Sparsity-Enforced Slice-Selective MRI RF Excitation Pulse Design

We introduce a novel algorithm for the design of fast slice-selective spatially-tailored magnetic resonance imaging (MRI) excitation pulses. This method, based on sparse approximation theory, uses a second-order cone optimization to place and modulate a small number of slice-selective sinc-like radio-frequency (RF) pulse segments (“spokes”) in excitation $k$-space, enforcing sparsity on the number of spokes allowed while simultaneously encouraging those that remain to be placed and modulated in a way that best forms a user-defined in-plane target magnetization. Pulses are designed to mitigate $B_{1}$ inhomogeneity in a water phantom at 7 T and to produce highly-structured excitations in an oil phantom on an eight-channel parallel excitation system at 3 T. In each experiment, pulses generated by the sparsity-enforced method outperform those created via conventional Fourier-based techniques, e.g., when attempting to produce a uniform magnetization in the presence of severe $B_{1}$ inhomogeneity, a 5.7-ms 15-spoke pulse generated by the sparsity-enforced method produces an excitation with 1.28 times lower root mean square error than conventionally-designed 15-spoke pulses. To achieve this same level of uniformity, the conventional methods need to use 29-spoke pulses that are 7.8 ms long.