# A Fast and Exact Algorithm for Total Variation Minimization

## 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)

```@InProceedings{	  darbon.05.ibpria,
author	= {J\'er\^ome Darbon and Marc Sigelle},
title		= {A Fast and Exact Algorithm for Total Variation
Minimization},
booktitle	= {Proceedings of the 2nd Iberian Conference on Pattern
Recognition and Image Analysis (IbPRIA)},
publisher	= {Springer-Verlag},
volume	= 3522,
pages		= {351--359},
year		= 2005,