An algorithm for the split feasible problem and image restoration

Abstract

© 2020, The Royal Academy of Sciences, Madrid. This paper proposes an accelerated algorithm for the split common fixed point problem, based on viscosity approximation methods and inertial effects. The main result will be applied to image restoration problems. This algorithm is constructed in such a way that its step sizes and the norm of a given linear operator are not related. Under some conditions, the strong convergence of the algorithm is obtained. Numerical investigations are carried out in order to illustrate high-performance of the present work, mainly using processing duration and the signal-to-noise ratio. It is also shown that this proposed algorithm is more efficient and effective than the published algorithm by Yao et al.