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Comparison of numerical methods in the contrast imaging problem in NMR
 In Decision and Control and European Control Conference (CDCECC), 2013 52nd IEEE Conference on
, 2013
"... Abstract — In this article, the contrast imaging problem in nuclear magnetic resonance is modeled as a Mayer problem in optimal control. A first synthesis of locally optimal solutions is given in the singleinput case using geometric methods based on Pontryagin’s maximum principle. We then compare t ..."
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Abstract — In this article, the contrast imaging problem in nuclear magnetic resonance is modeled as a Mayer problem in optimal control. A first synthesis of locally optimal solutions is given in the singleinput case using geometric methods based on Pontryagin’s maximum principle. We then compare these results using direct methods and a momentbased approach, and make a first step towards global optimality. Finally, some preliminary results are given in the biinput case.
A COMBINATION OF ALGEBRAIC, GEOMETRIC AND NUMERICAL METHODS IN THE CONTRAST PROBLEM BY SATURATION IN MAGNETIC RESONANCE IMAGING
"... 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 optim ..."
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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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"... Noname manuscript No. (will be inserted by the editor) Geometric and numerical methods in the contrast imaging problem in nuclear magnetic resonance ..."
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Noname manuscript No. (will be inserted by the editor) Geometric and numerical methods in the contrast imaging problem in nuclear magnetic resonance
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"... Noname manuscript No. (will be inserted by the editor) Geometric and numerical methods in the contrast imaging problem in nuclear magnetic resonance ..."
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Noname manuscript No. (will be inserted by the editor) Geometric and numerical methods in the contrast imaging problem in nuclear magnetic resonance
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"... Contrôle quantique de grands systèmes moléculaires: application aux intersections coniques ..."
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Contrôle quantique de grands systèmes moléculaires: application aux intersections coniques
ii ACKNOWLEDGMENTS
, 2013
"... I would first like to thank those who I could not have done this without. On the academic side, my advisers ..."
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I would first like to thank those who I could not have done this without. On the academic side, my advisers
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"... Noname manuscript No. (will be inserted by the editor) Geometric and numerical methods in the contrast imaging problem in nuclear magnetic resonance ..."
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Noname manuscript No. (will be inserted by the editor) Geometric and numerical methods in the contrast imaging problem in nuclear magnetic resonance