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.
2015
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]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/7962
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