When based on a k-space description, 2D RF pulses can be applied in segments to increase the excitation bandwidth relative to a single-shot implementation, at a cost of increased imaging time. The increased imaging time can be overcome by undersampling the acquisition in one phase-encoded dimension, where data from each segment are viewed as originating from “virtual receive coils” rather than multiple physical coils. The undersampled data are reconstructed using parallel imaging techniques (e.g. as in GRAPPA). The method was tested in vivo with brain imaging, and the GRAPPA-like reconstruction was comparable in quality to a fully sampled reconstruction.