The Radon Transform Inverse Problems And Tomography
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The Radon Transform Inverse Problems And Tomography
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Author : Gestur Ólafsson
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
The Radon Transform Inverse Problems And Tomography written by Gestur Ólafsson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
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.
Basic Methods Of Tomography And Inverse Problems
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Author : Gabor T. Herman
language : en
Publisher:
Release Date : 1987
Basic Methods Of Tomography And Inverse Problems written by Gabor T. Herman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Geometric tomography categories.
The Radon Transform
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Author : Sigurdur Helgason
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-08-01
The Radon Transform written by Sigurdur Helgason and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-08-01 with Mathematics categories.
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 And Local Tomography
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Author : Alexander G. Ramm
language : en
Publisher: CRC Press
Release Date : 2020-07-16
The Radon Transform And Local Tomography written by Alexander G. Ramm and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-16 with Mathematics categories.
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.
Radon Transforms And Tomography
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Author : Eric Todd Quinto
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Radon Transforms And Tomography written by Eric Todd Quinto and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
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
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Author : Ronny Ramlau
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-06-17
The Radon Transform written by Ronny Ramlau and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-17 with Mathematics categories.
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 throughout these years, and also discusses novel mathematical research topics and applications for the next century.
The Radon Transform And Medical Imaging
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Author : Peter Kuchment
language : en
Publisher: SIAM
Release Date : 2014-01-01
The Radon Transform And Medical Imaging written by Peter Kuchment and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-01 with Computers categories.
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
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Author : Stanley R. Deans
language : en
Publisher: Courier Corporation
Release Date : 2007-10-01
The Radon Transform And Some Of Its Applications written by Stanley R. Deans and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-01 with Mathematics categories.
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.
Introduction To The Mathematics Of Medical Imaging
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Author : Charles L. Epstein
language : en
Publisher: SIAM
Release Date : 2008-01-01
Introduction To The Mathematics Of Medical Imaging written by Charles L. Epstein and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.
At the heart of every medical imaging technology is a sophisticated mathematical model of the measurement process and an algorithm to reconstruct an image from the measured data. This book provides a firm foundation in the mathematical tools used to model the measurements and derive the reconstruction algorithms used in most of these modalities. The text uses X-ray computed tomography (X-ray CT) as a 'pedagogical machine' to illustrate important ideas and its extensive discussion of background material makes the more advanced mathematical topics accessible to people with a less formal mathematical education. This new edition contains a chapter on magnetic resonance imaging (MRI), a revised section on the relationship between the continuum and discrete Fourier transforms, an improved description of the gridding method, and new sections on both Grangreat's formula and noise analysis in MR-imaging. Mathematical concepts are illuminated with over 200 illustrations and numerous exercises.
Microlocal Analysis And Inverse Problems In Tomography And Geometry
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Author : Eric Todd Quinto
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-09-23
Microlocal Analysis And Inverse Problems In Tomography And Geometry written by Eric Todd Quinto and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-23 with Mathematics categories.
Microlocal Analysis has proven to be a powerful tool for analyzing and solving inverse problems; including answering questions about stability, uniqueness, recovery of singularities, etc. This volume, presents several studies on microlocal methods in problems in tomography, integral geometry, geodesic transforms, travel time tomography, thermoacoustic tomography, Compton CT, cosmology, nonlinear inverse problems, and others.