Analytic Tomography

This study contains elementary introductions to properties of the Radon transform plus coverage of more advanced topics.

Andrew Markoe (Author)

9780521793476, Cambridge University Press

Hardback, published 23 January 2006

410 pages
23.4 x 15.6 x 2.4 cm, 0.71 kg

'I recommend this book for everybody interested in Radon transform or tomography. This book is great to get acquainted, get involved and start research but also good for researchers of any kind of Radon tranform.' Acta Scientiarum Mathematicarum

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, such as the attenuated Radon transform and generalized Radon transforms defined by duality of homogeneous spaces and double fibrations. Questions of invertibility and the range of the Radon transform are dealt with and inversion formulas are developed with particular attention to functions on L2 spaces and some discussion of the case of Lp spaces.

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 variants of the Radon transform.

Subject Areas: Complex analysis, complex variables [PBKD], Real analysis, real variables [PBKB], Tomography [MMPJ]