  Finding a zero of the sum of two monotone operators is one of the most
important problems in monotone operator theory, and the forward-backward
algorithm is the most prominent approach for solving this type of problem. The
aim of this paper is to present a new preconditioning forward-backward
algorithm to obtain the zero of the sum of two operators in which one is
maximal monoton and the other one is M-cocoercive, where M is a linear bounded
operator. Furthermore, the strong convergence of the proposed algorithm, which
is a broader variant of previously known algorithms, has been proven in Hilbert
spaces. We also use our algorithm to tackle the convex minimization problem and
show that it outperforms existing algorithms. Finally, we discuss several image
restoration applications.
