Last edited by Nekree
Monday, May 18, 2020 | History

5 edition of The Radon Transform (Progress in Mathematics) found in the catalog.

# The Radon Transform (Progress in Mathematics)

## by Sigurdur Helgason

Written in English

Subjects:
• Differential & Riemannian geometry,
• Differential Geometry,
• Mathematics,
• Science/Mathematics,
• Applied,
• Calculus,
• Probability & Statistics - General,
• Mathematics / Applied,
• Mathematics / Mathematical Analysis,
• Mathematics : Calculus,
• Mathematics : Probability & Statistics - General,
• Geometry - Differential

• The Physical Object
FormatHardcover
Number of Pages188
ID Numbers
Open LibraryOL8074651M
ISBN 100817641092
ISBN 109780817641092

the Radon transform). In this paper, the author has decided to use functions of certain classesde•nedinclass. Unlessstatedotherwise,all f 2S(Rn)orD(Rn). Respectively, Schwartz functions and functions of compact support. For reference on the generaliza-tions of the transform and applications to integral geometry, see −e Radon TransformFile Size: KB. Generalized Radon Transforms and Orbital Integrals. Sigurdur Helgason. Back Matter. Pages PDF. About this book. Keywords. analysis electrical engineering engineering integral transform mathematics medicine Radon transform signal processing. Authors and affiliations.

Of value to mathematicians, physicists, engineers, and medical imaging scientists this excellent introduction to Radon transform covers both theory and applications. It also features a rich array of examples and literature that forms a valuable reference. The author, a professor in the Department of Physics at the University of South Florida, wrote this pioneering work in   Of value to mathematicians, physicists, engineers, and medical imaging scientists this excellent introduction to Radon transform covers both theory and applications. It also features a rich array of examples and literature that forms a valuable reference. The author, a professor in the Pages:

The Radon Transform by Sigurdur Helgason. Publisher: Birkhauser Boston ISBN/ASIN: ISBN Number of pages: Description: 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. The plot of the Radon transform, or scanner data, is referred to as a sinogram due to its characteristic sinusoid shape. Figure 2 shows a simple non-homogeneous shape and the sinogram created by taking the Radon transform at intervals of one degree from 0 to degrees.

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Books.

Books.

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 by: The Radon transform is a vital tool mathematical tool in medical imaging.

This book explores the mathematical ideas and techniques behind well-established imaging modalities such as X-ray CT and emission tomography, and newly developing coupled physics or hybrid by:   The Radon Transform book of Contents Preface to the Second Edition.-Preface to the First Edition.-The Radon Transform on R n.- A Duality in Integral Geometry.

Generalized Radon Transforms and Orbital Integrals.-The Radon Transform on Two-Point Homogeneous Spaces.-Orbital Integrals and the Wave Operator for Isotropic Lorentz Spaces.-Fourier Transforms and : Sigurdur Helgason.

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 : Birkhäuser Basel.

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,Brand: Springer US. Abstract. For a given function f defined in the plane, which may represent, for instance, the attenuation-coefficient function in a cross section of a sample, the fundamental question of image reconstruction calls on us to consider the value of the integral of f along a typical line $$\,\ell_{t,\,\theta }$$.For each pair of values of t and $$\,\theta$$, we will integrate f along a different by: 2.

This book discusses the definition of the Radon transform, it's properties, it's relation to other transforms (Fourier, et al.), it's inverse, and so on. It is well documented. (It even contains a translation of Radon's original paper!) This book is the most useful source of such information I've found, so far/5(4).

The Radon transform is a mapping from the Cartesian rectangular coordinates (x,y) to a distance and an angel (ρ,θ), also known as polar coordinates.

An example of the transform of an image for a speciﬁc angle is g iven in Figure on page 6 and Figure on page 7. From Radon to Leray; 4. Integral geometry on manifolds with boundary and applications; 5.

Non-Abelian Radon transform and its applications; 6. Remarks on the second century of the Funk–Radon theory; 7. V-line and conical Radon transforms with applications in imaging; 8. Uncertainty, ghosts, and resolution in Radon problems; 9.

Available in: n by a leading scholar in mathematics, this monograph discusses the Radon transform, a field that has wide rangingPrice: \$ The Radon transform. [Sigurdur Helgason] -- "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.

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 by: The Radon Transform Sigurdur Helgason (auth.) 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.

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.

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 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.

Readers will find here an accessible introduction to Radon transform theory, an elegant topic in integral geometry. 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. x2 The Radon Transform of the Spaces D(Rn) and S(Rn).

The Support Theorem Let fbe a function on Rn, integrable on each hyperplane in Rn. Let Pn denote the space of all hyperplanes in Rn, Pn being furnished with the obvious topology. The Radon transform of f is de ned as the function fb on Pngiven by fb(˘) = Z ˘ f(x)dm(x);File Size: 1MB. A b s tract Th e su b ject of t hi s PhD h esis is m a em ical Radon transform whic w ell suit ed for curv e d et ect ion in digit al im age s an for reconstru ct of Cited by: Years of the Radon Transform.

The Radon Institute of Computational and Applied Mathematics in Linz, Austria, is organizing a conference on the th anniversary of the publication of the famous paper “Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten” in Berichte über die Verhandlungen der Königlich-Sächsischen Gesellschaft der.

The Radon transform. [Sigurdur Helgason] Home. WorldCat Home About WorldCat Help. Search. Search for Library Items Search for Lists Search for Contacts Search for a Library. Create Book: All Authors / Contributors: Sigurdur Helgason. Find more information about: ISBN: OCLC Number:   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 representationsm X-ray technology, nuclear magnetic.to Linz, Austria, and thank you very much for attending the Conference Years of the Radon Transform, organized by the Johann Radon Institute for Computational and Applied Mathematics (RICAM), taking place from March, 27th to March, 31st.