Introduction To Radon Transforms

Author : Sigurdur Helgason
Publisher : Springer Science & Business Media
Page : 193 pages
File Size : 45,7 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.

Author : Stanley R. Deans
Publisher : Courier Corporation
Page : 306 pages
File Size : 53,7 Mb
Release : 2007-10-01
Category : Mathematics
ISBN : 9780486462417

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The Radon Transform and Some of Its Applications by Stanley R. Deans Pdf

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.

Author : Boris Rubin
Publisher : Cambridge University Press
Page : 595 pages
File Size : 50,6 Mb
Release : 2015-11-12
Category : Mathematics
ISBN : 9780521854597

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Introduction to Radon Transforms by Boris Rubin Pdf

A comprehensive introduction to basic operators of integral geometry and the relevant harmonic analysis for students and researchers.

Author : Sigurdur Helgason
Publisher : Springer Science & Business Media
Page : 214 pages
File Size : 52,6 Mb
Release : 1999-08-01
Category : Mathematics
ISBN : 0817641092

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The Radon Transform by Sigurdur Helgason Pdf

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.

Author : Sigurdur Helgason
Publisher : Springer Science & Business Media
Page : 309 pages
File Size : 41,9 Mb
Release : 2010-11-17
Category : Mathematics
ISBN : 9781441960542

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Integral Geometry and Radon Transforms by Sigurdur Helgason Pdf

In this text, integral geometry deals with Radon’s problem of representing a function on a manifold in terms of its integrals over certain submanifolds—hence the term the Radon transform. Examples and far-reaching generalizations lead to fundamental problems such as: (i) injectivity, (ii) inversion formulas, (iii) support questions, (iv) applications (e.g., to tomography, partial di erential equations and group representations). For the case of the plane, the inversion theorem and the support theorem have had major applications in medicine through tomography and CAT scanning. While containing some recent research, the book is aimed at beginning graduate students for classroom use or self-study. A number of exercises point to further results with documentation. From the reviews: “Integral Geometry is a fascinating area, where numerous branches of mathematics meet together. the contents of the book is concentrated around the duality and double vibration, which is realized through the masterful treatment of a variety of examples. the book is written by an expert, who has made fundamental contributions to the area.” —Boris Rubin, Louisiana State University

Author : Ronny Ramlau,Otmar Scherzer
Publisher : Walter de Gruyter GmbH & Co KG
Page : 469 pages
File Size : 53,9 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 : Andrew Markoe
Publisher : Cambridge University Press
Page : 358 pages
File Size : 42,6 Mb
Release : 2006-01-23
Category : Mathematics
ISBN : 9780521793476

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Analytic Tomography by Andrew Markoe Pdf

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

Author : Peter Kuchment
Publisher : SIAM
Page : 238 pages
File Size : 44,6 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 : Leon Ehrenpreis
Publisher : OUP Oxford
Page : 746 pages
File Size : 47,8 Mb
Release : 2003
Category : Mathematics
ISBN : 0198509782

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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.

Author : A. G. Ramm,Alex I. Katsevich
Publisher : CRC Press
Page : 512 pages
File Size : 40,9 Mb
Release : 2020-06-30
Category : Geometric tomography
ISBN : 036744867X

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The Radon Transform and Local Tomography by A. 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.

Author : Charles L. Epstein
Publisher : SIAM
Page : 794 pages
File Size : 54,5 Mb
Release : 2008-01-01
Category : Mathematics
ISBN : 0898717795

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Introduction to the Mathematics of Medical Imaging by Charles L. Epstein Pdf

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.

Author : Jorge L.C. Sanz,Eric B. Hinkle,Anil K. Jain
Publisher : Springer Science & Business Media
Page : 126 pages
File Size : 41,7 Mb
Release : 2013-03-07
Category : Computers
ISBN : 9783642730122

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Radon and Projection Transform-Based Computer Vision by Jorge L.C. Sanz,Eric B. Hinkle,Anil K. Jain Pdf

This book deals with novel machine vision architecture ideas that make real-time projection-based algorithms a reality. The design is founded on raster-mode processing, which is exploited in a powerful and flexible pipeline. We concern ourselves with several image analysis algorithms for computing: projections of gray-level images along linear patterns (i. e. , the Radon transform) and other curved contours; convex hull approximations; the Hough transform for line and curve detection; diameters; moments and principal components, etc. Addition ally, we deal with an extensive list of key image processing tasks, which involve generating: discrete approximations of the inverse Radon transform operator; computer tomography reconstructions; two-dimensional convolutions; rotations and translations; multi-color digital masks; the discrete Fourier transform in polar coordinates; autocorrelations, etc. Both the image analysis and image processing algorithms are supported by a similar architecture. We will also of some of the above algorithms to the solution of demonstrate the applicability various industrial visual inspection problems. The algorithms and architectural ideas surveyed here unleash the power of the Radon and other non-linear transformations for machine vision applications. We provide fast methods to transform images into projection space representa tions and to backtrace projection-space information into the image domain. The novelty of this approach is that the above algorithms are suitable for implementa tion in a pipeline architecture. Specifically, random access memory and other dedicated hardware components which are necessary for implementation of clas sical techniques are not needed for our algorithms.

Author : Elias M. Stein,Rami Shakarchi
Publisher : Princeton University Press
Page : 326 pages
File Size : 54,8 Mb
Release : 2011-02-11
Category : Mathematics
ISBN : 9781400831234

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Fourier Analysis by Elias M. Stein,Rami Shakarchi Pdf

This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions. The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as the isoperimetric inequality and equidistribution. The second part deals with the Fourier transform and its applications to classical partial differential equations and the Radon transform; a clear introduction to the subject serves to avoid technical difficulties. The book closes with Fourier theory for finite abelian groups, which is applied to prime numbers in arithmetic progression. In organizing their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous analysis. Students of mathematics, physics, engineering and other sciences will find the theory and applications covered in this volume to be of real interest. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Fourier Analysis is the first, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.

Author : Anonim
Publisher : Unknown
Page : 400 pages
File Size : 42,7 Mb
Release : 2006
Category : Geometric tomography
ISBN : 1461941474

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Analytic Tomography by Anonim Pdf

Author : National Research Council,Commission on Life Sciences,Board on Radiation Effects Research,Committee on Risk Assessment of Exposure to Radon in Drinking Water
Publisher : National Academies Press
Page : 293 pages
File Size : 53,8 Mb
Release : 1999-06-24
Category : Nature
ISBN : 9780309173674

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Risk Assessment of Radon in Drinking Water by National Research Council,Commission on Life Sciences,Board on Radiation Effects Research,Committee on Risk Assessment of Exposure to Radon in Drinking Water Pdf

The Safe Drinking Water Act directs the U.S. Environmental Protection Agency (EPA) to regulate the quality of drinking water, including its concentration of radon, an acknowledged carcinogen. This book presents a valuable synthesis of information about the total inhalation and ingestion risks posed by radon in public drinking water, including comprehensive reviews of data on the transfer of radon from water to indoor air and on outdoor levels of radon in the United States. It also presents a new analysis of a biokinetic model developed to determine the risks posed by ingestion of radon and reviews inhalation risks and the carcinogenesis process. The volume includes scenarios for quantifying the reduction in health risk that might be achieved by a program to reduce public exposure to radon. Risk Assessment of Radon in Drinking Water, reflecting research and analysis mandated by 1996 amendments to the Safe Drinking Water Act, provides comment on a variety of methods to reduce radon entry into homes and to reduce the concentrations of radon in indoor air and in water. The models, analysis, and reviews of literature contained in this book are intended to provide information that EPA will need to set a new maximum contaminant level, as it is required to do in 2000.