Convergence Analysis of a Modified Forward-Backward Splitting Algorithm for Minimization and Application to Image Recovery

Many applications in applied sciences and engineering can be considered as the convex minimization problem with the sum of two functions. One of the most popular techniques to solve this problem is the forward-backward algorithm. In this work, we aim to present a new version of splitting algorithms by adapting with Tseng’s extragradient method and using the linesearch technique with inertial conditions. We obtain its convergence result under mild assumptions. Moreover, as applications, we provide numerical experiments to solve image recovery problem. We also compare our algorithm and demonstrate the efficiency to some known algorithms.