Abstract:

In this talk, we discuss a novel numerical realization of X-ray computerized tomography by the use of boundary integration. X-ray computerized tomography is a typical inverse problem and many attentions have been paid from both theoretical and practical viewpoints. One of its mathematical models is the inverse source problem of the transport equation, to which the theory of A-analytic maps developed by A.L.Bukhgeim gives a reconstruction formula in the form of boundary integration. In this presentation, we discuss its numerical feasibility and properties. Particularly it is exhibited that treatments of the Neumann series appeared in the formula is essential in order to overcome the instability. It is also exhibit that the proposed numerical scheme is efficient in reconstruction from sinogram obtained in practical situations. This presentation is based on collaborations with Prof. A. Tamasan (University of Central Florida) and Prof. N. Oisni (Kyoto University).