Algebraic Classification Techniques for Optimal Control in Medical Imagery

Determinantal Sets, Singularities and Application to Optimal Control in Medical Imagery (ISSAC 2016)


Case of water

General case

Algebraic-geometric Techniques for the Feedback Classification and Robustness of the Optimal Control of a Pair of Bloch Equations with Application to Magnetic Resonance Imaging


Figure 1: Final classification in the case of water: the valid range \(2\Gamma_2 \geq \gamma_2 \geq 0\) of the parameter space \((\gamma_2,\Gamma_2)\) is divided into areas where the number of singularities in the Bloch ball is \(1\), \(2\) or \(3\).