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Cone-beam reconstruction from n-sin trajectories with transversely-truncated projections

Nicolas Gindrier 1 Rolf Clackdoyle 1 Simon Rit 2 Laurent Desbat 1
1 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
2 Imagerie Tomographique et Radiothérapie
CREATIS - Centre de Recherche en Acquisition et Traitement de l'Image pour la Santé
Abstract : In cone-beam tomography, we define the n-sin source trajectory as having n periods of a sinusoid traced on an imaginary cylinder enclosing the object. A 2-sin is commonly known as a saddle, and it is known that the convex hull of a saddle is the same as the union of all of its chords. The convex hull of a closed trajectory is the Tuy region, where cone-beam reconstructionis possible if there are no truncated projections. However, with truncated projections, the method of differentiated backprojection and Hilbert inversion can be applied along a chord if the chordis visible (not truncated) in the projections. Here, we consider a particular transaxial truncation which prevents chords from always being visible, but we establish that the more powerful method of M-lines can be applied to ensure reconstruction in the reduced field-of-view. The 3-sin, on the other hand, has a Tuy region which is not filled by its chords, and we do not have any cone-beam theory to determine if reconstruction is possible with transverse reconstruction. In our preliminary numerical experiment, the 3-sinseemed to perform equally well as the 2-sin trajectory even though there were no chords passing through the slice we examined. We tentatively suggest that there might be other, yet unknown theory that explains why 3-sin reconstruction is possible with the specified transaxial truncation. We believe that these results on transverse truncation and reconstruction from 2-sin and 3-sin trajectories are new.
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https://hal.archives-ouvertes.fr/hal-02928137
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Soumis le : jeudi 3 septembre 2020 - 14:17:03
Dernière modification le : mardi 24 novembre 2020 - 16:00:09
Archivage à long terme le : : mercredi 2 décembre 2020 - 18:50:26

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Nicolas Gindrier, Rolf Clackdoyle, Simon Rit, Laurent Desbat. Cone-beam reconstruction from n-sin trajectories with transversely-truncated projections. Sixth international conference on image formation in X-ray computed tomography, Aug 2020, Regensburg, Germany. pp.46-49. ⟨hal-02928137⟩

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