Radon transform and its properties

This thesis consists of three sections. In the first section some basic informations about the Radon transform and its applications are given and a basic mathematical model for the X-ray behavior is introduced. The second section is devoted to the definition and properties of Radon transform and to some examples on the computation of the Radon transform of some functions. In the third section, some methods on the inversion of Radon transform are investigated. In order to obtain the inversion of Radon transform, first, the back-projection method is considered, then the relation between the Radon transform and Fourier transform is given by the central slice theorem (Fourier slice theorem) and the filtered back-projection method is investigated. Moreover, some examples on the inversion of Radon transform are given.