The Universality of the Radon Transform

Written by a leading scholar in mathematics, this monograph discusses the Radon transform. This topic has wide ranging applications, in particular X-ray technology, partial differential equations, nuclear magnetic resonance scanning, and tomography.
This monograph discusses the Radon transform, a field that has wide-ranging applications to X-ray technology, partial differential equations, nuclear magnetic resonance scanning, and tomography. Ehrenpreis focuses on recent research and highlights the strong relationship between high-level pure mathematics and applications of the Radon transform to areas such as medical imaging The first part of the book discusses parametric and nonparametric Radon transforms, harmonic functions and Radon transform on algebraic varieties, nonlinear Radon and Fourier transforms, Radon transform on groups, and Radon transform as the interrelation of geometry and analysis. The later parts discuss the extension of solutions of differential equations, Periods of Eisenstein and Poincare, and some problems of integral geometry arising in tomography. Examples and proofs are provided throughout the book to aid the reader's understanding.