Variational methods for tomographic reconstruction with few views

Maïtine Bergounioux (1) , Isabelle Abraham (2) , Romain Abraham (1) , Guillaume Carlier (3, 4) , Erwan Le Pennec (5) , Emmanuel Trélat (6, 7)

1 IDP - Institut Denis Poisson
2 CEA - Commissariat à l'énergie atomique et aux énergies alternatives
3 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
4 MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales
5 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
6 CaGE - Control And GEometry
7 SU - Sorbonne Université

We deal with a severe ill posed problem, namely the reconstruction process of an image during tomography acquisition with (very) few views. We present different methods that we have been investigated during the past decade. They are based on variational analysis. This is a survey paper and we refer to the quoted papers for more details. Mathematics Subject Classification (2010). 49K40, 45Q05,65M32.

Mots clés: Spaces; Radon operator; transport; Needlets; Optimal; Variational method; Tomographic reconstruction; Fractional order Hilbert; Inverse problem

Domaines: Optimisation et contrôle [math.OC]

Maïtine Bergounioux, Isabelle Abraham, Romain Abraham, Guillaume Carlier, Erwan Le Pennec, et al.. Variational methods for tomographic reconstruction with few views. Milan Journal of Mathematics, 2018, 86 (2), pp.157--200. ⟨hal-01817172⟩