Geometric and numerical methods in the contrast imaging problem in nuclear magnetic resonance

Bernard Bonnard (1) , Mathieu Claeys (2) , Olivier Cots (3) , Pierre Martinon (4, 5)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
3 McTAO - Mathematics for Control, Transport and Applications
4 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
5 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems

In this article, the contrast imaging problem 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 techniques of geometric control. This leads to a numerical investigation based on so-called indirect methods using the HamPath software. The results are then compared with a direct method implemented within the Bocop toolbox. Finally lmi techniques are used to estimate a global optimum.

Domaines: Optimisation et contrôle [math.OC]; Imagerie

Bernard Bonnard, Mathieu Claeys, Olivier Cots, Pierre Martinon. Geometric and numerical methods in the contrast imaging problem in nuclear magnetic resonance. 2013. ⟨hal-00867753v1⟩