The Radon Transform Inverse Problems And Tomography

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The Radon Transform, Inverse Problems, and Tomography

Author : Gestur Ólafsson
Publisher : American Mathematical Soc.
ISBN 13 : 0821839306
Total Pages : 176 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Radon Transform, Inverse Problems, and Tomography by : Gestur Ólafsson

Download or read book The Radon Transform, Inverse Problems, and Tomography written by Gestur Ólafsson and published by American Mathematical Soc.. This book was released on 2006 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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, Inverse Problems, and Tomography

Author : Gestur îlafsson Eric Todd Quinto
Publisher : American Mathematical Soc.
ISBN 13 : 9780821867686
Total Pages : 186 pages
Book Rating : 4.8/5 (676 download)

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Book Synopsis The Radon Transform, Inverse Problems, and Tomography by : Gestur îlafsson Eric Todd Quinto

Download or read book The Radon Transform, Inverse Problems, and Tomography written by Gestur îlafsson Eric Todd Quinto and published by American Mathematical Soc.. This book was released on 2006-02-07 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 as metabolic 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 Inverse Problems 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 included references for further reading.

Radon Transforms and Tomography

Author : Eric Todd Quinto
Publisher : American Mathematical Soc.
ISBN 13 : 0821821350
Total Pages : 274 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Radon Transforms and Tomography by : Eric Todd Quinto

Download or read book Radon Transforms and Tomography written by Eric Todd Quinto and published by American Mathematical Soc.. This book was released on 2001 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most exciting features of the fields of Radon transforms and tomography is the strong relationship between high-level pure mathematics and applications to areas such as medical imaging and industrial nondestructive evaluation. The proceedings featured in this volume bring together fundamental research articles in the major areas of Radon transforms and tomography. This volume includes expository papers that are of special interest to beginners as well as advanced researchers. Topics include local tomography and wavelets, Lambda tomography and related methods, tomographic methods in RADAR, ultrasound, Radon transforms and differential equations, and the Pompeiu problem. The major themes in Radon transforms and tomography are represented among the research articles. Pure mathematical themes include vector tomography, microlocal analysis, twistor theory, Lie theory, wavelets, harmonic analysis, and distribution theory. The applied articles employ high-quality pure mathematics to solve important practical problems. Effective scanning geometries are developed and tested for a NASA wind tunnel. Algorithms for limited electromagnetic tomographic data and for impedance imaging are developed and tested. Range theorems are proposed to diagnose problems with tomography scanners. Principles are given for the design of X-ray tomography reconstruction algorithms, and numerical examples are provided. This volume offers readers a comprehensive source of fundamental research useful to both beginners and advanced researchers in the fields.

The Radon Transform and Medical Imaging

Author : Peter Kuchment
Publisher : SIAM
ISBN 13 : 1611973295
Total Pages : 256 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis The Radon Transform and Medical Imaging by : Peter Kuchment

Download or read book The Radon Transform and Medical Imaging written by Peter Kuchment and published by SIAM. This book was released on 2014-01-01 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Ronny Ramlau
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311055951X
Total Pages : 469 pages
Book Rating : 4.1/5 (15 download)

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Book Synopsis The Radon Transform by : Ronny Ramlau

Download or read book The Radon Transform written by Ronny Ramlau and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-06-17 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Inverse Problems, Tomography, and Image Processing

Author : Alexander G. Ramm
Publisher : Springer Science & Business Media
ISBN 13 : 1402079753
Total Pages : 262 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Inverse Problems, Tomography, and Image Processing by : Alexander G. Ramm

Download or read book Inverse Problems, Tomography, and Image Processing written by Alexander G. Ramm and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of Sessions from the First Congress of the International Society for Analysis, Applications, and Computind held in Newark, Delaware, June 2-6, 1997

Applied Problems of Radon Transform

Author : Semen Grigorʹevich Gindikin
Publisher : American Mathematical Soc.
ISBN 13 : 9780821875087
Total Pages : 276 pages
Book Rating : 4.8/5 (75 download)

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Book Synopsis Applied Problems of Radon Transform by : Semen Grigorʹevich Gindikin

Download or read book Applied Problems of Radon Transform written by Semen Grigorʹevich Gindikin and published by American Mathematical Soc.. This book was released on 1994 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection is designed to acquaint readers with advances in Radon transforms carried out in the former Soviet Union. The papers focus on mathematical problems related to applications of Radon transforms. Some of the problems arose from practical tomography, while others are theoretical problems originating in tomography. The book should be of use to mathematicians working in integral geometry and mathematical problems of tomography, as well as scientists who work on inverse problems and their computer realization.

Applied Problems of Radon Transform

Author :
Publisher :
ISBN 13 : 9781470433734
Total Pages : 261 pages
Book Rating : 4.4/5 (337 download)

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Book Synopsis Applied Problems of Radon Transform by :

Download or read book Applied Problems of Radon Transform written by and published by . This book was released on 1994 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Basic Methods of Tomography and Inverse Problems

Author : Gabor T. Herman
Publisher :
ISBN 13 :
Total Pages : 736 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Basic Methods of Tomography and Inverse Problems by : Gabor T. Herman

Download or read book Basic Methods of Tomography and Inverse Problems written by Gabor T. Herman and published by . This book was released on 1987 with total page 736 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Analytic Tomography

Author : Andrew Markoe
Publisher : Cambridge University Press
ISBN 13 : 0521793475
Total Pages : 358 pages
Book Rating : 4.5/5 (217 download)

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Book Synopsis Analytic Tomography by : Andrew Markoe

Download or read book Analytic Tomography written by Andrew Markoe and published by Cambridge University Press. This book was released on 2006-01-23 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study contains elementary introductions to properties of the Radon transform plus coverage of more advanced topics.

Computed Radiation Imaging

Author : Esam M A Hussein
Publisher : Elsevier
ISBN 13 : 0123877784
Total Pages : 303 pages
Book Rating : 4.1/5 (238 download)

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Book Synopsis Computed Radiation Imaging by : Esam M A Hussein

Download or read book Computed Radiation Imaging written by Esam M A Hussein and published by Elsevier. This book was released on 2011-06-01 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer-assisted imaging with radiation (x- and gamma rays) is an integral part of modern medical-diagnostic practice. This imaging technology is also slowly finding its way into industrial applications. Although the technology is well developed, there is a need for further improvement to enhance image quality, reduce artifacts, minimize patient radiation exposure, compete with and complement other imaging methods (such as magnetic resonance imaging and ultrasonics), and accommodate dense and large objects encountered in industrial applications.Scientists and engineers, attempting to progress this technology, are faced with an enormous amount of literature, addressing the imaging problem from various view points. This book provides a single source that addresses both the physical and mathematical aspects of the imaging problem in a consistent and comprehensive manner. Discusses the inherent physical and numerical capabilities and limitations of the methods presented for both the forward and inverse problems Provides information on available Internet resources and software Written in a manner that makes it readable by physicists, mathematicians, engineers and computer scientists – avoids, as much as possible, the use of specialized terminology without clear introduction and definition

The Radon Transform

Author : Sigurdur Helgason
Publisher : Springer Science & Business Media
ISBN 13 : 1475714637
Total Pages : 193 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis The Radon Transform by : Sigurdur Helgason

Download or read book The Radon Transform written by Sigurdur Helgason and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of this book has been out of print for some time and I have decided to follow the publisher's kind suggestion to prepare a new edition. Many examples with explicit inversion formulas and range theo rems have been added, and the group-theoretic viewpoint emphasized. For example, the integral geometric viewpoint of the Poisson integral for the disk leads to interesting analogies with the X-ray transform in Euclidean 3-space. To preserve the introductory flavor of the book the short and self-contained Chapter Von Schwartz' distributions has been added. Here §5 provides proofs of the needed results about the Riesz potentials while §§3-4 develop the tools from Fourier analysis following closely the account in Hormander's books (1963] and [1983]. There is some overlap with my books (1984] and [1994b] which however rely heavily on Lie group theory. The present book is much more elementary. I am indebted to Sine Jensen for a critical reading of parts of the manuscript and to Hilgert and Schlichtkrull for concrete contributions men tioned at specific places in the text. Finally I thank Jan Wetzel and Bonnie Friedman for their patient and skillful preparation of the manuscript.

Inverse Problems and Tomography in Acoustics and Seismology

Author : Philip Carrion
Publisher :
ISBN 13 :
Total Pages : 324 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Inverse Problems and Tomography in Acoustics and Seismology by : Philip Carrion

Download or read book Inverse Problems and Tomography in Acoustics and Seismology written by Philip Carrion and published by . This book was released on 1987 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Mathematics of Computerized Tomography

Author : F. Natterer
Publisher : Springer-Verlag
ISBN 13 : 3663014096
Total Pages : 235 pages
Book Rating : 4.6/5 (63 download)

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Book Synopsis The Mathematics of Computerized Tomography by : F. Natterer

Download or read book The Mathematics of Computerized Tomography written by F. Natterer and published by Springer-Verlag. This book was released on 2013-03-09 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Inverse Problems, Image Analysis, and Medical Imaging

Author : M. Zuhair Nashed
Publisher : American Mathematical Soc.
ISBN 13 : 0821829793
Total Pages : 322 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Inverse Problems, Image Analysis, and Medical Imaging by : M. Zuhair Nashed

Download or read book Inverse Problems, Image Analysis, and Medical Imaging written by M. Zuhair Nashed and published by American Mathematical Soc.. This book was released on 2002 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the Special Session, Interaction of Inverse Problems and Image Analysis, held at the January 2001 meeting of the AMS in New Orleans, LA. The common thread among inverse problems, signal analysis, and image analysis is a canonical problem: recovering an object (function, signal, picture) from partial or indirect information about the object. Both inverse problems and imaging science have emerged in recent years as interdisciplinary research fields with profound applications in many areas of science, engineering, technology, and medicine. Research in inverse problems and image processing shows rich interaction with several areas of mathematics and strong links to signal processing, variational problems, applied harmonic analysis, and computational mathematics. This volume contains carefully referred and edited original research papers and high-level survey papers that provide overview and perspective on the interaction of inverse problems, image analysis, and medical imaging. The book is suitable for graduate students and researchers interested in signal and image processing and medical imaging.

Generalized Radon Transforms And Imaging By Scattered Particles: Broken Rays, Cones, And Stars In Tomography

Author : Gaik Ambartsoumian
Publisher : World Scientific
ISBN 13 : 9811242453
Total Pages : 248 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Generalized Radon Transforms And Imaging By Scattered Particles: Broken Rays, Cones, And Stars In Tomography by : Gaik Ambartsoumian

Download or read book Generalized Radon Transforms And Imaging By Scattered Particles: Broken Rays, Cones, And Stars In Tomography written by Gaik Ambartsoumian and published by World Scientific. This book was released on 2023-03-14 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: A generalized Radon transform (GRT) maps a function to its weighted integrals along a family of curves or surfaces. Such operators appear in mathematical models of various imaging modalities. The GRTs integrating along smooth curves and surfaces (lines, planes, circles, spheres, amongst others) have been studied at great lengths for decades, but relatively little attention has been paid to transforms integrating along non-smooth trajectories. Recently, an interesting new class of GRTs emerged at the forefront of research in integral geometry. The two common features of these transforms are the presence of a 'vertex' in their paths of integration (broken rays, cones, and stars) and their relation to imaging techniques based on physics of scattered particles (Compton camera imaging, single scattering tomography, etc).This book covers the relevant imaging modalities, their mathematical models, and the related GRTs. The discussion of the latter comprises a thorough exploration of their known mathematical properties, including injectivity, inversion, range description and microlocal analysis. The mathematical background required for reading most of the book is at the level of an advanced undergraduate student, which should make its content attractive for a large audience of specialists interested in imaging. Mathematicians may appreciate certain parts of the theory that are particularly elegant with connections to functional analysis, PDEs and algebraic geometry.

The Radon Transform and Medical Imaging

Author : Peter Kuchment
Publisher : SIAM
ISBN 13 : 1611973287
Total Pages : 238 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis The Radon Transform and Medical Imaging by : Peter Kuchment

Download or read book The Radon Transform and Medical Imaging written by Peter Kuchment and published by SIAM. This book was released on 2014-03-20 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.