A fast and exact algorithm for total variation minimization

Authors

Jérôme Darbon, Marc Sigelle

Place

Paris, France

Type

techreport

Projects

Olena

Keywords

Image

Date

2005-01-01

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.

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},
  address	= {Paris, France},
  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.}
}