Clipped DeepControl: Deep neural network two-dimensional pulse design with an amplitude constraint layer

Advanced radio-frequency pulse design used in magnetic resonance imaging has recently been demonstrated with deep learning of (convolutional) neural networks and reinforcement learning. For two-dimensionally selective radio-frequency pulses, the (convolutional) neural network pulse prediction time (a few milliseconds) was in comparison more than three orders of magnitude faster than the conventional optimal control computation. The network pulses were from the supervised training capable of compensating scan-subject dependent inhomogeneities of B₀ and B₁⁺ fields. Unfortunately, the network presented with a small percentage of pulse amplitude overshoots in the test subset, despite the optimal control pulses used in training were fully constrained. Here, we have extended the convolutional neural network with a custom-made clipping layer that completely eliminates the risk of pulse amplitude overshoots, while preserving the ability to compensate for the inhomogeneous field conditions.