# 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.
Document type :
Journal articles
Domain :

https://hal.archives-ouvertes.fr/hal-00202001
Contributor : Jean-François Aujol Connect in order to contact the contributor
Submitted on : Thursday, January 3, 2008 - 5:47:34 PM
Last modification on : Thursday, August 4, 2022 - 5:05:30 PM

### Identifiers

• 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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