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Sunday, October 11, 2020 | History

6 edition of The radon transform, inverse problems, and tomography found in the catalog.

The radon transform, inverse problems, and tomography

American Mathematical Society short course, January 3-4, 2005, Atlanta, Georgia

  • 225 Want to read
  • 31 Currently reading

Published by American Mathematical Society in Providence, R.I .
Written in English

    Subjects:
  • Radon transforms -- Congresses,
  • Imaging systems in medicine -- Congresses,
  • Inverse problems (Differential equations) -- Congresses,
  • Integral transforms -- Congresses,
  • Sampling (Statistics) -- Congresses,
  • Wavelets (Mathematics) -- Congresses

  • Edition Notes

    Includes bibliographical references and index.

    StatementGestur Ólafsson, Eric Todd Quinto, editors.
    GenreCongresses.
    SeriesProceedings of symposia in applied mathematics,, v. 63., AMS short course lecture notes, Proceedings of symposia in applied mathematics ;, v. 63., Proceedings of symposia in applied mathematics.
    ContributionsÓlafsson, Gestur., Quinto, Eric Todd, 1951-, American Mathematical Society.
    Classifications
    LC ClassificationsQA672 .R33 2006
    The Physical Object
    Paginationp. cm.
    ID Numbers
    Open LibraryOL3431469M
    ISBN 100821839306
    LC Control Number2005057107

    Radon transform. The Radon Transform allows us to create \ lm images" of objects that are very similar to those actually occurring in x-rays or CT scans. The inverse problem allows us to convert Radon transforms back into attenuation coe cients using the inverse Radon transform{to reconstruct the body from a CT scan. Thesis Objectives. Download The Radon Transform And Local Tomography books, 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.

    Contents: Theoretical Aspects: : Helgason' s support theorem for Radon transforms-a newproof and a generalization : Singular value de- compositions for Radon transforms- : Image recon- struction in Hilbert space etov: A problem of in- tegral geometry for a family of rays with multiple reflec- tions -V.P.   This is the required formula for inversion of the Radon transform. Here is the recipe: given the Radon transform, a function of polar coordinates, Take the 1D Fourier transform with respect to the radial variable ; Multiply each component by the absolute value of frequency ; Take the inverse Fourier transform; Take the back projection.

    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 , , brings together articles on mathematical aspects of tomography and related inverse problems. The Radon transform fits badly Single Photon Emission Tomography (SPECT). However, Thin Holes Collimator (THC) and Radon model are widely used. The CACAO project has been proposed to enhance the quality of SPECT images. CACAO is a short hand notation for computer aided collimation tomography. The main idea of this project is to use collimators with much larger holes to increase the .


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The radon transform, inverse problems, and tomography Download PDF EPUB FB2

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, brings together articles on mathematical aspects of tomography and related inverse problems.

The Radon Transform, Inverse Problems, and Tomography Gestur Olafsson and Eric Todd Quinto (Editor) (ed.) Since their emergence intomography and inverse problems remain active and important fields that combine pure and applied mathematics and provide strong interplay between diverse mathematical problems and applications.

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,brings together articles on mathematical aspects of tomography and related inverse problems.

The articles cover introductory material, theoretical. In mathematics, the Radon transform is the integral transform which takes a function f defined on the plane to a function Rf defined on the (two-dimensional) space of lines in the plane, whose value at a particular line is equal to the line integral of the function over that line.

The transform was introduced in by Johann Radon, who also provided a formula for the inverse transform. The Radon Transform, Inverse Problems, and Tomography About this Title.

Gestur Ólafsson, Louisiana State University, Baton Rouge, LA and Eric Todd Quinto, Tufts University, Medford, MA, Editors. Publication: Proceedings and tomography book Symposia in Applied MathematicsCited by: This thesis is devoted to studies of inverse problems for weighted Radon tranforms in euclidean spaces.

On one hand, our studies are motivated by applications of weighted Radon transforms in. Inverse Problems is pleased to announce the following upcoming special issue celebrating years of the Radon transform. This special issue is now open for submissions via our submissions page.

We also kindly ask you to distribute this call among all colleagues who might be interested in submitting their work. Keywords: radon transform, tomography, medical imaging, inverse problems - Hide Description 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.

The circular and spherical Radon transforms have been used in ultrasound reflection tomography, as well as in thermo- and photo-acoustic tomography. Recent developments in imaging technology based on particle scattering, such as Compton cameras, single-scattering optical tomography, and so forth, have led to the study of broken-ray transform.

Tomographic reconstruction is a type of multidimensional inverse problem where the challenge is to yield an estimate of a specific system from a finite number of mathematical basis for tomographic imaging was laid down by Johann Radon.A notable example of applications is the reconstruction of computed tomography (CT) where cross-sectional images of patients are obtained.

Scientists discover defects in objects, the topography of the ocean floor, and geological information using X-rays, geophysical measurements, sonar, or other 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.

The Radon transform is the mathematical basis of computed tomography and finds application in many other medical imaging modalities as well. In this chapter we present the fundamental mathematics of this transform and its inverse, with emphasis on the central-slice theorem.

Single-photon emission computed tomography by inverting the attenuated Radon transform with least-squares collocation, Inverse problems2, pp. Ryan Walker CT Scans and an Introduction to Inverse Problems Inverse Problems CT Inverse Problem Reconstruction Advanced Issues References Radon Transform Sinograms The Inverse Problem for CT We want to nd (x) which is essentially a proxy for the density of the patient’s head in the slice at the point x.

MS Radon-type transforms: Basis for Emerging Imaging Organizers: Bernadette Hahn and Gaël Rigaud Room: UC G; MS Theory and numerical methods for inverse problems and tomography Organizer: Michael V. Klibanov Room: SP2 ; Fri, March 31; – Plenary Talk: Frank Natterer Wave equation imaging by the Kaczmarz method.

Tomography with incomplete data The exterior Radon transform is the transform R as a map from integrable functions on E to integrable functions on E‘.The problem posed in the first sentence of this article, recovering a function defined outside a disc from integrals over lines not.

Radon Transform and Local Tomography presents new theories and computational methods that cannot be found in any other book.

New material, aimed at solving important problems in tomographic imaging and image processing in general, as well as detailed descriptions of the new algorithms and the results of their testing, are expertly covered.

The Radon transform is a linear transform that integrates a real-valued function on a d-dimensional Euclidean space over all possible (d − 1)-dimensional hyperplanes.

The transform is a widely used model in tomography, and many inverse problems involving the transform or its variant have been carefully studied. Radon transform. In computed tomography, the tomography reconstruction problem is to obtain a tomographic slice image from a set of projections 1.A projection is formed by drawing a set of parallel rays through the 2D object of interest, assigning the integral of the object’s contrast along each ray to a single pixel in the projection.

Sampling, wavelets, and tomography are three active areas of contemporary mathematics sharing common roots that lie at the heart of harmonic and Fourier analysis. The advent of new techniques in mathematical analysis has strengthened their interdependence and led to some new and interesting results in the field.

This state-of-the-art book not only presents new results in these research areas. C.A. Berenstein, D. WalnutLocal inversion of the Radon transform in even dimensions using wavelets S. Gindikin, P. Michor (Eds.), 75 Years of Radon Transform, International Press, Cambridge (), pp. The Radon transform of an integrable function over ℝ 2 is the integral of that function over lines.

A key application of the Radon transform is tomography where the interior density of a 2-D object (e.g., slices of a 3-D object) is reconstructed from its Radon transform data.This article provides an introduction to the mathematics behind X-ray tomography.

After explaining the mathematical model, we will consider some of the fundamental theoretical ideas in the field, including the projection slice theorem, range theorem, inversion formula, and microlocal properties of the underlying Radon transform.

We will use this microlocal analysis to predict which.