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The Shinnar-Le-Roux (SLR) algorithm is widely used to design frequencyselective pulses with large flip angles. We improve its design process togenerate pulses with lower energy (by as much as 26%) and more accurate phaseprofiles.  Concretely, the SLR algorithm consists of two steps: (1) an invertibletransform between frequency selective pulses and polynomial pairs thatrepresent Cayley-Klein (CK) parameters and (2) the design of the CK polynomialpair to match the desired magnetization profiles. Because the CK polynomialpair is bi-linearly coupled, the original algorithm sequentially solves foreach polynomial instead of jointly. This results in sub-optimal pulses.  Instead, we leverage a convex relaxation technique, commonly used for lowrank matrix recovery, to address the bi-linearity. Our numerical experimentsshow that the resulting pulses are almost always globally optimal in practice.For slice excitation, the proposed algorithm results in more accurate linearphase profiles. And in general the improved pulses have lower energy than theoriginal SLR pulses.

SLfRank: Shinnar-Le-Roux Pulse Design with Reduced Energy and Accurate Phase Profiles using Rank Factorization