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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Vydáno v:Soft computing (Berlin, Germany) Ročník 27; číslo 22; s. 16571 - 16587
Hlavní autoři: Izuchukwu, Chinedu, Shehu, Yekini, Reich, Simeon
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2023
Springer Nature B.V
Témata:
Artificial Intelligence
Computational Intelligence
Control
Engineering
Hilbert space
Image restoration
Iterative methods
Mathematical Logic and Foundations
Mechatronics
Methods
Optimization
Robotics
Weak convergence
Douglas–Rachford splitting
Image Restoration
Hilbert space
Inertial Krasnosel’skiĭ-Mann method
ISSN:1432-7643, 1433-7479
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Shrnutí: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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ISSN:1432-7643
1433-7479
DOI:10.1007/s00500-023-08921-3