Image Restoration with Discrete Constrained Total Variation Part I: Fast and Exact Optimization

Abstract

Abstract. This paper deals with the total variation minimization problem in image restoration for convex data fidelity functionals. We propose a new and fast algorithm which computes an exact solution in the discrete framework. Our method relies on the decomposition of an image into its level sets. It maps the original problems into independent binary Markov Random Field optimization problems at each level. Exact solutions of these binary problems are found thanks to minimum cost cut techniques in graphs. These binary solutions are proved to be monotone increasing with levels and yield thus an exact solution of the discrete original problem. Furthermore we show that minimization of total variation under L 1 data fidelity term yields a self-dual contrast invariant filter. Finally we present some results.

Copula density estimation by total variation penalized likelihood with linear equality constraints

“…They include the latest graph-cut/max-flow algorithms (Chambolle (2005), Darbon and Sigelle (2006), Goldfarb and Yin (2009)). We use the parametric max-flow code from Yin (2010).…”

Enhancement of historical printed document images by combining Total Variation regularization and Non-local Means filtering

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“…The main characteristics of the TV prior is that the solution lives in the space of functions of Bounded Variation that allows for sharp edges and discontinuities. We follow [13] and define TV as the l 1 -norm of a discrete gradient. More formally we have…”

An Augmented Lagrangian Method for TV g +L 1-norm Minimization

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