The Shinnar-Le-Roux (SLR) algorithm is widely used for designing frequency selective pulses with large flip angles. We improve its design process to generate pulses with lower energy (by as much as 26%) and more accurate phase profiles.
Concretely, the SLR algorithm consists of designing two polynomials that represent Cayley-Klein (CK) parameters. Because the CK polynomial pair is bi-linearly coupled, the original algorithm sequentially solves for each polynomial. This results in sub-optimal pulses.
Instead, we leverage a convex relaxation technique to jointly recover the CK polynomials. Our experiments show that the resulting pulses almost always attain the global solution in practice.