Inertial self‐adaptive algorithm for solving split feasible problems with applications to image restoration

Abstract

We introduce a new self-adaptive algorithm for applications to image restoration problems. In order to study an image restoration, we consider the algorithm that contains inertial effects and step sizes, which is independent from the norm of the bounded linear operator. With some control conditions, the strong convergence to the minimum norm solution of the algorithm is obtained. Convergence analysis of the proposed algorithm is also discussed. Moreover, numerical results of image restoration problems illustrate that the proposed algorithm is efficient and outperforms other ones. KEYWORDSdemicontractive operator, image restoration problem, inertial algorithm, self-adaptive algorithm MSC CLASSIFICATION 47J25; 65K10wherex is an original image, y is the observed image, A is a blurring matrix, and is a noise term.The split common fixed point problem has received much attention due to its applications in image reconstruction, signal processing, intensity-modulated radiation therapy, computed tomography, control theory, approximation theory, Math Meth Appl Sci. 2019;42:7268-7284.

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