University of Oulu

M Burger et al 2021 Inverse Problems 37 075006.

Sequentially optimized projections in X-ray imaging

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Author: Burger, Martin1; Hauptmann, Andreas2; Helin, Tapio3;
Organizations: 1Friedrich-Alexander-Universitat Erlangen-Nurnberg Technische Fakultat, Cauerstr. 11, Erlangen, 91058, Germany
2Research Unit of Mathematical Sciences, University of Oulu, P.O. Box 3000, Oulu, Pohjois-Pohjanmaa, 90014, Finland
3School of Engineering Science, LUT University, P.O. Box 20, Lappeenranta, 53850, Finland
4Department of Mathematics and Systems Analysis, Aalto University, PO Box 11100, Aalto, 00076, Finland
Format: article
Version: accepted version
Access: embargoed
Persistent link:
Language: English
Published: IOP Publishing, 2021
Publish Date: 2022-06-22


This work applies Bayesian experimental design to selecting optimal projection geometries in (discretized) parallel beam X-ray tomography assuming the prior and the additive noise are Gaussian. The introduced greedy exhaustive optimization algorithm proceeds sequentially, with the posterior distribution corresponding to the previous projections serving as the prior for determining the design parameters, i.e. the imaging angle and the lateral position of the source-receiver pair, for the next one. The algorithm allows redefining the region of interest after each projection as well as adapting parameters in the (original) prior to the measured data. Both A and D-optimality are considered, with emphasis on efficient evaluation of the corresponding objective functions. Two-dimensional numerical experiments demonstrate the functionality of the approach.

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Series: Inverse problems
ISSN: 0266-5611
ISSN-E: 1361-6420
ISSN-L: 0266-5611
Volume: 37
Issue: 7
Article number: 075006
DOI: 10.1088/1361-6420/ac01a4
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Funding: The work of MB was supported by the Bundesministerium für Bildung und Forschung under the project id 05M16PMB (MED4D). The work of AH was supported by the Academy of Finland (decision 312123). The work of TH was supported by the the Academy of Finland (decisions 320082 and 326961). The work of NH and JP was supported by the Academy of Finland (decision 312124).
Academy of Finland Grant Number: 312123
Detailed Information: 312123 (Academy of Finland Funding decision)
Copyright information: © 2021 IOP Publishing Ltd. This is a peer-reviewed, un-copyedited version of an article accepted for publication/published in Inverse Problems. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at