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Image decomposition into a bounded variation component and an oscillating component

Chambolle, Antonin; Blanc Feraud, Laure; Aujol, Jean-François; Aubert, Gilles (2005), Image decomposition into a bounded variation component and an oscillating component, Journal of Mathematical Imaging and Vision, 22, 1, p. 71-88. http://dx.doi.org/10.1007/s10851-005-4783-8

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Type
Article accepté pour publication ou publié
Date
2005
Journal name
Journal of Mathematical Imaging and Vision
Volume
22
Number
1
Publisher
Springer Netherlands
Pages
71-88
Publication identifier
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Author(s)
Chambolle, Antonin cc
Blanc Feraud, Laure cc
Aujol, Jean-François
Aubert, Gilles
Abstract (EN)
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 froma 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.
Subjects / Keywords
Total variation minimization; BV; Texture; Restoration; SAR images; Speckle