Efficient and accurate computation of spherical mean values at scattered center points

Torsten Görner; Ralf Hielscher; Stefan Kunis

doi:10.3934/ipi.2012.6.645

Article Contents

2012, Volume 6, Issue 4: 645-661. Doi: 10.3934/ipi.2012.6.645

This issue Previous Article Global minimization of Markov random fields with applications to optical flow Next Article Simultaneous determination of the diffusion and absorption coefficient from boundary data

Efficient and accurate computation of spherical mean values at scattered center points

1.
University Osnabrück, Institute of Mathematics, 49069 Osnabrück
2.
University Chemnitz, Department of Mathematics, 09107 Chemnitz
3.
University Osnabrück, Institute of Mathematics, 49069 Osnabrück, and, Helmholtz Zentrum München, Institute for Biomathematics and Biometry, 85764 Neuherberg

Received: November 30, 2011

Revised: August 31, 2012

Published: October 2012

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Abstract

Spherical means are a widespread model in modern imaging modalities like photoacoustic tomography. Besides direct inversion methods for specific geometries, iterative methods are often used as reconstruction scheme such that each iteration asks for the efficient and accurate computation of spherical means. We consider a spectral discretization via trigonometric polynomials such that the computation can be done via nonequispaced fast Fourier transforms. Moreover, a recently developed sparse fast Fourier transform is used in the three dimensional case and gives optimal arithmetic complexity. All theoretical results are illustrated by numerical experiments.

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Mathematics Subject Classification: 65T40, 65T50, 44A12, 92C55.

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