The Radon Transform

Author : Sigurdur Helgason
Publisher : Springer Science & Business Media
ISBN 13 : 1475714637
Total Pages : 203 pages
Book Rating : 4.30/5 ( download)

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Download or read book The Radon Transform written by Sigurdur Helgason and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
ISBN 13 : 0486462412
Total Pages : 306 pages
Book Rating : 4.17/5 ( download)

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Download or read book The Radon Transform and Some of Its Applications written by Stanley R. Deans and published by Courier Corporation. This book was released on 2007-10-01 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Ronny Ramlau
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311055951X
Total Pages : 469 pages
Book Rating : 4.14/5 ( download)

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Download or read book The Radon Transform written by Ronny Ramlau and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-06-17 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Peter Kuchment
Publisher : SIAM
ISBN 13 : 1611973295
Total Pages : 238 pages
Book Rating : 4.97/5 ( download)

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Download or read book The Radon Transform and Medical Imaging written by Peter Kuchment and published by SIAM. This book was released on 2014-01-01 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Sigurdur Helgason
Publisher : Springer Science & Business Media
ISBN 13 : 1441960546
Total Pages : 309 pages
Book Rating : 4.42/5 ( download)

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Download or read book Integral Geometry and Radon Transforms written by Sigurdur Helgason and published by Springer Science & Business Media. This book was released on 2010-11-17 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Leon Ehrenpreis
Publisher : OUP Oxford
ISBN 13 : 9780198509783
Total Pages : 746 pages
Book Rating : 4.82/5 ( download)

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Download or read book The Universality of the Radon Transform written by Leon Ehrenpreis and published by OUP Oxford. This book was released on 2003 with total page 746 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Jorge L.C. Sanz
Publisher : Springer Science & Business Media
ISBN 13 : 3642730124
Total Pages : 126 pages
Book Rating : 4.22/5 ( download)

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Download or read book Radon and Projection Transform-Based Computer Vision written by Jorge L.C. Sanz and published by Springer Science & Business Media. This book was released on 2013-03-07 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Alexander G. Ramm
Publisher : CRC Press
ISBN 13 : 1000151778
Total Pages : 516 pages
Book Rating : 4.70/5 ( download)

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Download or read book The Radon Transform and Local Tomography written by Alexander G. Ramm and published by CRC Press. This book was released on 2020-07-16 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Gaik Ambartsoumian
Publisher : World Scientific
ISBN 13 : 9811242453
Total Pages : 248 pages
Book Rating : 4.58/5 ( download)

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Download or read book Generalized Radon Transforms And Imaging By Scattered Particles: Broken Rays, Cones, And Stars In Tomography written by Gaik Ambartsoumian and published by World Scientific. This book was released on 2023-03-14 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Boris Rubin
Publisher : Cambridge University Press
ISBN 13 : 0521854598
Total Pages : 595 pages
Book Rating : 4.97/5 ( download)

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Download or read book Introduction to Radon Transforms written by Boris Rubin and published by Cambridge University Press. This book was released on 2015-11-12 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to basic operators of integral geometry and the relevant harmonic analysis for students and researchers.