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

Jenwit Puangpee and Suthep Suantai
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Jenwit Puangpee: PhD Degree Program in Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
Suthep Suantai: Data Science Research Center, Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Mathematics, 2020, vol. 8, issue 4, 1-20

Abstract: 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.

Keywords: image restoration problem; viscosity; inertial; nonexpansive mapping (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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