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Research Article | Open Access

Image restoration by using a modified proximal point algorithm

Areerat Arunchai1, Thidaporn Seangwattana2,5, Kanokwan Sitthithakerngkiet3,5, Kamonrat Sombut4,5( )
Department of Mathematics and Statistics, Faculty of Science and Technology, Nakhon Sawan Rajabhat University, 60000, Nakhon Sawan, Thailand
Faculty of Science Energy and Environment, King Mongkut's University of Technology North Bangkok, Rayong Campus (KMUTNB), 21120, Rayong, Thailand
Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics Faculty of Applied Science, King Mongkut's University of Technology North Bangkok (KMUTNB), 10800, Bangkok, Thailand
Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), 12110, Pathum Thani, Thailand
Applied Mathematics for Science and Engineering Research Unit (AMSERU), Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), 12110, Rungsit-Nakorn Nayok Rd., Klong 6, Khlong Luang, Thanyaburi, Pathum thani, Thailand
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Abstract

In this paper, we establish a modified proximal point algorithm for solving the common problem between convex constrained minimization and modified variational inclusion problems. The proposed algorithm base on the proximal point algorithm in [19] and the method of Khuangsatung and Kangtunyakarn in [21] by using suitable conditions in Hilbert spaces. The proposed algorithm is not only presented in this article; however has also been demonstrated to generate a robust convergence theorem. The proposed algorithm could be used to solve image restoration problems where the images have suffered a variety of blurring operations. Additionally, we contrast the signal-to-noise ratio (SNR) of the proposed algorithm against that of Khuangsatung and Kangtunyakarn's method in [21] in order to compare image quality.

Keywords

convex minimizationimage restorationoptimizationproximal point algorithmvariational inclusion problem
CLC number: 37N40, 49J40

References

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AIMS Mathematics
Volume 8 Issue 4,
April 2023
Pages 9557-9575
DOI: 10.3934/math.2023482

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Cite this article:
Arunchai A, Seangwattana T, Sitthithakerngkiet K, et al. Image restoration by using a modified proximal point algorithm. AIMS Mathematics, 2023, 8(4): 9557-9575. https://doi.org/10.3934/math.2023482

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Received: 20 September 2022
Revised: 13 February 2023
Accepted: 14 February 2023
Published: 15 April 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)