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

Bernard Bonnard 1 Olivier Cots 1
1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
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.
Keywords : Contrast Imaging In NMR Shooting And Continuation Methods Geometric Optimal Control
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Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2014, vol. 24 (n° 1), pp. 187-212. <10.1142/S0218202513500504>
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Bernard Bonnard, Olivier Cots. Geometric Numerical Methods and Results in the Control Imaging Problem in Nuclear Magnetic Resonance. Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2014, vol. 24 (n° 1), pp. 187-212. <10.1142/S0218202513500504>. <hal-01136896>

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