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Parallel transmission has been a very promising candidate technology tomitigate the inevitable radio-frequency field inhomogeneity in magneticresonance imaging (MRI) at ultra-high field (UHF). For the first few years,pulse design utilizing this technique was expressed as a least squares problemwith crude power regularizations aimed at controlling the specific absorptionrate (SAR), hence the patient safety. This approach being suboptimal for manyapplications sensitive mostly to the magnitude of the spin excitation, and notits phase, the magnitude least squares (MLS) problem then was first formulatedin 2007. Despite its importance and the availability of other powerfulnumerical optimization methods, this problem yet has been faced exclusively bythe pulse designer with the so-called variable exchange method. In this paper,we investigate other strategies and incorporate directly the strict SAR andhardware constraints. Different schemes such as sequential quadraticprogramming (SQP), interior point (I-P) methods, semi-definite programming(SDP) and magnitude squared least squares (MSLS) relaxations are studied bothin the small and large tip angle regimes with real data sets obtained in-vivoon a human brain at 7 Tesla. Convergence and robustness of the differentapproaches are analyzed, and recommendations to tackle this specific problemare finally given. Small tip angle and inversion pulses are returned in a fewseconds and in under a minute respectively while respecting the constraints,allowing the use of the proposed approach in routine.

On Variant Strategies To Solve The Magnitude Least Squares Optimization  Problem In Parallel Transmission Pulse Design And Under Strict SAR And Power  Constraints