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Theorems that Characterize Artifacts for Arbitrary Limited X-ray CT Data

  • This article provides a mathematical classification of artifacts from arbitrary incom-plete X-ray tomography data when using the classical filtered backprojection algorithm. Usingmicrolocal analysis, we prove that all artifacts arise from points at the boundary of the data set.Our results show that, depending on the geometry of the data set boundary, two types of artifactscan arise: object-dependent and object-independent artifacts. The object-dependent artifacts aregenerated by singularities of the object being scanned and these artifacts can extend all along lines.This is a generalization of the streak artifacts observed in limited angle CT. The article also char-acterizes two new phenomena: the object-independent artifacts are caused only by the geometryof the data set boundary; they occur along lines if the boundary of the data set is not smooth andalong curves if the boundary of the data set is smooth. In addition to the geometric descriptionof artifacts, the article also provides characterizations of their strength in Sobolev scale in certaincases. Moreover, numerical reconstructions from simulated and real data are presented illustratingour theorems.This work is motivated by a reconstruction we present from a synchrotron data set in whichartifacts along lines appeared that were independent of the object.The results of this article apply to a wide range of well-known incomplete data problems, in-cluding limited angle CT and region of interest tomography, as well as to unconventional x-ray CTimaging setups. Some of those problems are explicitly addressed in this article, theoretically and numerically.

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Metadaten
Author:Leise Borg, Jürgen FrikelORCiD, Jakob Jørgensen, Eric Todd Quinto
URL / DOI:https://www.researchgate.net/publication/318360078_Theorems_that_Characterize_Artifacts_for_Arbitrary_Limited_X-ray_CT_Data
ArXiv Id:http://arxiv.org/abs/1707.03055v3
Document Type:Preprint
Language:English
Year of first Publication:2017
Release Date:2022/09/29
Edition:version 6
Institutes:Fakultät Informatik und Mathematik
research focus:Digitalisierung
Licence (German):Keine Lizenz - Es gilt das deutsche Urheberrecht: § 53 UrhG