Analytic Tomography

Andrew Markoe - Collection Encyclopedia of Mathematics and its Applications

400 pages, parution le 23/03/2006

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Résumé

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

Sommaire

Computerized tomography, X-rays, and the Radon transform
The Radon transform
The k Plane transform, the Radon- John transform
Range and differential equations
Generalizations and variants of the Radon transform

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	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Andrew Markoe
Collection	Encyclopedia of Mathematics and its Applications
Parution	23/03/2006
Nb. de pages	400
Format	16 x 24
Couverture	Relié
Poids	710g
Intérieur	Noir et Blanc
EAN13	9780521793476
ISBN13	978-0-521-79347-6