CS: Sparsity-Enforced Slice-Selective MRI RF Excitation Pulse Design, Treelets and Diffusion Geometries and Wavelet Codes

Among the technologies that are performing subsampling because of the known sparsity of the unknown signal, MRI stands to be the technology that is the most advanced in turns of cranking out interesting sampling schemes and supporting hardware (since there is virtually no change in the hardware). Case in point the last publication by Adam Zelinski, Lawrence L. Wald, Kawin Setsompop, Vivek Goyal and Elfar Adalsteinsson entitled: Sparsity-Enforced Slice-Selective MRI RF Excitation Pulse Design. The abstract reads:

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.

I think this is the first time I see the enforcement on simultaneous sparsity between different vectors and the use of the l1 norm of the l2 norms of the rows of a matrix in the regularization. As I am looking at the gridding performed in the k-world, I cannot but stop thinking about the scheme mentioned by Yves Meyer and Basarab Matei where one would fit the trajectories through points in a quasicrystal lattice, and wonder how this would fit into this picture ? I don't know. Does it improve the adaptive strategy as adopted in the paper or else ?



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.