Use of box splines in computer tomography
type: Item
instance of: scholarly article
title: Use of box splines in computer tomography
zbMATH Open document ID: 0916.65125
DOI: 10.1007/BF02684410
author: K. Appert
published in: Computing
publication date: 1999-07-06T00:00:00Z
review text: Numerical computerized tomography tackles the problem of constructing an approximation \(f^*\) of \(f\) from a finite set of measurements of \(Rf\). The approximation \(f^*\) of \(f\) belongs to the space of box splines. Box splines are attractive multivariate approximations, since they possess good approximation power and can be evaluated very efficiently. The author wants to give an idea of how their qualities can be made to come into play in the field of image reconstruction in computerized tomography. To keep the exposition simple, he concentrates on a special situation: His tomograph is characterized by the bivariate standard scanning geometry and his reconstructions always lie in scales of the linear space spanned by the integer translates of a fixed piecewise quadratic box produces approximations of optimal order for the box splines used, whilst the amount of computational work required is of no higher-order than for classical Fourier reconstruction. The author presents another reconstruction procedure based on quasi-interpolation, which compares to filtered backprojection in computational complexity. Along with his exposition, he gives a generalization of a certain theorem due to \textit{Y. Nievergelt} [SIAM Rev. 28, 79-84 (1986; Zbl 0623.65139)] which may be of interest of practical applications.
reviewed by: R. S. Dahiya
Mathematics Subject Classification ID: 65R10
Mathematics Subject Classification ID: 65R30
Mathematics Subject Classification ID: 44A12
zbMATH DE Number: 1220841
zbMATH Keywords: numerical computerized tomography
zbMATH Keywords: box splines
zbMATH Keywords: image reconstruction
zbMATH Keywords: Fourier reconstruction
zbMATH Keywords: quasi-interpolation
zbMATH Keywords: filtered backprojection
zbMATH Keywords: computational complexity
MaRDI profile type: Publication
cites work: Q4112369
cites work: Recurrence Relations for Multivariate B-Splines
cites work: B-splines from parallelepipeds
cites work: Box splines
cites work: A characterization of multivariate quasi-interpolation formulas and its applications
cites work: Q3754464
cites work: Elementary Inversion of Radon’s Transform
cites work: Q4877221
cites work: Q3895980
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description: scientific article; zbMATH DE number 1220841