# Difference between revisions of "Publications/darbon.06.jmiv"

### From LRDE

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| pages = 261 to 276 |
| pages = 261 to 276 |
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| lrdeprojects = Olena |
| lrdeprojects = Olena |
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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 L^1 data fidelity term yields a self-dual contrast invariant filter. Finally we present some results. |
+ | | 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 <math>L^1</math> data fidelity term yields a self-dual contrast invariant filter. Finally we present some results. |

| lrdekeywords = Image |
| lrdekeywords = Image |
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| lrdenewsdate = 2006-03-24 |
| lrdenewsdate = 2006-03-24 |

## Revision as of 19:20, 5 January 2018

- 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 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.} }