Image Decomposition into a Bounded Variation Component and an Oscillating Component

Authors:
Jean-François Aujol;Gilles Aubert;Laure Blanc-Féraud;Antonin Chambolle
Affiliations:
Aff1 Aff2 Aff6;Laboratoire J.A. Dieudonné, UMR CNRS 6621, Université de Nice Sophia-Antipolis, Nice Cedex 2, France 06108;ARIANA, Projet Commun CNRS/INRIA/UNSA, INRIA Sophia Antipolis, Sophia Antipolis Cedex, France 06902;CEREMADE, UMR CNRS 7534, Université Paris - Dauphine, Paris Cedex 16, France 75775
Venue:
Journal of Mathematical Imaging and Vision
Year:
2005

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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.