The Radon Transform Inverse Problems And Tomography

Author : Gestur Ólafsson,Eric Todd Quinto
Publisher : American Mathematical Soc.
Page : 176 pages
File Size : 49,9 Mb
Release : 2006
Category : Imagerie médicale - Congrès
ISBN : 9780821839300

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The Radon Transform, Inverse Problems, and Tomography by Gestur Ólafsson,Eric Todd Quinto Pdf

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.

Author : Gestur îlafsson Eric Todd Quinto
Publisher : American Mathematical Soc.
Page : 186 pages
File Size : 44,7 Mb
Release : 2006-02-07
Category : Imaging systems in medicine
ISBN : 0821867687

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The Radon Transform, Inverse Problems, and Tomography by Gestur îlafsson Eric Todd Quinto Pdf

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.

Author : Eric Todd Quinto
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 46,9 Mb
Release : 2001
Category : Radon transforms
ISBN : 9780821821350

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Radon Transforms and Tomography by Eric Todd Quinto Pdf

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.

Author : Alexander G. Ramm
Publisher : Springer Science & Business Media
Page : 262 pages
File Size : 53,8 Mb
Release : 2013-11-11
Category : Technology & Engineering
ISBN : 9781402079757

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Inverse Problems, Tomography, and Image Processing by Alexander G. Ramm Pdf

Proceedings of Sessions from the First Congress of the International Society for Analysis, Applications, and Computind held in Newark, Delaware, June 2-6, 1997

Author : Gabor T. Herman
Publisher : Unknown
Page : 696 pages
File Size : 48,8 Mb
Release : 1987
Category : Geometric tomography
ISBN : STANFORD:36105032405354

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Basic Methods of Tomography and Inverse Problems by Gabor T. Herman Pdf

Author : Esam M A Hussein
Publisher : Elsevier
Page : 303 pages
File Size : 51,5 Mb
Release : 2011-06-01
Category : Science
ISBN : 9780123877789

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Computed Radiation Imaging by Esam M A Hussein Pdf

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

Author : Semen Grigorʹevich Gindikin
Publisher : American Mathematical Soc.
Page : 276 pages
File Size : 42,9 Mb
Release : 1994
Category : Mathematics
ISBN : 0821875086

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Applied Problems of Radon Transform by Semen Grigorʹevich Gindikin Pdf

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.

Author : Peter Kuchment
Publisher : SIAM
Page : 238 pages
File Size : 51,9 Mb
Release : 2014-01-01
Category : Computers
ISBN : 9781611973297

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The Radon Transform and Medical Imaging by Peter Kuchment Pdf

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.

Author : Anonim
Publisher : Unknown
Page : 261 pages
File Size : 41,5 Mb
Release : 1994
Category : Electronic
ISBN : 1470433737

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Applied Problems of Radon Transform by Anonim Pdf

Author : Ronny Ramlau,Otmar Scherzer
Publisher : Walter de Gruyter GmbH & Co KG
Page : 469 pages
File Size : 55,6 Mb
Release : 2019-06-17
Category : Mathematics
ISBN : 9783110559514

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The Radon Transform by Ronny Ramlau,Otmar Scherzer Pdf

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

Author : Philip Carrion
Publisher : Unknown
Page : 324 pages
File Size : 50,7 Mb
Release : 1987
Category : Acoustic imaging
ISBN : UCSD:31822002416600

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Inverse Problems and Tomography in Acoustics and Seismology by Philip Carrion Pdf

Author : F. Natterer
Publisher : Springer-Verlag
Page : 235 pages
File Size : 41,7 Mb
Release : 2013-03-09
Category : Technology & Engineering
ISBN : 9783663014096

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The Mathematics of Computerized Tomography by F. Natterer Pdf

Author : Peter Kuchment
Publisher : SIAM
Page : 238 pages
File Size : 54,5 Mb
Release : 2014-03-20
Category : Computers
ISBN : 9781611973280

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The Radon Transform and Medical Imaging by Peter Kuchment Pdf

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.

Author : M. Zuhair Nashed,Otmar Scherzer,AMS Special Session on Interaction of Inverse Problems
Publisher : American Mathematical Soc.
Page : 322 pages
File Size : 54,6 Mb
Release : 2002
Category : Diagnostic imaging
ISBN : 9780821829790

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Inverse Problems, Image Analysis, and Medical Imaging by M. Zuhair Nashed,Otmar Scherzer,AMS Special Session on Interaction of Inverse Problems Pdf

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.

Author : Gaik Ambartsoumian
Publisher : World Scientific
Page : 248 pages
File Size : 53,7 Mb
Release : 2023-03-14
Category : Mathematics
ISBN : 9789811242458

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

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.