Introduction To Radon Transforms
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Introduction To Radon Transforms
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Author : Boris Rubin
language : en
Publisher: Cambridge University Press
Release Date : 2015-11-12
Introduction To Radon Transforms written by Boris Rubin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-12 with Mathematics categories.
A comprehensive introduction to basic operators of integral geometry and the relevant harmonic analysis for students and researchers.
The Radon Transform
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Author : Sigurdur Helgason
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11
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 2013-12-11 with Mathematics categories.
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.
Integral Geometry And Radon Transforms
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Author : Sigurdur Helgason
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-17
Integral Geometry And Radon Transforms 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 2010-11-17 with Mathematics categories.
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
Generalized Radon Transforms And Imaging By Scattered Particles Broken Rays Cones And Stars In Tomography
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Author : Gaik Ambartsoumian
language : en
Publisher: World Scientific
Release Date : 2023-03-14
Generalized Radon Transforms And Imaging By Scattered Particles Broken Rays Cones And Stars In Tomography written by Gaik Ambartsoumian and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-14 with Mathematics categories.
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.
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.
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.
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 And Projection Transform Based Computer Vision
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Author : Jorge L.C. Sanz
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-07
Radon And Projection Transform Based Computer Vision written by Jorge L.C. Sanz 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 2013-03-07 with Computers categories.
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.