Time efficient design of multi dimensional RF pulses: application of a multi shift CGLS algorithm

Designing multi dimensional ratio frequency excitation pulses in the small flip angle regime commonly reduces to the solution of a least squares problem, which requires regularization to be solved numerically. Usually, regularization is carried out by the introduction of a penalty, λ, on the solution norm. In most cases, the optimal regularization parameter is not known a priori and the problem needs to be solved for several values of λ. The optimal value can be selected, typically by plotting the L-curve. In this article, a conjugate gradients-based algorithm is applied to design ratio frequency pulses in a time-efficient way without a priori knowledge of the optimal regularization parameter. The computation time is reduced considerably (by a factor 10 in a typical set up) with respect to the standard conjugate gradients for least square since just one run of the algorithm is required. Simulations are shown and the performance is compared to that of conjugate gradients for least square.