Improved Shinnar-Le Roux algorithm

Selective excitation pulses are widely used in magnetic resonance imaging in order to excite predetermined slices of the body under examination. Such pulses are optimally designed by means of the Shinnar-Le Roux algorithm. In this paper, we show that under minimal assumptions, the complexity and computing cost of the original Shinnar-Le Roux algorithm can be drastically reduced. We further propose an improved version of the algorithm, involving only real quantities, which is both easier to implement and faster to execute, so it is suitable for implementation at the hardware level, in the context of a real-time fully digital magnetic resonance transceiver.