On variant strategies to solve the Magnitude Least Squares optimization problem in parallel transmission RF pulse design and under strict SAR and power constraints

Despite the importance of the magnitude least squares problem in parallel transmission pulse design and the availability of other powerful numerical optimization methods, this problem has been faced almost exclusively with the so-called variable exchange method. Here, we investigate various two stage strategies and incorporate directly the SAR and power constraints. Different schemes such as sequential quadratic programming, interior point methods, semi-definite relaxation and magnitude squared least squares relaxations are studied in the small and large flip angle regimes with B1 and DB0 maps obtained in-vivo on a human brain at 7 Tesla.

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