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, PAOLO;LIGABO', MARILENA;
2015

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11586/139601
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