The Radon Transform, Inverse Problems, and Tomography
The Radon Transform, Inverse Problems, and Tomography

Author: Gestur Ólafsson

Publisher: American Mathematical Soc.

Published: 2006

Total Pages: 176

ISBN-13: 0821839306

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Since their emergence in 1917, tomography and inverse problems remain active and important fields that combine pure and applied mathematics and provide strong interplay between diverse mathematical problems and applications. The applied side is best known for medical and scientific use, in particular, medical imaging, radiotherapy, and industrial non-destructive testing. Doctors use tomography to see the internal structure of the body or to find functional information, such asmetabolic processes, noninvasively. Scientists discover defects in objects, the topography of the ocean floor, and geological information using X-rays, geophysical measurements, sonar, or other data. This volume, based on the lectures in the Short Course The Radon Transform and Applications to InverseProblems at the American Mathematical Society meeting in Atlanta, GA, January 3-4, 2005, brings together articles on mathematical aspects of tomography and related inverse problems. The articles cover introductory material, theoretical problems, and practical issues in 3-D tomography, impedance imaging, local tomography, wavelet methods, regularization and approximate inverse, sampling, and emission tomography. All contributions are written for a general audience, and the authors have includedreferences for further reading.

The Radon Transform and Medical Imaging
The Radon Transform and Medical Imaging

Author: Peter Kuchment

Publisher: SIAM

Published: 2014-03-20

Total Pages: 238

ISBN-13: 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.

Analytic Tomography
Analytic Tomography

Author: Andrew Markoe

Publisher: Cambridge University Press

Published: 2006-01-23

Total Pages: 358

ISBN-13: 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
The Radon Transform

Author: Sigurdur Helgason

Publisher: Springer Science & Business Media

Published: 1999-08-01

Total Pages: 214

ISBN-13: 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.

The Radon Transform
The Radon Transform

Author: Ronny Ramlau

Publisher: de Gruyter

Published: 2019

Total Pages: 0

ISBN-13: 9783110559415

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In 1917, Johann Radon published his fundamental work, where he introduced what is now called the Radon transform. Including important contributions by several experts, this book reports on ground-breaking developments related to the Radon transform

Integral Geometry and Radon Transforms
Integral Geometry and Radon Transforms

Author: Sigurdur Helgason

Publisher: Springer Science & Business Media

Published: 2010-11-17

Total Pages: 309

ISBN-13: 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

The Radon Transform
The Radon Transform

Author: Ronny Ramlau

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2019-06-17

Total Pages: 469

ISBN-13: 311055951X

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The series is devoted to the publication of high-level monographs, surveys and proceedings which cover the whole spectrum of computational and applied mathematics. The books of this series are addressed to both specialists and advanced students. Interested authors may submit book proposals to the Managing Editor or to any member of the Editorial Board. Managing EditorUlrich Langer, Johannes Kepler University Linz, Austria Editorial BoardHansj rg Albrecher, University of Lausanne, SwitzerlandRonald H. W. Hoppe, University of Houston, USAKarl Kunisch, RICAM, Linz, Austria; University of Graz, AustriaHarald Niederreiter, RICAM, Linz, AustriaChristian Schmeiser, University of Vienna, Austria

The Radon Transform and Medical Imaging
The Radon Transform and Medical Imaging

Author: Peter Kuchment

Publisher: SIAM

Published: 2014-01-01

Total Pages: 238

ISBN-13: 1611973295

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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 Radon Transform and Some of Its Applications
The Radon Transform and Some of Its Applications

Author: Stanley R. Deans

Publisher: Courier Corporation

Published: 2007-10-01

Total Pages: 306

ISBN-13: 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.

The Radon Transform and Local Tomography
The Radon Transform and Local Tomography

Author: Alexander G. Ramm

Publisher: CRC Press

Published: 2020-07-16

Total Pages: 516

ISBN-13: 1000151778

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Over the past decade, the field of image processing has made tremendous advances. One type of image processing that is currently of particular interest is "tomographic imaging," a technique for computing the density function of a body, or discontinuity surfaces of this function. Today, tomography is widely used, and has applications in such fields as medicine, engineering, physics, geophysics, and security. The Radon Transform and Local Tomography clearly explains the theoretical, computational, and practical aspects of applied tomography. It includes sufficient background information to make it essentially self-contained for most readers.