Mathematics (Apr 2023)

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

  • Kamonrat Sombut,
  • Kanokwan Sitthithakerngkiet,
  • Areerat Arunchai,
  • Thidaporn Seangwattana

DOI
https://doi.org/10.3390/math11092107
Journal volume & issue
Vol. 11, no. 9
p. 2107

Abstract

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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.

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