A variational method using fractional order Hilbert spaces for tomographic reconstruction of blurred and noised binary images

Abstract : We provide in this article a refined functional analysis of the Radon operator restricted to axisymmetric functions, and show that it enjoys strong regularity properties in fractional order Hilbert spaces. This study is motivated by a problem of tomographic reconstruction of binary axially symmetric ob jects, for which we have available one single blurred and noised snapshot. We propose a variational approach to handle this problem, consisting in solving a minimization problem settled in adapted fractional order Hilbert spaces. We show the existence of solutions, and then derive first order necessary conditions for optimality in the form of optimality systems.
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Article dans une revue
Journal of Functional Analysis, Elsevier, 2010, pp.2296--2332
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https://hal.archives-ouvertes.fr/hal-00458340
Contributeur : Emmanuel Trélat <>
Soumis le : samedi 20 février 2010 - 18:08:33
Dernière modification le : jeudi 3 mai 2018 - 15:32:06
Document(s) archivé(s) le : jeudi 18 octobre 2012 - 15:35:46

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  • HAL Id : hal-00458340, version 1

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Maïtine Bergounioux, Emmanuel Trélat. A variational method using fractional order Hilbert spaces for tomographic reconstruction of blurred and noised binary images. Journal of Functional Analysis, Elsevier, 2010, pp.2296--2332. 〈hal-00458340〉

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