iPiano: Inertial Proximal Algorithm for Non-Convex Optimization

Peter Ochs, Yunjin Chen, Thomas Brox, Thomas Pock

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we study an algorithm for solving a minimization problem composed of a differentiable (possibly nonconvex) and a convex (possibly nondifferentiable) function. The algorithm iPiano combines forward-backward splitting with an inertial force. It can be seen as a nonsmooth 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 nonconvex problems. The convergence result is obtained based on the Kurdyka--Łojasiewicz 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.
Original languageEnglish
Pages (from-to)1388-1419
JournalSIAM Journal on Imaging Sciences
Volume7
Issue number2
DOIs
Publication statusPublished - 2014

Fields of Expertise

  • Information, Communication & Computing

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