EFFICIENT AND ACCURATE COMPUTATION OF SPHERICAL MEAN VALUES AT SCATTERED CENTER POINTS
DC Element | Wert | Sprache |
---|---|---|
dc.contributor.author | Goerner, Torsten | |
dc.contributor.author | Hielscher, Ralf | |
dc.contributor.author | Kunis, Stefan | |
dc.date.accessioned | 2021-12-23T16:17:39Z | - |
dc.date.available | 2021-12-23T16:17:39Z | - |
dc.date.issued | 2012 | |
dc.identifier.issn | 19308337 | |
dc.identifier.uri | https://osnascholar.ub.uni-osnabrueck.de/handle/unios/12350 | - |
dc.description.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. | |
dc.description.sponsorship | DFGGerman Research Foundation (DFG)European Commission [KU 2557/1-2]; Helmholtz grant [VH-NG-526]; German Research FoundationGerman Research Foundation (DFG) [KU 2557/1-2]; Helmholtz AssociationHelmholtz Association [VH-NG-526]; TG and SK are partially supported by DFG grant KU 2557/1-2 and by the Helmholtz grant VH-NG-526.; The authors thank the reviewers for their valuable suggestions and gratefully acknowledge support by the German Research Foundation within the project KU 2557/1-2 and by the Helmholtz Association within the young investigator group VH-NG-526. | |
dc.language.iso | en | |
dc.publisher | AMER INST MATHEMATICAL SCIENCES | |
dc.relation.ispartof | INVERSE PROBLEMS AND IMAGING | |
dc.subject | ALGORITHM | |
dc.subject | CIRCULAR INTEGRATING DETECTORS | |
dc.subject | fast Fourier transform | |
dc.subject | FORMULAS | |
dc.subject | GEOMETRY | |
dc.subject | INVERSION | |
dc.subject | Mathematics | |
dc.subject | Mathematics, Applied | |
dc.subject | PHOTOACOUSTIC TOMOGRAPHY | |
dc.subject | Physics | |
dc.subject | Physics, Mathematical | |
dc.subject | RADON-TRANSFORM | |
dc.subject | RECONSTRUCTION | |
dc.subject | SPARSE FOURIER-TRANSFORM | |
dc.subject | Spherical means | |
dc.subject | THERMOACOUSTIC TOMOGRAPHY | |
dc.subject | tomography | |
dc.subject | trigonometric approximation | |
dc.title | EFFICIENT AND ACCURATE COMPUTATION OF SPHERICAL MEAN VALUES AT SCATTERED CENTER POINTS | |
dc.type | journal article | |
dc.identifier.doi | 10.3934/ipi.2012.6.645 | |
dc.identifier.isi | ISI:000311940500004 | |
dc.description.volume | 6 | |
dc.description.issue | 4 | |
dc.description.startpage | 645 | |
dc.description.endpage | 661 | |
dc.publisher.place | PO BOX 2604, SPRINGFIELD, MO 65801-2604 USA | |
dcterms.isPartOf.abbreviation | Inverse Probl. Imaging | |
dcterms.oaStatus | Green Submitted, hybrid | |
crisitem.author.dept | FB 06 - Mathematik/Informatik | - |
crisitem.author.deptid | fb06 | - |
crisitem.author.parentorg | Universität Osnabrück | - |
crisitem.author.netid | KuSt212 | - |
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