Analytic Tomography
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.
- Comprehensive coverage of the Radon transform
- Includes advanced topics such as the attenuated Radon transform and generalized Radon transforms
- Includes an informal, graphical introduction to how a CT scanner works
Reviews & endorsements
'This book was written to appeal to the broadest possible group of readers. The first chapter, which introduces computerized tomography, X-ray imaging and the Radon transform requires almost no mathematical background.' L'enseignement mathematique
'The book is very carefully written and may be read at various levels. The bibliography is very detailed (it contains 630 items) and at the end of each chapter there is a section of additional references and results which constitute a guide for further study. In conclusion, this is a valuable book for everyone interested in Radon transforms and its applications, from beginners to experts.' Zentralblatt MATH
'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
Product details
April 2006Hardback
9780521793476
410 pages
234 × 156 × 24 mm
0.71kg
Available
Table of Contents
- 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.
