Analytic Tomography
Published on 23. January 2006
Book
Hardback
410 pages
978-0-521-79347-6 (ISBN)
Description
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.
Reviews / Votes
'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 MathematicarumMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Dimensions
Height: 240 mm
Width: 161 mm
Thickness: 27 mm
Weight
778 gr
ISBN-13
978-0-521-79347-6 (9780521793476)
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Schweitzer Classification
Other editions
Additional editions
Andrew Markoe
Analytic Tomography
Book
08/2014
Cambridge University Press
€77.20
Shipment within 15-20 days
Andrew Markoe
Analytic Tomography
E-Book
02/2011
1st Edition
Cambridge University Press
€54.49
Available for download
Person
Professor Andrew Markoe is a Professor of Mathematics at Rider University, Lawrenceville, New Jersey. He lives in Lawrenceville, NJ with his wife and the youngest of his three daughters. He graduated with a B.S. in Mathematics from the City College of New York in 1964 and received his Ph.D. in Mathematics from Brown University in 1969. His fields of research include several complex variables, integral geometry and tomography. He is a member of the American Mathematical Society. His hobbies include playing Lacrosse, playing squash and flying.
Content
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.