# Approche pénalisée en tomographie hélicoïdale en vue de l'application à la conception d'une prothèse personnalisée du genou

Abstract : In order to design an ergonomic knee prosthesis, we present a new reconstruction method that produces significant improvement in the precision of helical tomographic reconstructions. Whereas the standard approach is based on interpolation and convolution backprojection, our technique relies on a penalized approach ; in this framework, the 3D image is defined as the minimizer of a penalized least-square criterion, which leads to a very large scale optimization problem. An adequate regularization of the tomographic problem is provided by a convex penalization yielding a precise localization of the edges in the image at a reasonable numerical cost. Experiments carried out on synthetic data show that our method produces a significant improvement in precision over standard reconstruction techniques. However, the very large-scale nature of the numerical reconstruction problem leads to major implementation difficulties. In order to keep the computer cost reasonable, we used a spatial invariance of the observation model and minimized the penalized criterion with a successive over relaxation algorithm. Alternatively, an approximation in the observation model leads to a separable 3D reconstruction problem: as a result, the 3D image can be obtained by successive 2D problems of reduced size. Finally, our work yields an in-depth study of Half-quadratic'' (HQ) algorithms widely used in image or data processing. We were able to point out the connections between these HQ algorithms and already known algorithmic forms; weaker global convergence conditions were provided and faster HQ variants were deduced.
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https://tel.archives-ouvertes.fr/tel-00003756
Contributor : Marc Allain <>
Submitted on : Friday, November 14, 2003 - 6:09:10 PM
Last modification on : Friday, February 14, 2020 - 10:30:03 PM
Long-term archiving on: : Friday, April 2, 2010 - 7:46:52 PM

### Identifiers

• HAL Id : tel-00003756, version 1

### Citation

Marc Allain. Approche pénalisée en tomographie hélicoïdale en vue de l'application à la conception d'une prothèse personnalisée du genou. Interface homme-machine [cs.HC]. Université Paris Sud - Paris XI, 2002. Français. ⟨tel-00003756⟩

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