The Radon Transform And Local Tomography
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The Radon Transform And Local Tomography
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Author : Alexander G. Ramm
language : en
Publisher: CRC Press
Release Date : 1996-02-06
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 1996-02-06 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.
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.
The Radon Transform And Local Tomography
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Author : Alexander G. Ramm
language : en
Publisher:
Release Date : 1996
The Radon Transform And Local Tomography written by Alexander G. Ramm and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with MATHEMATICS categories.
The theory described in this book solves the important problem of finding discontinuities of function from its tomographic data. A detailed theoretical analysis and three different solutions to this problem are given, as well as algorithms for practical solutions and examples of applications for both simulated and real-life data.
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 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.
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 Universality Of The Radon Transform
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Author : Leon Ehrenpreis
language : en
Publisher: Oxford University Press, USA
Release Date : 2003
The Universality Of The Radon Transform written by Leon Ehrenpreis and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
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.
Tomography
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Author : Pierre Grangeat
language : en
Publisher: John Wiley & Sons
Release Date : 2013-03-04
Tomography written by Pierre Grangeat and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-04 with Technology & Engineering categories.
The principle of tomography is to explore the structure and composition of objects non-destructively along spatial and temporal dimensions, using penetrating radiation, such as X- and gamma-rays, or waves, such as electromagnetic and acoustic waves. Based on computer-assisted image reconstruction, tomography provides maps of parameters that characterize the emission of the employed radiation or waves, or their interaction with the examined objects, for one or several cross-sections. Thus, it gives access to the inner structure of inert objects and living organisms in their full complexity. In this book, multidisciplinary specialists explain the foundations and principles of tomographic imaging and describe a broad range of applications. The content is organized in five parts, which are dedicated to image reconstruction, microtomography, industrial tomography, morphological medical tomography and functional medical tomography.
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.
Transforms And Applications Handbook
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Author : Alexander D. Poularikas
language : en
Publisher: CRC Press
Release Date : 2018-09-03
Transforms And Applications Handbook written by Alexander D. Poularikas and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-03 with Mathematics categories.
Updating the original, Transforms and Applications Handbook, Third Edition solidifies its place as the complete resource on those mathematical transforms most frequently used by engineers, scientists, and mathematicians. Highlighting the use of transforms and their properties, this latest edition of the bestseller begins with a solid introduction to signals and systems, including properties of the delta function and some classical orthogonal functions. It then goes on to detail different transforms, including lapped, Mellin, wavelet, and Hartley varieties. Written by top experts, each chapter provides numerous examples and applications that clearly demonstrate the unique purpose and properties of each type. The material is presented in a way that makes it easy for readers from different backgrounds to familiarize themselves with the wide range of transform applications. Revisiting transforms previously covered, this book adds information on other important ones, including: Finite Hankel, Legendre, Jacobi, Gengenbauer, Laguerre, and Hermite Fraction Fourier Zak Continuous and discrete Chirp-Fourier Multidimensional discrete unitary Hilbert-Huang Most comparable books cover only a few of the transforms addressed here, making this text by far the most useful for anyone involved in signal processing—including electrical and communication engineers, mathematicians, and any other scientist working in this field.