A relaxed inertial and viscosity method for split feasibility problem and applications to image recovery

In this paper, by combining Polyak's inertial extrapolation technique for minimization problem with the viscosity approximation for fixed point problem, we develop a new type of numerical solution method for split feasibility problem. Under suitable assumptions, we establish the global convergence of the designed method. The given experimental results applied on the sparse reconstruction problem show that the proposed algorithm is not only robust to different levels of sparsity and amplitude of signals and the noise pixels but also insensitive to the diverse values of scalar weight. Further, the proposed algorithm achieves better restoration performance compared with some other algorithms for image recovery.