  In this paper we study an algorithm for solving a minimization problem
composed of a differentiable (possibly non-convex) and a convex (possibly
non-differentiable) function. The algorithm iPiano combines forward-backward
splitting with an inertial force. It can be seen as a non-smooth split version
of the Heavy-ball method from Polyak. A rigorous analysis of the algorithm for
the proposed class of problems yields global convergence of the function values
and the arguments. This makes the algorithm robust for usage on non-convex
problems. The convergence result is obtained based on the \KL inequality. This
is a very weak restriction, which was used to prove convergence for several
other gradient methods. First, an abstract convergence theorem for a generic
algorithm is proved, and, then iPiano is shown to satisfy the requirements of
this theorem. Furthermore, a convergence rate is established for the general
problem class. We demonstrate iPiano on computer vision problems: image
denoising with learned priors and diffusion based image compression.
