| Author | Izuchukwu, Chinedu Reich, Simeon Shehu, Yekini |
| Author_xml | – sequence: 1 givenname: Chinedu surname: Izuchukwu fullname: Izuchukwu, Chinedu organization: School of Mathematics, University of the Witwatersrand – sequence: 2 givenname: Yekini orcidid: 0000-0001-9224-7139 surname: Shehu fullname: Shehu, Yekini email: yekini.shehu@zjnu.edu.cn organization: School of Mathematical Sciences, Zhejiang Normal University – sequence: 3 givenname: Simeon orcidid: 0000-0003-0780-1559 surname: Reich fullname: Reich, Simeon organization: Department of Mathematics, The Technion – Israel Institute of Technology |
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| Keywords | Weak convergence Douglas–Rachford splitting Image Restoration Hilbert space Inertial Krasnosel’skiĭ-Mann method |
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