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Dual Norms and Image Decomposition Models

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Abstract

Following a recent work by Y. Meyer, decomposition models into a geometrical component and a textured component have recently been proposed in image processing. In such approaches, negative Sobolev norms have seemed to be useful to modelize oscillating patterns. In this paper, we compare the properties of various norms that are dual of Sobolev or Besov norms. We then propose a decomposition model which splits an image into three components: a first one containing the structure of the image, a second one the texture of the image, and a third one the noise. Our decomposition model relies on the use of three different semi-norms: the total variation for the geometrical component, a negative Sobolev norm for the texture, and a negative Besov norm for the noise. We illustrate our study with numerical examples.

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Authors and Affiliations

  1. Laboratoire J.A. Dieudonné, UMR CNRS 6621 and ARIANA, Projet Commun CNRS/INRIA/UNSA, France

    Jean-François Aujol

  2. CMAP (UMR 7641), Ecole Polytechnique, 91128, Palaiseau Cedex, France

    Antonin Chambolle

Authors
  1. Jean-François Aujol
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  2. Antonin Chambolle
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Correspondence to Jean-François Aujol.

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Aujol, JF., Chambolle, A. Dual Norms and Image Decomposition Models. Int J Comput Vision 63, 85–104 (2005). https://doi.org/10.1007/s11263-005-4948-3

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  • DOI: https://doi.org/10.1007/s11263-005-4948-3

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