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Analyzing Reconstruction Artifacts from Arbitrary Incomplete X-ray CT Data

  • This article provides a mathematical analysis of singular (nonsmooth) artifacts added to reconstructions by filtered backprojection (FBP) type algorithms for X-ray computed tomography (CT) with arbitrary incomplete data. We prove that these singular artifacts arise from points at the boundary of the data set. Our results show that, depending on the geometry of this boundary, two types of artifacts can arise: object-dependent and object-independent artifacts. Object-dependent artifacts are generated by singularities of the object being scanned, and these artifacts can extend along lines. They generalize the streak artifacts observed in limited-angle tomography. Object-independent artifacts, on the other hand, are essentially independent of the object and take one of two forms: streaks on lines if the boundary of the data set is not smooth at a point and curved artifacts if the boundary is smooth locally. We prove that these streak and curve artifacts are the only singular artifacts that can occur for FBP in the continuous case. In addition to the geometric description of artifacts, the article provides characterizations of their strength in Sobolev scale in certain cases. The results of this article apply to the well-known incomplete data problems, including limited-angle and regionof-interest tomography, as well as to unconventional X-ray CT imaging setups that arise in new practical applications. Reconstructions from simulated and real data are analyzed to illustrate our theorems, including the reconstruction that motivated this work a synchrotron data set in which artifacts appear on lines that have no relation to the object.

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Metadaten
Author:Leise Borg, Jürgen FrikelORCiD, Jakob Sauer Jorgensen, Eric Todd QuintoORCiD
DOI:https://doi.org/10.1137/18M1166833
Parent Title (English):SIAM Journal on Imaging Sciences
Publisher:SIAM PUBLICATIONS
Document Type:Article
Language:English
Year of first Publication:2018
Release Date:2022/03/29
Tag:DATA TOMOGRAPHY; Fourier integral operators; GENERALIZED RADON-TRANSFORM; IMAGE-RECONSTRUCTION; METAL ARTIFACTS; PROJECTIONS; SINGULARITIES; X-ray tomography; incomplete data tomography; limited-angle tomography; microlocal analysis; reconstruction artifact; region-of-interest tomography; wavefront set
Volume:11
Issue:4
First Page:2786
Last Page:2814
Institutes:Fakultät Informatik und Mathematik
Begutachtungsstatus:peer-reviewed
research focus:Digitalisierung
Licence (German):Keine Lizenz - Es gilt das deutsche Urheberrecht: § 53 UrhG