Analytic Tomography

AvAndrew Markoe

Häftad, Engelska, 2014

744 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2014-08-21
Mått:156 x 234 x 21 mm
Vikt:570 g
Format:Häftad
Språk:Engelska
Antal sidor:410
Förlag:Cambridge University Press
ISBN:9781107438620

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Mer om författaren

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.

Recensioner i media

'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

Innehållsförteckning

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.