Analytic Tomography [Paperback]

This study contains elementary introductions to properties of the Radon transform plus coverage of more advanced topics.This book is a comprehensive study of the analytic aspects of mathematical tomography, which is primarily the study of Radon transform. The Radon transform operates on a function by integrating it over hyperplanes. The first three chapters are devoted to elementary and graphical introductions to the Radon transform, tomography and CT scanners, a rigorous development of the basic prope rties of the Radon transform, and Grassmann manifolds to the study of k- plane transform. The remaining chapters are concerned with some more advanced topics.This book is a comprehensive study of the analytic aspects of mathematical tomography, which is primarily the study of Radon transform. The Radon transform operates on a function by integrating it over hyperplanes. The first three chapters are devoted to elementary and graphical introductions to the Radon transform, tomography and CT scanners, a rigorous development of the basic prope rties of the Radon transform, and Grassmann manifolds to the study of k- plane transform. The remaining chapters are concerned with some more advanced topics.This book is a comprehensive study of the Radon transform, which operates on a function by integrating it over hyperplanes. The book begins with an elementary and graphical introduction to the Radon transform, tomography and CT scanners, followed by a rigorous development of the basic properties of the Radon transform. Next the author introduces Grassmann manifolds in the study of the k-plane transform (a version of the Radon transform) which integrates over k-dimensional planes rather than hyperplanes. The remaining chapters are concerned with more advanced topics.1. Computerized tomography, X-rays, and the Radon transform; 2. The Radon transform; 3. The k Plane transform, the Radon- John transform; 4. Range and differential equations; 5. Generalizations and variantsl³‡