# Image decomposition into a bounded variation component and an oscillating component

Abstract : We construct an algorithm to split an image into a sum $u+v$ of a bounded variation component and a component containing the textures and the noise. This decomposition is inspired from a recent work of Y. Meyer. We find this decomposition by minimizing a convex functional which depends on the two variables u and v, alternately in each variable. Each minimization is based on a projection algorithm to minimize the total variation. We carry out the mathematical study of our method. We present some numerical results. In particular, we show how the u component can be used in nontextured SAR image restoration.
Type de document :
Article dans une revue
Journal of Mathematical Imaging and Vision, Springer Verlag, 2005, 22 (1), p. 71-88
Domaine :

https://hal.archives-ouvertes.fr/hal-00202001
Contributeur : Jean-François Aujol <>
Soumis le : jeudi 3 janvier 2008 - 17:47:34
Dernière modification le : jeudi 7 février 2019 - 16:02:33

### Identifiants

• HAL Id : hal-00202001, version 1

### Citation

Jean-François Aujol, Gilles Aubert, Laure Blanc-Féraud, Antonin Chambolle. Image decomposition into a bounded variation component and an oscillating component. Journal of Mathematical Imaging and Vision, Springer Verlag, 2005, 22 (1), p. 71-88. 〈hal-00202001〉

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