The Radon Transform

The Radon Transform
Title The Radon Transform PDF eBook
Author Sigurdur Helgason
Publisher Springer Science & Business Media
Pages 214
Release 1999-08-01
Genre Mathematics
ISBN 9780817641092

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The Radon transform is an important topic in integral geometry which deals with the problem of expressing a function on a manifold in terms of its integrals over certain submanifolds. Solutions to such problems have a wide range of applications, namely to partial differential equations, group representations, X-ray technology, nuclear magnetic resonance scanning, and tomography. This second edition, significantly expanded and updated, presents new material taking into account some of the progress made in the field since 1980. Aimed at beginning graduate students, this monograph will be useful in the classroom or as a resource for self-study. Readers will find here an accessible introduction to Radon transform theory, an elegant topic in integral geometry.

Introduction to Radon Transforms

Introduction to Radon Transforms
Title Introduction to Radon Transforms PDF eBook
Author Boris Rubin
Publisher Cambridge University Press
Pages 595
Release 2015-11-12
Genre Mathematics
ISBN 0521854598

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A comprehensive introduction to basic operators of integral geometry and the relevant harmonic analysis for students and researchers.

The Radon Transform and Some of Its Applications

The Radon Transform and Some of Its Applications
Title The Radon Transform and Some of Its Applications PDF eBook
Author Stanley R. Deans
Publisher Courier Corporation
Pages 306
Release 2007-10-01
Genre Mathematics
ISBN 0486462412

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Of value to mathematicians, physicists, and engineers, this excellent introduction to Radon transform covers both theory and applications, with a rich array of examples and literature that forms a valuable reference. This 1993 edition is a revised and updated version by the author of his pioneering work.

Integral Geometry and Radon Transforms

Integral Geometry and Radon Transforms
Title Integral Geometry and Radon Transforms PDF eBook
Author Sigurdur Helgason
Publisher Springer Science & Business Media
Pages 309
Release 2010-11-17
Genre Mathematics
ISBN 1441960546

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In this text, integral geometry deals with Radon’s problem of representing a function on a manifold in terms of its integrals over certain submanifolds—hence the term the Radon transform. Examples and far-reaching generalizations lead to fundamental problems such as: (i) injectivity, (ii) inversion formulas, (iii) support questions, (iv) applications (e.g., to tomography, partial di erential equations and group representations). For the case of the plane, the inversion theorem and the support theorem have had major applications in medicine through tomography and CAT scanning. While containing some recent research, the book is aimed at beginning graduate students for classroom use or self-study. A number of exercises point to further results with documentation. From the reviews: “Integral Geometry is a fascinating area, where numerous branches of mathematics meet together. the contents of the book is concentrated around the duality and double vibration, which is realized through the masterful treatment of a variety of examples. the book is written by an expert, who has made fundamental contributions to the area.” —Boris Rubin, Louisiana State University

Analytic Tomography

Analytic Tomography
Title Analytic Tomography PDF eBook
Author Andrew Markoe
Publisher Cambridge University Press
Pages 358
Release 2006-01-23
Genre Mathematics
ISBN 0521793475

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

The Radon Transform and Medical Imaging

The Radon Transform and Medical Imaging
Title The Radon Transform and Medical Imaging PDF eBook
Author Peter Kuchment
Publisher SIAM
Pages 238
Release 2014-03-20
Genre Computers
ISBN 1611973287

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This book surveys the main mathematical ideas and techniques behind some well-established imaging modalities such as X-ray CT and emission tomography, as well as a variety of newly developing coupled-physics or hybrid techniques, including thermoacoustic tomography. The Radon Transform and Medical Imaging emphasizes mathematical techniques and ideas arising across the spectrum of medical imaging modalities and explains important concepts concerning inversion, stability, incomplete data effects, the role of interior information, and other issues critical to all medical imaging methods. For nonexperts, the author provides appendices that cover background information on notation, Fourier analysis, geometric rays, and linear operators. The vast bibliography, with over 825 entries, directs readers to a wide array of additional information sources on medical imaging for further study.

The Universality of the Radon Transform

The Universality of the Radon Transform
Title The Universality of the Radon Transform PDF eBook
Author Leon Ehrenpreis
Publisher OUP Oxford
Pages 746
Release 2003
Genre Mathematics
ISBN 9780198509783

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Written by a leading scholar in mathematics, this monograph discusses the Radon transform, a field that has wide ranging applications to X-ray technology, partial differential equations, nuclear magnetic resonance scanning and tomography. In this book, Ehrenpreis focuses on recent research and highlights the strong relationship between high-level pure mathematics and applications of the Radon transform to areas such as medical imaging.