Quadrature formula for computed tomography
type: Item
instance of: scholarly article
title: Quadrature formula for computed tomography
zbMATH Open document ID: 1209.33006
author: Guergana Petrova
author: Borislav D. Bojanov
published in: Journal of Approximation Theory
publication date: 2010-11-18T00:00:00Z
review text: The authors present a Gaussian quadrature formula for integrals of the form \[ \int_B f(x,y) U_n(x\cos\theta+y\sin\theta)\,dx\,dy \] over the unit disk \(B\) for the Chebyshev polynomials \(U_n\) of second kind. The formula involves \(n\) Radon projections on \(B\), has the maximal degree \(3n+1\) of precision, and is unique by this property. It may be seen as a two-dimensional extension of a formula of Micchelli-Rivlin on \([-1, 1]\) for the \(U_n\).
reviewed by: Michael Voit
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 65D32
zbMATH DE Number: 5817260
zbMATH Keywords: Gaussian quadrature on the unit disk
zbMATH Keywords: Radon projections
zbMATH Keywords: Chebyshev polynomials
MaRDI profile type: Publication
full work available at URL: j.jat.2009.08.003
OpenAlex ID: W2168384487
cites work: A new approach to the reconstruction of images from Radon projections
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DOI: 10.1016/J.JAT.2009.08.003
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description: scientific article; zbMATH DE number 5817260