Image restoration with discrete constrained Total Variation—Part I: Fast and exact optimization

From LRDE

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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 ${\displaystyle L^{1}}$ data fidelity term yields a self-dual contrast invariant filter. Finally we present some results.

Bibtex (lrde.bib)

```@Article{	  darbon.06.jmiv,
author	= {J\'er\^ome Darbon and Marc Sigelle},
title		= {Image restoration with discrete constrained {T}otal
{Variation}---Part~{I}: Fast and exact optimization},
journal	= {Journal of Mathematical Imaging and Vision},
year		= 2006,
volume	= 26,
number	= 3,
month		= dec,
pages		= {261--276},
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.}
}```