An Inertial Forward–Backward Splitting Method for Solving Modified Variational Inclusion Problems and Its Application

Kamonrat Sombut, Kanokwan Sitthithakerngkiet, Areerat Arunchai and Thidaporn Seangwattana ()
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Kamonrat Sombut: Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Pathum Thani 12110, Thailand
Kanokwan Sitthithakerngkiet: 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), 39 Rungsit-Nakorn Nayok Rd., Klong 6, Khlong Luang, Thanyaburi, Pathum Thani 12110, Thailand
Areerat Arunchai: Department of Mathematics and Statistics, Faculty of Science and Technology Nakhon Sawan, Rajabhat University, Nakhon Sawan 60000, Thailand
Thidaporn Seangwattana: 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), 39 Rungsit-Nakorn Nayok Rd., Klong 6, Khlong Luang, Thanyaburi, Pathum Thani 12110, Thailand

Mathematics, 2023, vol. 11, issue 9, 1-16

Abstract: In this paper, we propose an inertial forward–backward splitting method for solving the modified variational inclusion problem. The concept of the proposed method is based on Cholamjiak’s method. and Khuangsatung and Kangtunyakarn’s method. Cholamjiak’s inertial technique is utilized in the proposed method for increased acceleration. Moreover, we demonstrate that the proposed method strongly converges under appropriate conditions and apply the proposed method to solve the image restoration problem where the images have been subjected to various obscuring processes. In our example, we use the proposed method and Khuangsatung and Kangtunyakarn’s method to restore two medical images. To compare image quality, we also evaluate the signal-to-noise ratio (SNR) of the proposed method to that of Khuangsatung and Kangtunyakarn’s method.

Keywords: inertial technique; variational inclusion problem; forward–backward splitting method; fixed point problem; image restoration (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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