A modified inertial Tseng’s algorithm with adaptive parameters for solving monotone inclusion problems with efficient applications to image deblurring problems

Abstract

In this paper, we have found a method to make use of some adaptive step size parameters to increase the algorithm’s efficiency and produce superior numerical results. We introduce and study a modified inertial Tseng’s algorithm with adaptive terms for solving the sum of two monotone inclusion problems in order to result in effective applications to solve image deblur‑ ring problems in the framework of realHilbert spaces. We achieve weak convergence to a zero point of the sum of two monotone operators by restricting the scalar control conditions, utilizing certain monotone operator properties, and using the identity associated with the norm square. Furthermore, a novel suggested algorithm is applied to image deblurring problems as part of the applications of this recently obtained theoretical knowledge. To illustrate the strong points and benefits of this recently suggested algorithm, we express some advantages in numerical tests on the signal‑to‑noise ratio (ISNR) and structural similarity index measure (SSIM) comparing with some previous related methods.