We introduce a novel algorithm for the design of fast slice-selective spatially-tailored 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 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 B1 inhomogeneity in a water phantom at 7T and to produce highly-structured excitations in an oil phantom on an eight-channel parallel excitation system at 3T. 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 B1 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.
In a different area, I have mentioned Treelets before. Ann Lee now has a rejoinder to that paper here. A code in Matlab is available here. While we are on the subject of codes, Mauro Maggioni , James Bremer Jr. and Arthur Szlam have just released a Matlab code for Diffusion Geometry and Diffusion Wavelets. Both links have been added to the Big Picture and to The List.
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