ALGEBRAIC GEOMETRIC CLASSIFICATION OF THE SINGULAR FLOW IN THE CONTRAST IMAGING PROBLEM IN NUCLEAR MAGNETIC RESONANCE

作者：Bonnard Bernard^*; Chyba Monique; Jacquemard Alain; Marriott John

来源：Mathematical Control and Related Fields, 2013, 3(4): 397-432.

DOI：10.3934/mcrf.2013.3.397

• Mayer problem
• geometric optimal control
• contrast imaging
• invariant theory

The analysis of the contrast problem in NMR medical imaging is essentially reduced to the analysis of the so-called singular trajectories of the system modeling the problem: a coupling of two spin 1/2 control systems. They are solutions of a constraint Hamiltonian vector field and restricting the dynamics to the zero level set of the Hamiltonian they de fine a vector field on B-1 x B-2, where B-1 and B-2 are the Bloch balls of the two spin particles. In this article we classify the behaviors of the solutions in relation with the relaxation parameters using the concept of feedback classification. The optimality status is analyzed using the feedback invariant concept of conjugate points.

• 出版日期2013-12