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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 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 k+1/2 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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Metadaten
Author:Lyudmyla L. Barannyk, Jürgen FrikelORCiD, Linh V. Nguyen
DOI:https://doi.org/10.1088/0266-5611/32/1/015012
ISSN:1361-6420
ISSN:0266-5611
Parent Title (German):Inverse Problems
Publisher:Institute of Physics
Place of publication:Bristol [u.a.]
Document Type:Article
Language:German
Year of first Publication:2016
Release Date:2022/11/26
Volume:32
Issue:1
Article Number:015012
Institutes:Fakultät Informatik und Mathematik
Begutachtungsstatus:peer-reviewed
research focus:Produktion und Systeme
Licence (German):Keine Lizenz - Es gilt das deutsche Urheberrecht: § 53 UrhG