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Open AccessArticle

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

1
PhD Degree Program in Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
2
Data Science Research Center, Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(4), 615; https://doi.org/10.3390/math8040615
Received: 16 March 2020 / Revised: 5 April 2020 / Accepted: 9 April 2020 / Published: 16 April 2020
(This article belongs to the Special Issue Mathematical Methods in Images and Signals Processing)
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. View Full-Text
Keywords: image restoration problem; viscosity; inertial; nonexpansive mapping image restoration problem; viscosity; inertial; nonexpansive mapping
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Puangpee, J.; Suantai, S. A New Accelerated Viscosity Iterative Method for an Infinite Family of Nonexpansive Mappings with Applications to Image Restoration Problems. Mathematics 2020, 8, 615.

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