On the uniqueness of the Radon transform over lines, planes and spheres -

Abstract

This thesis will discuss the uniqueness problem of the Radon transform over lines in the space, hyper planes in the Euclidean N space for N 2 and in more detail, the Radon transform over spheres whose centers are restricted subsets of the Euclidean N space. It will also examine the connection between probability theory, and the injectivity of the Radon transform over lines. The study of the uniqueness of the spherical Radon transform is important to the development of some medical imaging methods such as Thermo Acoustic Tomography (TAT). It also has applications in approximation theory, integral geometry, inverse problems for PDE's, and other fields.