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An efficient algorithm to compute the X-ray transform
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-1118-6483
2021 (English)In: International Journal of Computer Mathematics, ISSN 0020-7160, E-ISSN 1029-0265Article in journal (Refereed) Published
Abstract [en]

We propose a new algorithm to compute the X-ray transform of an image represented by unit (pixel/voxel) basis functions. The fundamental task is equivalently calculating the intersection lengths of the ray with associated units. For the given ray, we derive the sufficient and necessary condition for non-vanishing intersectability. By this condition, we can distinguish the units that produce valid intersections with the ray. Only for those units, we calculate the intersection lengths by the obtained analytic formula. The proposed algorithm is adapted to various two-dimensional (2D)/three-dimensional (3D) scanning geometries, and its several issues are also discussed, including the intrinsic ambiguity, flexibility, computational cost and parallelization. The proposed method is fast and easy to implement, more complete and flexible than the existing alternatives with respect to different scanning geometries and different basis functions. Finally, we validate the correctness of the algorithm.

Place, publisher, year, edition, pages
Informa UK Limited , 2021.
Keywords [en]
65R32, 68U10, 92C55, 94A08, ambiguity and flexibility, intersection length, non-vanishing intersectability, projection matrix, tomographic image reconstruction, X-ray transform, Computerized tomography, Functions, Analytic formula, Computational costs, Intrinsic ambiguities, Parallelizations, Scanning geometry, Sufficient and necessary condition, Two Dimensional (2 D), X-ray transforms, X rays
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:kth:diva-311206DOI: 10.1080/00207160.2021.1969017ISI: 000690307600001Scopus ID: 2-s2.0-85113620599OAI: oai:DiVA.org:kth-311206DiVA, id: diva2:1653208
Note

QC 20220421

Available from: 2022-04-21 Created: 2022-04-21 Last updated: 2022-06-25Bibliographically approved

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Öktem, Ozan

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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf