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- Title
ALGEBRAIC GEOMETRIC CLASSIFICATION OF THE SINGULAR FLOW IN THE CONTRAST IMAGING PROBLEM IN NUCLEAR MAGNETIC RESONANCE.
- Authors
BONNARD, BERNARD; CHYBA, MONIQUE; JACQUEMARD, ALAIN; MARRIOTT, JOHN
- Abstract
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 define a vector field on B1 x B2, where B1 and B2 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.
- Subjects
MAGNETIC resonance imaging; NUCLEAR magnetic resonance; TRAJECTORIES (Mechanics); HAMILTONIAN systems; VECTOR fields
- Publication
Mathematical Control & Related Fields, 2013, Vol 3, Issue 4, p397
- ISSN
2156-8472
- Publication type
Article
- DOI
10.3934/mcrf.2013.3.397