The Radon Transform And Local Tomography

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The Radon Transform and Local Tomography

Alexander G. Ramm,Alex I. Katsevich
The Radon Transform and Local Tomography Book PDF

Author : Alexander G. Ramm,Alex I. Katsevich
Publisher : CRC Press
Page : 516 pages
File Size : 53,9 Mb
Release : 2020-07-16
Category : Mathematics
ISBN : 9781000151770

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The Radon Transform and Local Tomography by Alexander G. Ramm,Alex I. Katsevich Pdf

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

Alexander G. Ramm,Alex I. Katsevich
The Radon Transform and Local Tomography Book PDF

Author : Alexander G. Ramm,Alex I. Katsevich
Publisher : CRC Press
Page : 512 pages
File Size : 53,9 Mb
Release : 2020-07-16
Category : Mathematics
ISBN : 9781000108620

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The Radon Transform and Local Tomography by Alexander G. Ramm,Alex I. Katsevich Pdf

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, Inverse Problems, and Tomography

Gestur Ólafsson,Eric Todd Quinto
The Radon Transform Inverse Problems and Tomography Book PDF

Author : Gestur Ólafsson,Eric Todd Quinto
Publisher : American Mathematical Soc.
Page : 176 pages
File Size : 45,8 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.

Radon Transforms and Tomography

Eric Todd Quinto
Radon Transforms and Tomography Book PDF

Author : Eric Todd Quinto
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 48,9 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.

The Radon Transform, Inverse Problems, and Tomography

Gestur îlafsson Eric Todd Quinto
The Radon Transform Inverse Problems and Tomography Book PDF

Author : Gestur îlafsson Eric Todd Quinto
Publisher : American Mathematical Soc.
Page : 186 pages
File Size : 55,5 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.

The Universality of the Radon Transform

Leon Ehrenpreis
The Universality of the Radon Transform Book PDF

Author : Leon Ehrenpreis
Publisher : OUP Oxford
Page : 740 pages
File Size : 49,9 Mb
Release : 2003-10-02
Category : Mathematics
ISBN : 9780191523267

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The Universality of the Radon Transform by Leon Ehrenpreis Pdf

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. The first part of the book discusses parametric and nonparametric Radon transforms, Harmonic Functions and Radon transform on Algebraic Varieties, nonlinear Radon and Fourier transforms, Radon transform on groups, and Radon transform as the interrelation of geometry and analysis. The later parts discuss the extension of solutions of differential equations, Periods of Eisenstein and Poincaré, and some problems of integral geometry arising in tomography. Examples and proofs are provided throughout the book to aid the reader's understanding. This is the latest title in the Oxford Mathematical Monographs, which includes texts and monographs covering many topics of current research interest in pure and applied mathematics. Other titles include: Carbone and Semmes: A graphic apology for symmetry and implicitness; Higson and Roe: Analytic K-Homology; Iwaniec and Martin: Geometric Function Theory and Nonlinear Analysis; Lyons and Qian: System Control and Rough Paths. Also new in paperback Johnson and Lapidus: The Feynman Integral and Feynman's Operational Calculus; Donaldson and Kronheimer: The geometry of four-manifolds.

Analytic Tomography

Andrew Markoe
Analytic Tomography Book PDF

Author : Andrew Markoe
Publisher : Unknown
Page : 409 pages
File Size : 42,5 Mb
Release : 2014-05-14
Category : Electronic
ISBN : 1107398746

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Analytic Tomography by Andrew Markoe Pdf

This 2006 study contains elementary introductions to properties of the Radon transform plus coverage of more advanced topics.

The Radon Transform and Medical Imaging

Peter Kuchment
The Radon Transform and Medical Imaging Book PDF

Author : Peter Kuchment
Publisher : SIAM
Page : 238 pages
File Size : 40,8 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.

Encyclopaedia of Mathematics, Supplement III

Michiel Hazewinkel
Encyclopaedia of Mathematics Supplement III Book PDF

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 564 pages
File Size : 52,8 Mb
Release : 2007-11-23
Category : Mathematics
ISBN : 9780306483738

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Encyclopaedia of Mathematics, Supplement III by Michiel Hazewinkel Pdf

This is the third supplementary volume to Kluwer's highly acclaimed twelve-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.

Wavelets in Medicine and Biology

Akram Aldroubi,Michael Unser
Wavelets in Medicine and Biology Book PDF

Author : Akram Aldroubi,Michael Unser
Publisher : Routledge
Page : 597 pages
File Size : 51,8 Mb
Release : 2017-11-22
Category : Mathematics
ISBN : 9781351404716

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Wavelets in Medicine and Biology by Akram Aldroubi,Michael Unser Pdf

Considerable attention from the international scientific community is currently focused on the wide ranging applications of wavelets. For the first time, the field's leading experts have come together to produce a complete guide to wavelet transform applications in medicine and biology. Wavelets in Medicine and Biology provides accessible, detailed, and comprehensive guidelines for all those interested in learning about wavelets and their applications to biomedical problems.

The Radon Transform

Sigurdur Helgason
The Radon Transform Book PDF

Author : Sigurdur Helgason
Publisher : Springer Science & Business Media
Page : 193 pages
File Size : 41,6 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781475714630

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The Radon Transform by Sigurdur Helgason Pdf

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.

Transforms and Applications Handbook

Alexander D. Poularikas
Transforms and Applications Handbook Book PDF

Author : Alexander D. Poularikas
Publisher : CRC Press
Page : 911 pages
File Size : 49,8 Mb
Release : 2018-09-03
Category : Mathematics
ISBN : 9781420066531

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Transforms and Applications Handbook by Alexander D. Poularikas Pdf

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.

Partial Differential Equations and Inverse Problems

Carlos Conca
Partial Differential Equations and Inverse Problems Book PDF

Author : Carlos Conca
Publisher : American Mathematical Soc.
Page : 426 pages
File Size : 47,7 Mb
Release : 2004
Category : Differential equations, Partial
ISBN : 9780821834480

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Partial Differential Equations and Inverse Problems by Carlos Conca Pdf

This proceedings volume is a collection of articles from the Pan-American Advanced Studies Institute on partial differential equations, nonlinear analysis and inverse problems held in Santiago (Chile). Interactions among partial differential equations, nonlinear analysis, and inverse problems have produced remarkable developments over the last couple of decades. This volume contains survey articles reflecting the work of leading experts who presented minicourses at the event. Contributors include J. Busca, Y. Capdeboscq, M.S. Vogelius, F. A. Grunbaum, L. F. Matusevich, M. de Hoop, and P. Kuchment. The volume is suitable for graduate students and researchers interested in partial differential equations and their applications in nonlinear analysis and inverse problems.

Inverse Problems, Tomography, and Image Processing

Alexander G. Ramm
Inverse Problems Tomography and Image Processing Book PDF

Author : Alexander G. Ramm
Publisher : Springer Science & Business Media
Page : 262 pages
File Size : 52,8 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

Inside Out

Gunther Uhlmann
Inside Out Book PDF

Author : Gunther Uhlmann
Publisher : Cambridge University Press
Page : 424 pages
File Size : 48,5 Mb
Release : 2003-11-10
Category : Mathematics
ISBN : 0521824699

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Inside Out by Gunther Uhlmann Pdf

In this book, leading experts in the theoretical and applied aspects of inverse problems offer extended surveys on several important topics.