Inversion of radon transform by some series methods

This thesis consists of three sections. In the first section, basic information about Radon transform and its inverse are given. In the second section, the definitions and some properties of gamma function, Tchebycheff polynomials, Legendre polynomials, Gegenbauer polynomials and spherical harmonics are given. In the third section, the relationship between Radon transform and Gegenbauer transform is presented. Then, for the inverse of the Radon transform, circular harmonics and spherical harmonic series expansions are examined. Various examples are provided on determining a function from its Radon transformation using circular and spherical harmonic series expansions.