Magnitude-least squares optimization is widely used to design RF shims that produce homogeneous B1+ fields at high field strengths, but the MLS optimization problem is non-convex and prone to becoming stuck in local minima corresponding to unacceptable voids in the shimmed field. We describe a simple, improved Gerchberg-Saxton algorithm for MLS RF shimming in which randomly selected subsets of the B1+ map matrix's singular vectors are used in each shim update. Shims are then refined using conventional GS. Simulations of 8- and 30-channel head coils at 7T verify the method's robustness, and demonstrate advantages over conventional RF shim design techniques.
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