A combination of algebraic, geometric and numerical methods in the contrast problem by saturation in magnetic resonance imaging

Bernard Bonnard 1, 2 Mathieu Claeys 3 Olivier Cots 1 Alain Jacquemard 2, 4 Pierre Martinon 5, 6
1 McTAO - Mathematics for Control, Transport and Applications
CRISAM - Inria Sophia Antipolis - Méditerranée
3 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes [Toulouse]
6 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, Polytechnique - X, CNRS - Centre National de la Recherche Scientifique : UMR7641
Abstract : In this article, the contrast imaging problem by saturation in nuclear magnetic resonance is modeled as a Mayer problem in optimal control. The optimal solution can be found as an extremal solution of the Maximum Principle and analyzed with the recent advanced techniques of geometric optimal control. This leads to a numerical investigation based on shooting and continuation methods implemented in the HamPath software. The results are compared with a direct approach to the optimization problem and implemented within the Bocop toolbox. In complement lmi techniques are used to estimate a global optimum. It is completed with the analysis of the saturation problem of an ensemble of spin particles to deal with magnetic fields inhomogeneities.
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Rapport
[Research Report] LAAS-CNRS. 2014
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Dernière modification le : vendredi 12 janvier 2018 - 01:55:58
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  • HAL Id : hal-01001975, version 1

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Bernard Bonnard, Mathieu Claeys, Olivier Cots, Alain Jacquemard, Pierre Martinon. A combination of algebraic, geometric and numerical methods in the contrast problem by saturation in magnetic resonance imaging. [Research Report] LAAS-CNRS. 2014. 〈hal-01001975〉

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