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Geometric Numerical Methods and Results in the Control Imaging Problem in Nuclear Magnetic Resonance

Bonnard, Bernard and Cots, Olivier Geometric Numerical Methods and Results in the Control Imaging Problem in Nuclear Magnetic Resonance. (2014) Mathematical Models and Methods in Applied Sciences, 24 (1). 187-212. ISSN 0218-2025

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Official URL: http://dx.doi.org/10.1142/S0218202513500504

Abstract

The purpose of this paper is to present numerical methods and results about the contrast imaging problem in nuclear magnetic resonance which corresponds to a Mayer problem in optimal control. The candidates as minimizers are selected among a set of extremals, solutions of a Hamiltonian system given by the Pontryagin Maximum Principle and sufficient second order conditions are described. They form the geometric foundations of the HAMPATH code which combines shooting and continuation methods, see Ref. 9. The main contribution of this paper is to present a numerical analysis of the contrast imaging problem in NMR in the case of deoxygenated/oxygenated blood samples as an application of the aforementioned techniques.

Item Type:Article
Additional Information:Thanks to World Scientific Publishing editor. The definitive version is available at http://www.worldscientific.com/doi/abs/10.1142/S0218202513500504
HAL Id:hal-01136896
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Other partners > Université de Bourgogne - UB (FRANCE)
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Deposited By: IRIT IRIT
Deposited On:30 Mar 2015 06:56

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