Dual Norms and Image Decomposition Models

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 propert...

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Bibliographic Details
Published in:International journal of computer vision 2005-06, Vol.63 (1), p.85-104
Main Authors: Aujol, Jean-Fran ois, Chambolle, Antonin
Format: Article
Language:English
Subjects:
Analysis of PDEs
Computer Science
Decomposition
Image Processing
Mathematics
Norms
Studies
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Summary: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.[PUBLICATION ABSTRACT]
ISSN:0920-5691
1573-1405
DOI:10.1007/s11263-005-4948-3