Journal of Mathematical Imaging and Vision

, Volume 22, Issue 1, pp 71–88

Image Decomposition into a Bounded Variation Component and an Oscillating Component

Authors

    • Laboratoire J.A. Dieudonné, UMR CNRS 6621Université de Nice Sophia-Antipolis
    • ARIANA, Projet Commun CNRS/INRIA/UNSAINRIA Sophia Antipolis
    • UCLA Department of Mathematics
  • Gilles Aubert
    • Laboratoire J.A. Dieudonné, UMR CNRS 6621Université de Nice Sophia-Antipolis
  • Laure Blanc-Féraud
    • ARIANA, Projet Commun CNRS/INRIA/UNSAINRIA Sophia Antipolis
  • Antonin Chambolle
    • CEREMADE, UMR CNRS 7534Université Paris - Dauphine
Article

DOI: 10.1007/s10851-005-4783-8

Cite this article as:
Aujol, J., Aubert, G., Blanc-Féraud, L. et al. J Math Imaging Vis (2005) 22: 71. doi:10.1007/s10851-005-4783-8

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.

Keywords

total variation minimizationBVtexturerestorationSAR imagesspeckle

Copyright information

© Springer Science + Business Media, Inc. 2005