On artifacts in limited data spherical Radon transform: curved observation surface
We study the limited data problem of the spherical Radon transform in two and three-dimensional spaces with general acquisition surfaces. In such situations, it is known that the application of filtered-backprojection reconstruction formulas might generate added artifacts and degrade the quality of...
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Published in | Inverse problems Vol. 32; no. 1; pp. 15012 - 15043 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
IOP Publishing
01.01.2016
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Subjects | |
Online Access | Get full text |
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Summary: | We study the limited data problem of the spherical Radon transform in two and three-dimensional spaces with general acquisition surfaces. In such situations, it is known that the application of filtered-backprojection reconstruction formulas might generate added artifacts and degrade the quality of reconstructions. In this article, we explicitly analyze a family of such inversion formulas, depending on a smoothing function that vanishes to order k on the boundary of the acquisition surfaces. We show that the artifacts are k orders smoother than their generating singularity. Moreover, in two-dimensional space, if the generating singularity is conormal satisfying a generic condition then the artifacts are even orders smoother than the generating singularity. Our analysis for three-dimensional space contains an important idea of lifting up space. We also explore the theoretical findings in a series of numerical experiments. Our experiments show that a good choice of the smoothing function leads to a significant improvement of reconstruction quality. |
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Bibliography: | IP-100668.R1 ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
ISSN: | 0266-5611 1361-6420 |
DOI: | 10.1088/0266-5611/32/1/015012 |