6533b827fe1ef96bd1285865

RESEARCH PRODUCT

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

Bernard BonnardMathieu ClaeysOlivier CotsAlain JacquemardPierre Martinon

subject

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]Moment optimization[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Direct methodContrast imaging in NMR[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]Geometric optimal controlShooting and continuation techniques

description

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.

yearjournalcountryeditionlanguage
2014-01-01
https://hal.inria.fr/hal-01001975/document