Image restoration by using a modified proximal point algorithm

Areerat Arunchai; Thidaporn Seangwattana; Kanokwan Sitthithakerngkiet; Kamonrat Sombut; Areerat Arunchai; Thidaporn Seangwattana; Kanokwan Sitthithakerngkiet; Kamonrat Sombut

doi:10.3934/math.2023482

AIMS Mathematics

2023, Volume 8, Issue 4: 9557-9575. doi: 10.3934/math.2023482

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Image restoration by using a modified proximal point algorithm

1.
Department of Mathematics and Statistics, Faculty of Science and Technology, Nakhon Sawan Rajabhat University, 60000, Nakhon Sawan, Thailand
2.
Faculty of Science Energy and Environment, King Mongkut's University of Technology North Bangkok, Rayong Campus (KMUTNB), 21120, Rayong, Thailand
3.
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
4.
Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), 12110, Pathum Thani, Thailand
5.
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

Received: 20 September 2022 Revised: 13 February 2023 Accepted: 14 February 2023 Published: 20 February 2023
MSC : 37N40, 49J40

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.
- convex minimization,
- image restoration,
- optimization,
- proximal point algorithm,
- variational inclusion problem
Citation: Areerat Arunchai, Thidaporn Seangwattana, Kanokwan Sitthithakerngkiet, Kamonrat Sombut. Image restoration by using a modified proximal point algorithm[J]. AIMS Mathematics, 2023, 8(4): 9557-9575. doi: 10.3934/math.2023482

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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.

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