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

Authors

Jérôme Darbon, Marc Sigelle

Journal

Journal of Mathematical Imaging and Vision

Type

article

Projects

Olena

Keywords

Image

Date

2006-03-24

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.

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.}
}