Strong convergence analysis of common variational inclusion problems involving an inertial parallel monotone hybrid method for a novel application to image restoration

In this paper, we propose inertial forward-backward splitting algorithm to approximate the solution of common variational inclusion problems. By using the inertial technique with parallel monotone hybrid methods we prove strong convergence results under some suitable conditions in Hilbert spaces. We then give some applications and numerical experiments for supporting our main results which shows that our proposed inertial hybrid method has better convergence rate than existing algorithms. Further, we apply our result to solve a common convex minimization problem and a common split feasibility problem. Finally, we use our proposed algorithm to solve the unconstrained image restoration problems and we can show that our algorithm is flexibility and good quality to use for common types of blur effects.