In this article we present a review of the Radon transform and the instability of the tomographic reconstruction process. We show some new mathematical results in tomography obtained by a variational formulation of the reconstruction problem based on the minimization of a Mumford?Shah type functional. Finally, we exhibit a physical interpretation of this new technique and discuss some possible generalizations.
Tomography: mathematical aspects and applications / Facchi, P; Ligabò, M; Solimini, Sergio Fausto. - In: PHYSICA SCRIPTA. - ISSN 0031-8949. - 90:7; Special Issue(2015). [10.1088/0031-8949/90/7/074007]
Tomography: mathematical aspects and applications
SOLIMINI, Sergio Fausto
2015-01-01
Abstract
In this article we present a review of the Radon transform and the instability of the tomographic reconstruction process. We show some new mathematical results in tomography obtained by a variational formulation of the reconstruction problem based on the minimization of a Mumford?Shah type functional. Finally, we exhibit a physical interpretation of this new technique and discuss some possible generalizations.File in questo prodotto:
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