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Modèles dynamiques en tomographie - Application à l'imagerie cardiaque

Sébastien Roux 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
Abstract : Image reconstruction techniques are a fundamental tool in medicine. Applied to the inverse problem in X-ray Computed Tomography (XRCT), they give access to the map of tissues density. With the technical progress of CT scanner, dynamic imaging of organs such as the heart is now feasible. However the classical mathematical reconstruction methods have to be improved to take into account the evolution of the organs during the acquisition, which can lead to strong artifacts in the images. The goal of this thesis work is to investigate the use of additional models to regularize the reconstruction problem. We first study the classical model used in cardiac CT, based on the heart periodic evolution. We treat the synchronization problem in the parallel and divergent acquisition geometries, linking it with sampling theory. Moreover we propose an improved reconstruction scheme for the divergent geometries. The second part of this work deals with the motion compensation methods, where an a priori known model of spatial deformation is integrated into the reconstruction process. We extend the class of deformations where admissibility conditions and analytic reconstruction formulas exist by considering the class of general time-dependent affine deformations.
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Submitted on : Friday, December 17, 2004 - 11:06:11 AM
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Sébastien Roux. Modèles dynamiques en tomographie - Application à l'imagerie cardiaque. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2004. Français. ⟨tel-00007803⟩

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