Optimal control theory for applications in magnetic resonance imaging

Abstract

We apply innovative mathematical tools coming from optimal control theory to improve theoretical and experimental techniques in Magnetic Resonance Imaging (MRI). This approach allows us to explore and to experimentally reach the physical limits of the corresponding spin dynamics in the presence of typical experimental imperfections and limitations. We study in this paper two important goals, namely the optimization of image contrast and the maximization of the signal to noise per unit time. We anticipate that the proposed techniques will find practical applications in medical imaging in a near future to help the medical diagnosis.

arXiv comment19 pages, 7 figures, to be published in Pacific Journal of Mathematics for Industry

References in corpus (13)

• Training Schrödinger's cat: quantum optimal control
• Quantum control theory and applications: A survey
• Second order gradient ascent pulse engineering
• Robust quantum control by shaped pulse
• Comparing, Optimising and Benchmarking Quantum Control Algorithms in a Unifying Programming Framework
• Sub-Riemannian Geometry and Time Optimal Control of Three Spin Systems: Quantum Gates and Coherence Transfer
• Singular extremals for the time-optimal control of dissipative spin 1/2 particles
• Time-optimal control of SU(2) quantum operations
• Speeding up and slowing down the relaxation of a qubit by optimal control
• Time-Minimal Control of Dissipative Two-level Quantum Systems: the Generic Case
• Simultaneous time-optimal control of the inversion of two spin 1/2 particles
• Geometric optimal control of the contrast imaging problem in Nuclear Magnetic Resonance
• Optimal control of the signal to noise ratio per unit time for a spin 1/2 particle