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An Improved Extrapolation Scheme for Truncated CT Data Using 2D Fourier-Based Helgason-Ludwig Consistency Conditions

Please always quote using this URN: urn:nbn:de:bvb:29-opus4-95048
  • We improve data extrapolation for truncated computed tomography (CT) projections by using Helgason-Ludwig (HL) consistency conditions that mathematically describe the overlap of information between projections. First, we theoretically derive a 2D Fourier representation of the HL consistency conditions from their original formulation (projection moment theorem), for both parallel-beam and fan-beam imaging geometry. The derivation result indicates that there is a zero energy region forming a double-wedge shape in 2D Fourier domain. This observation is also referred to as the Fourier property of a sinogram in the previous literature. The major benefit of this representation is that theWe improve data extrapolation for truncated computed tomography (CT) projections by using Helgason-Ludwig (HL) consistency conditions that mathematically describe the overlap of information between projections. First, we theoretically derive a 2D Fourier representation of the HL consistency conditions from their original formulation (projection moment theorem), for both parallel-beam and fan-beam imaging geometry. The derivation result indicates that there is a zero energy region forming a double-wedge shape in 2D Fourier domain. This observation is also referred to as the Fourier property of a sinogram in the previous literature. The major benefit of this representation is that the consistency conditions can be efficiently evaluated via 2D fast Fourier transform (FFT). Then, we suggest a method that extrapolates the truncated projections with data from a uniform ellipse of which the parameters are determined by optimizing these consistency conditions. The forward projection of the optimized ellipse can be used to complete the truncation data. The proposed algorithm is evaluated using simulated data and reprojections of clinical data. Results show that the root mean square error (RMSE) is reduced substantially, compared to a state-of-the-art extrapolation method.show moreshow less

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Metadaten
Author:Yan Xia, Martin Berger, Sebastian Bauer, Shiyang Hu, Andre Aichert, Andreas Maier
Persistent identifiers - URN:urn:nbn:de:bvb:29-opus4-95048
Persistent identifiers - DOI:https://doi.org/10.1155/2017/1867025
Title of the journal / compilation (English):International Journal of Biomedical Imaging
Document Type:Article
Language:English
Year of publication:2017
Date of online publication (Embargo Date):2018/03/12
Publishing Institution:Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)
Release Date:2018/03/15
SWD-Keyword:-
Volume/year:2017
Original publication:International Journal of Biomedical Imaging 2017 (2017). <https://www.hindawi.com/journals/ijbi/2017/1867025/>
Institutes:Technische Fakultät
Dewey Decimal Classification:0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 000 Informatik, Informationswissenschaft, allgemeine Werke
open_access (DINI-Set):open_access
Collections:Universität Erlangen-Nürnberg / Von der FAU geförderte Open Access Artikel / Von der FAU geförderte Open Access Artikel 2017
Licence (German):Creative Commons - CC BY - Namensnennung 4.0 International