Convergence of an inertial reflected-forward-backward splitting algorithm for solving monotone inclusion problems with application to image recovery

We first propose a reflected-forward-backward splitting algorithm with two inertial effects for solving monotone inclusions and then establish that the sequence of iterates it generates converges weakly in a real Hilbert space to a zero of the sum of a set-valued maximal monotone operator and a single-valued monotone Lipschitz continuous operator. The proposed algorithm involves only one forward evaluation of the single-valued operator and one backward evaluation of the set-valued operator at each iteration. One inertial parameter is non-negative while the other is non-positive. These features are absent in many other available inertial splitting algorithms in the literature. Finally, we discuss some problems in image restoration in connection with the implementation of our algorithm and compare it with some known related algorithms in the literature.