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Communication dans un congrès

ROI CT reconstruction combining analytic inversion of the finite Hilbert transform and SVD

Aurélien Coussat 1 Simon Rit 1 Rolf Clackdoyle 2 Michel Defrise Laurent Desbat 2 Jean Michel Létang 1
1 Imagerie Tomographique et Radiothérapie
CREATIS - Centre de Recherche en Acquisition et Traitement de l'Image pour la Santé
2 TIMC-GMCAO - Gestes Medico-chirurgicaux Assistés par Ordinateur
TIMC - Techniques de l'Ingénierie Médicale et de la Complexité - Informatique, Mathématiques et Applications, Grenoble - UMR 5525
Abstract : In computed tomography, a scan of the whole object may be impossible, leading to truncated projection data. Using differentiated backprojection, the reconstruction problem can be reduced to a set of independent and one-dimensional Hilbert transforms to invert. Depending on the truncation pattern, this inversion problem can either be "zero-", "one-" or "two-endpoint". The zero-endpoint case is known as the interior problem: the field-of-view is completely contained in the object and the reconstruction problem has no unique solution. The two-endpoint case possesses an analytic, numerically stable inverse. The one-endpoint case has a unique and mathematically stable inverse, but no analytic formula for its inverse has been derived so far. A field-of-view (FOV) which is not interior generally contains both one-and two-endpoint sub-regions and we propose here to combine them by using the analytic two-endpoint reconstruction as additional knowledge for the one-endpoint inversion in the rest of the FOV. We hence obtain two reconstructed regions, which we chose to slightly overlap to partially correct for a small residual error appearing in the one-endpoint reconstructions.
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Communication dans un congrès
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https://hal.archives-ouvertes.fr/hal-03014228
Contributeur : Simon Rit <>
Soumis le : jeudi 19 novembre 2020 - 12:27:25
Dernière modification le : jeudi 11 février 2021 - 14:10:06
Archivage à long terme le : : samedi 20 février 2021 - 19:09:52

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coussat2020.pdf
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  • HAL Id : hal-03014228, version 1

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Aurélien Coussat, Simon Rit, Rolf Clackdoyle, Michel Defrise, Laurent Desbat, et al.. ROI CT reconstruction combining analytic inversion of the finite Hilbert transform and SVD. Sixth international conference on image formation in X-ray computed tomography, Aug 2020, Regensburg, Germany. pp.526-529. ⟨hal-03014228⟩

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