TIME MINIMAL SATURATION OF A PAIR OF SPINS AND APPLICATION IN MAGNETIC RESONANCE IMAGING

被引：0
作者：
Bonnard, Bernard [1 ,2 ]
Cots, Olivier [3 ]
Rouot, Jeremy [1 ,4 ]
Verron, Thibaut [5 ]
机构：
[1] Univ Bourgogne, Inst Math Bourgogne, 9 Ave Alain Savary, F-21078 Dijon, France
[2] INRIA, 2004 Route Lucioles, F-06902 Sophia Antipolis, France
[3] Toulouse Univ, INP ENSEEIHT IRIT, UMR CNRS 5505, 2 Rue Camichel, F-31071 Toulouse, France
[4] EPF Ecole Ingenieur ES, 2 Rue F Sastre, F-10430 Rosieres Pres Troyes, France
[5] Johannes Kepler Univ Linz, Inst Algebra, A-4040 Linz, Austria
来源：
MATHEMATICAL CONTROL AND RELATED FIELDS | 2020年 / 10卷 / 01期
关键词：
Geometric optimal control; contrast imaging in NMR; direct method; shooting and continuation techniques; moment optimization; Grobner basis; SINGULAR TRAJECTORIES; OCCUPATION MEASURES; SYSTEMS; OPTIMIZATION; OPTIMALITY;
D O I：
10.3934/mcrf.2019029
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, we analyze the time minimal control for the saturation of a pair of spins of the same species but with inhomogeneities of the applied RF-magnetic field, in relation with the contrast problem in Magnetic Resonance Imaging. We make a complete analysis based on geometric control to classify the optimal syntheses in the single spin case to pave the road to analyze the case of two spins. The Bocop software is used to determine local minimizers for physical test cases and Linear Matrix Inequalities approach is applied to estimate the global optimal value and validate the previous computations. This is complemented by numerical computations combining shooting and continuation methods implemented in the HamPath software to analyze the structure of the time minimal solution with respect to the set of parameters of the species. Symbolic computations techniques are used to handle the singularity analysis.
引用
收藏
页码：47 / 88
页数：42
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