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

Maïtine Bergounioux (1) , Emmanuel Trélat (1)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

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.

Mots clés: fractional order Hilbert spaces; minimization; Radon operator

Domaines: Optimisation et contrôle [math.OC]

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, 2010, 259, pp.2296--2332. ⟨hal-00458340⟩