2014/04/18 by Peter Ochs, Yunjin Chen, Ochs, Peter +5 · 9 citations
Computer Science · Mathematics · #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Mathematics #Optimization and Control (math.OC) #cs.CV #math.OC
paper · pdf · doi:10.48550/arxiv.1404.4805
32pages, 7 figures, to appear in SIAM Journal on Imaging Sciences
arxiv created 2014/04/18 · arxiv updated 2014/04/21
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.