Current parallel transmit pulse design methods are based on a spatial domain formulation that has prohibitive memory and computational requirements when the number of coils or the number of dimensions is large. We describe a k-space domain parallel transmit pulse design method that directly solves for the columns of a sparse design matrix with a much smaller memory footprint than existing methods, and is highly parallelizable. The method is validated with phantom and in vivo 7T 8-channel spiral excitations.
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