Efficient and accurate computation of spherical mean values at scattered center points
type: Item
instance of: scholarly article
title: Efficient and accurate computation of spherical mean values at scattered center points
zbMATH Open document ID: 1263.65138
author: Torsten Görner
author: Ralf Hielscher
author: Stefan Kunis
published in: Inverse Problems and Imaging
publication date: 2013-03-06T00:00:00Z
review text: From a mathematical point of view (it means without any connection to a practical use described in the summary), the authors consider spherical means defined by \[ f:\mathbb R^d \rightarrow \mathbb R,\quad Mf(y,r)=\frac 1 {\omega_{d-1}} \int_{S^{d-1}}f(y+r\xi)d\sigma(\xi) \] (centerpoint \(y\in \mathbb R^d\), radius \(r>0\), \(\sigma\) denotes the surface measure on the sphere and \(\omega_{d-1}=\sigma(S^{d-1})\)) and use iterative methods for their computation. A spectral discretization via trigonometric polynomials in such a way that computations can be done via a nonequispaced fast Fourier transform (FFT), however, the sparse FFT is used in the three-dimensional case. The studied theory is illustrated numerically.
Mathematics Subject Classification ID: 65T40
Mathematics Subject Classification ID: 65R10
Mathematics Subject Classification ID: 65T50
Mathematics Subject Classification ID: 44A12
Mathematics Subject Classification ID: 92C55
Mathematics Subject Classification ID: 42A10
zbMATH DE Number: 6141949
zbMATH Keywords: spherical means
zbMATH Keywords: trigonometric approximation
zbMATH Keywords: fast Fourier transform
zbMATH Keywords: tomography
zbMATH Keywords: numerical examples
reviewed by: Josef Kofroň
describes a project that uses: NFFT3
describes a project that uses: ShearLab
describes a project that uses: NFFT
describes a project that uses: Wavelet and Multiscale Library
MaRDI profile type: Publication
full work available at URL: ipi.2012.6.645
OpenAlex ID: W2316101443
DOI: 10.3934/IPI.2012.6.645
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description: scientific article; zbMATH DE number 6141949