The Radon Transform
Sigurdur Helgason
Birkhäuser Boston
The Radon transform is an important topic in integral  geometry which deals with the problem of expressing a function on a  manifold in terms of its integrals over certain  submanifolds. Solutions to such problems have a wide range of  applications, namely to partial differential equations, group  representationsm X-ray technology, nuclear magnetic resonance  scanning, and tomography.  This second edition, significantly expanded  and updated, presents new material taking into account some of the  progress in the field since 1980.