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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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https://hal.archives-ouvertes.fr/hal-00458340
Contributor : Emmanuel Trélat <>
Submitted on : Saturday, February 20, 2010 - 6:08:33 PM
Last modification on : Thursday, May 3, 2018 - 3:32:06 PM
Document(s) archivé(s) le : Thursday, October 18, 2012 - 3:35:46 PM

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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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