Fast pulse design for parallel transmission in MRI using under-determined systems

Spatial tailored RF pulses in parallel transmission can be designed using a spatial domain method under the small-tip-angle approximation. Parallel transmission pulse design problems are normally well conditioned, i.e., over-determined, since data points are from the target excitation pattern, which can be sampled at arbitrary high resolution. However, the computation cost in RF pulses design can be very high, especially for multi-channel three-dimensional pulses. In this work, we propose an efficient method to design parallel RF pulses by using system matrices that are under-determined. Computer simulations show that the proposed method can gain up to 19 times computation speedup while maintaining the excitation accuracy for smooth patterns.