Journal of Mathematical Imaging and Vision

, Volume 22, Issue 1, pp 71–88 | Cite as

Image Decomposition into a Bounded Variation Component and an Oscillating Component

  • Jean-François Aujol
  • Gilles Aubert
  • Laure Blanc-Féraud
  • Antonin Chambolle


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.


total variation minimization BV texture restoration SAR images speckle 


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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • Jean-François Aujol
    • 1
    • 2
    • 6
  • Gilles Aubert
    • 3
  • Laure Blanc-Féraud
    • 4
  • Antonin Chambolle
    • 5
  1. 1.Laboratoire J.A. Dieudonné, UMR CNRS 6621Université de Nice Sophia-AntipolisNice Cedex 2France
  2. 2.ARIANA, Projet Commun CNRS/INRIA/UNSAINRIA Sophia AntipolisSophia Antipolis CedexFrance
  3. 3.Laboratoire J.A. Dieudonné, UMR CNRS 6621Université de Nice Sophia-AntipolisNice Cedex 2France
  4. 4.ARIANA, Projet Commun CNRS/INRIA/UNSAINRIA Sophia AntipolisSophia Antipolis CedexFrance
  5. 5.CEREMADE, UMR CNRS 7534Université Paris - DauphineParis Cedex 16France
  6. 6.UCLA Department of MathematicsLos Angeles

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