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

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• 作者：M. Bergounioux ; E. Tré ; lat
• 关键词：Radon operator ; Fractional order Hilbert spaces ; Minimization
• 刊名：Journal of Functional Analysis
• 出版年：2010
• 出版时间：1 November 2010
• 年：2010
• 卷：259
• 期：9
• 页码：2296-2332
• 全文大小：321 K

文摘

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 objects, 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.