Tomography: mathematical aspects and applications
arXiv:1501.07385 · doi:10.1088/0031-8949/90/7/074007
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.
11 pages, 5 figures