A Continuity Flow Based Tomographic Reconstruction Algorithm for 4D Multi-Beam High Temporal—Low Angular Sampling

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 tomog...

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Autores principales:	Axel Henningsson, Stephen A. Hall
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	tomography 4D temporal dynamic continuity equations Photography TR1-1050 Computer applications to medicine. Medical informatics R858-859.7 Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/1d050c9aca9541ee9f306e3e7b97f0d6
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id	oai:doaj.org-article:1d050c9aca9541ee9f306e3e7b97f0d6
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spelling	oai:doaj.org-article:1d050c9aca9541ee9f306e3e7b97f0d62021-11-25T18:03:35ZA Continuity Flow Based Tomographic Reconstruction Algorithm for 4D Multi-Beam High Temporal—Low Angular Sampling10.3390/jimaging71102462313-433Xhttps://doaj.org/article/1d050c9aca9541ee9f306e3e7b97f0d62021-11-01T00:00:00Zhttps://www.mdpi.com/2313-433X/7/11/246https://doaj.org/toc/2313-433XA 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.Axel HenningssonStephen A. HallMDPI AGarticletomography4Dtemporaldynamiccontinuity equationsPhotographyTR1-1050Computer applications to medicine. Medical informaticsR858-859.7Electronic computers. Computer scienceQA75.5-76.95ENJournal of Imaging, Vol 7, Iss 246, p 246 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	tomography 4D temporal dynamic continuity equations Photography TR1-1050 Computer applications to medicine. Medical informatics R858-859.7 Electronic computers. Computer science QA75.5-76.95
spellingShingle	tomography 4D temporal dynamic continuity equations Photography TR1-1050 Computer applications to medicine. Medical informatics R858-859.7 Electronic computers. Computer science QA75.5-76.95 Axel Henningsson Stephen A. Hall A Continuity Flow Based Tomographic Reconstruction Algorithm for 4D Multi-Beam High Temporal—Low Angular Sampling
description	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.
format	article
author	Axel Henningsson Stephen A. Hall
author_facet	Axel Henningsson Stephen A. Hall
author_sort	Axel Henningsson
title	A Continuity Flow Based Tomographic Reconstruction Algorithm for 4D Multi-Beam High Temporal—Low Angular Sampling
title_short	A Continuity Flow Based Tomographic Reconstruction Algorithm for 4D Multi-Beam High Temporal—Low Angular Sampling
title_full	A Continuity Flow Based Tomographic Reconstruction Algorithm for 4D Multi-Beam High Temporal—Low Angular Sampling
title_fullStr	A Continuity Flow Based Tomographic Reconstruction Algorithm for 4D Multi-Beam High Temporal—Low Angular Sampling
title_full_unstemmed	A Continuity Flow Based Tomographic Reconstruction Algorithm for 4D Multi-Beam High Temporal—Low Angular Sampling
title_sort	continuity flow based tomographic reconstruction algorithm for 4d multi-beam high temporal—low angular sampling
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/1d050c9aca9541ee9f306e3e7b97f0d6
work_keys_str_mv	AT axelhenningsson acontinuityflowbasedtomographicreconstructionalgorithmfor4dmultibeamhightemporallowangularsampling AT stephenahall acontinuityflowbasedtomographicreconstructionalgorithmfor4dmultibeamhightemporallowangularsampling AT axelhenningsson continuityflowbasedtomographicreconstructionalgorithmfor4dmultibeamhightemporallowangularsampling AT stephenahall continuityflowbasedtomographicreconstructionalgorithmfor4dmultibeamhightemporallowangularsampling
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A Continuity Flow Based Tomographic Reconstruction Algorithm for 4D Multi-Beam High Temporal—Low Angular Sampling

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