Optimal control gradient precision trade-offs: Application to fast generation of DeepControl libraries for MRI

Area of Science:

• Magnetic Resonance Imaging
• Quantum Optimal Control
• Machine Learning

Background:

• Deep learning methods enable rapid, real-time generation of radiofrequency pulses for MRI.
• Traditional methods for generating training data rely on computationally intensive gradient calculations.
• Accelerating these calculations is crucial for making deep learning in MRI more practical.

Purpose of the Study:

• To explore and evaluate methods for accelerating gradient calculations in quantum optimal control.
• To identify computationally efficient yet accurate techniques for gradient computation.
• To facilitate the realistic generation of training databases for deep learning in MRI.

Main Methods:

• Investigated four gradient calculation acceleration techniques: zeroth-order and first-order truncated commutator series expansions, a novel first-order midpoint truncation scheme, and the exact complex-step method.
• Compared the accuracy and speed of these methods for spin systems relevant to MRI.
• Evaluated the performance against machine precision gradients.

Main Results:

• The first-order midpoint truncation scheme demonstrated sufficient accuracy for MRI-relevant spin systems.
• This method was significantly faster than machine precision gradient calculations.
• The optimized gradient calculation significantly improves the feasibility of generating large training datasets.

Conclusions:

• The first-order midpoint truncation offers a practical and efficient approach to accelerate gradient computations in quantum optimal control for MRI.
• This acceleration makes the generation of training libraries for deep learning-based MRI pulse design considerably more feasible.
• The findings pave the way for more widespread adoption of real-time, patient-specific pulse generation in MRI.