# Difference between revisions of "Publications/darbon.05.tr"

## Abstract

This paper deals with the minimization of the total variation under a convex data fidelity term. We propose an algorithm which computes an exact minimizer of this problem. The method relies on the decomposition of an image into its level sets. Using these level sets, we map the problem into optimizations of independent binary Markov Random Fields. Binary solutions are found thanks to graph-cut techniques and we show how to derive a fast algorithm. We also study the special case when the fidelity term is the ${\displaystyle L^{1}}$-norm. Finally we provide some experiments.

## Bibtex (lrde.bib)

```@TechReport{	  darbon.05.tr,
author	= {J\'er\^ome Darbon and Marc Sigelle},
title		= {A fast and exact algorithm for total variation
minimization},
institution	= {ENST},
year		= 2005,
number	= {2005D002},
month		= jan,
annote	= {This technical report corresponds to the publication
darbon.05.ibpria.},
abstract	= {This paper deals with the minimization of the total
variation under a convex data fidelity term. We propose an
algorithm which computes an exact minimizer of this
problem. The method relies on the decomposition of an image
into its level sets. Using these level sets, we map the
problem into optimizations of independent binary Markov
Random Fields. Binary solutions are found thanks to
graph-cut techniques and we show how to derive a fast
algorithm. We also study the special case when the fidelity
term is the \$L^1\$-norm. Finally we provide some
experiments.}
}```