A primal-dual line search method and applications in image processing

Operator splitting algorithms are enjoying wide acceptance in signal processing for their ability to solve generic convex optimization problems exploiting their structure and leading to efficient implementations. These algorithms are instances of the Krasnosel'skil-Mann scheme for finding fixed points of averaged operators. Despite their popularity, however, operator splitting algorithms are sensitive to ill conditioning and often converge slowly. In this paper we propose a line search primal-dual method to accelerate and robustify the Chambolle-Pock algorithm based on SuperMann: a recent extension of the Kras-nosel'skil-Mann algorithmic scheme. We discuss the convergence properties of this new algorithm and we showcase its strengths on the problem of image denoising using the anisotropic total variation regularization.