Orthogonal function series formulas for inversion of the spherical Radon transform

A spherical Radon transform that averages a function over all spheres centered on a given sphere is related to not only pure but also applied mathematics topics. Especially, the problem of inverting this spherical Radon transform arising in photoacoustic tomography and sonar has been studied in many...

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Bibliographic Details
Published in:Inverse problems 2020-03, Vol.36 (3), p.35007
Main Author: Moon, Sunghwan
Format: Article
Language:English
Subjects:
photoacoustic
Radon transform
singular value decomposition
spherical means
tomography
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Summary:A spherical Radon transform that averages a function over all spheres centered on a given sphere is related to not only pure but also applied mathematics topics. Especially, the problem of inverting this spherical Radon transform arising in photoacoustic tomography and sonar has been studied in many articles. We provide two series formulas for inversion: one does not require the compact support of the source function unlike most inversion formulas and the other is singular value decomposition type, i.e., the series formula is based on the complete orthogonal system. Last, we discuss its continuity.
ISSN:0266-5611
1361-6420
DOI:10.1088/1361-6420/ab6d54