Geometric optimal control of the contrast imaging problem in Nuclear Magnetic Resonance

Abstract

The objective of this article is to introduce the tools to analyze the contrast imaging problem in Nuclear Magnetic Resonance. Optimal trajectories can be selected among extremal solutions of the Pontryagin Maximum Principle applied to this Mayer type optimal problem. Such trajectories are associated to the question of extremizing the transfer time. Hence the optimal problem is reduced to the analysis of the Hamiltonian dynamics related to singular extremals and their optimality status. This is illustrated by using the examples of cerebrospinal fluid / water and grey / white matter of cerebrum.

30 pages, 13 figure

References in corpus (2)

• Singular extremals for the time-optimal control of dissipative spin 1/2 particles
• Time-optimal control of a two-level dissipative quantum system

Cited by in corpus (18)

• Introduction to the Pontryagin Maximum Principle for Quantum Optimal Control
• Speeding up and slowing down the relaxation of a qubit by optimal control
• Robust control of a NOT gate by composite pulses
• Time-optimal purification of a qubit in contact with a structured environment
• Time-optimal selective pulses of two uncoupled spin 1/2 particles
• Comparison between optimal control and shortcut to adiabaticity protocols in a linear control system
• Minimum-Time Selective Control of Homonuclear Spins
• Optimal amplification of the dynamical Casimir effect in a parametrically driven system
• On the time optimal thermalization of single mode Gaussian states
• A greedy reconstruction algorithm for the identification of spin distribution
• Purity Speed Limit of Open Quantum Systems from Magic Subspaces
• Determinantal sets, singularities and application to optimal control in medical imagery
• Optimal control of distributed ensembles with application to Bloch equations
• Exploring the limits of the generation of non-classical states of spins coupled to a cavity by optimal control
• Tangency property and prior-saturation points in minimal time problems in the plane
• Exact solutions for the time-evolution of quantum spin systems under arbitrary waveforms using algebraic graph theory
• Exploring the physical limits of saturation contrast in Magnetic Resonance Imagign
• Optimal control theory for applications in magnetic resonance imaging