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A continuity flow based tomographic reconstruction algorithm for 4D multi-beam high temporal—low angular sampling

Henningsson, Axel LU and Hall, Stephen A. LU (2021) In Journal of Imaging 7(11).
Abstract

A mathematical framework and accompanying numerical algorithm exploiting the continuity equation for 4D reconstruction of spatiotemporal attenuation fields from multi-angle full-field transmission measurements is presented. The algorithm is geared towards rotation-free dynamic multi-beam X-ray tomography measurements, for which angular information is sparse but the temporal information is rich. 3D attenuation maps are recovered by propagating an initial discretized density volume in time according to the advection equations using the Finite Volumes method with a total variation diminishing monotonic upstream-centered scheme (TVDMUSCL). The benefits and limitations of the algorithm are explored using dynamic granular system phantoms... (More)

A mathematical framework and accompanying numerical algorithm exploiting the continuity equation for 4D reconstruction of spatiotemporal attenuation fields from multi-angle full-field transmission measurements is presented. The algorithm is geared towards rotation-free dynamic multi-beam X-ray tomography measurements, for which angular information is sparse but the temporal information is rich. 3D attenuation maps are recovered by propagating an initial discretized density volume in time according to the advection equations using the Finite Volumes method with a total variation diminishing monotonic upstream-centered scheme (TVDMUSCL). The benefits and limitations of the algorithm are explored using dynamic granular system phantoms modelled via discrete elements and projected by an analytical ray model independent from the numerical ray model used in the reconstruction scheme. Three phantom scenarios of increasing complexity are presented and it is found that projections from only a few (unknowns:equations > 10) angles can be sufficient for characterisation of the 3D attenuation field evolution in time. It is shown that the artificial velocity field produced by the algorithm sub-iteration, which is used to propagate the attenuation field, can to some extent approximate the true kinematics of the system. Furthermore, it is found that the selection of a temporal interpolation scheme for projection data can have a significant impact on error build up in the reconstructed attenuation field.

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author
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organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
4D, Continuity equations, Dynamic, Temporal, Tomography
in
Journal of Imaging
volume
7
issue
11
article number
246
publisher
MDPI AG
external identifiers
  • pmid:34821877
  • scopus:85121369386
ISSN
2313-433X
DOI
10.3390/jimaging7110246
language
English
LU publication?
yes
additional info
Publisher Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland.
id
e8c2c098-bca1-445c-b5b0-6b647226ccab
date added to LUP
2022-01-31 21:19:15
date last changed
2025-01-13 22:29:37
@article{e8c2c098-bca1-445c-b5b0-6b647226ccab,
  abstract     = {{<p>A mathematical framework and accompanying numerical algorithm exploiting the continuity equation for 4D reconstruction of spatiotemporal attenuation fields from multi-angle full-field transmission measurements is presented. The algorithm is geared towards rotation-free dynamic multi-beam X-ray tomography measurements, for which angular information is sparse but the temporal information is rich. 3D attenuation maps are recovered by propagating an initial discretized density volume in time according to the advection equations using the Finite Volumes method with a total variation diminishing monotonic upstream-centered scheme (TVDMUSCL). The benefits and limitations of the algorithm are explored using dynamic granular system phantoms modelled via discrete elements and projected by an analytical ray model independent from the numerical ray model used in the reconstruction scheme. Three phantom scenarios of increasing complexity are presented and it is found that projections from only a few (unknowns:equations &gt; 10) angles can be sufficient for characterisation of the 3D attenuation field evolution in time. It is shown that the artificial velocity field produced by the algorithm sub-iteration, which is used to propagate the attenuation field, can to some extent approximate the true kinematics of the system. Furthermore, it is found that the selection of a temporal interpolation scheme for projection data can have a significant impact on error build up in the reconstructed attenuation field.</p>}},
  author       = {{Henningsson, Axel and Hall, Stephen A.}},
  issn         = {{2313-433X}},
  keywords     = {{4D; Continuity equations; Dynamic; Temporal; Tomography}},
  language     = {{eng}},
  month        = {{11}},
  number       = {{11}},
  publisher    = {{MDPI AG}},
  series       = {{Journal of Imaging}},
  title        = {{A continuity flow based tomographic reconstruction algorithm for 4D multi-beam high temporal—low angular sampling}},
  url          = {{http://dx.doi.org/10.3390/jimaging7110246}},
  doi          = {{10.3390/jimaging7110246}},
  volume       = {{7}},
  year         = {{2021}},
}