2D-GRAPPA-operator for faster 3D parallel MRI

When using parallel MRI (pMRI) methods in combination with three-dimensional (3D) imaging, it is beneficial to subsample the k-space along both phase-encoding directions because one can then take advantage of coil sensitivity variations along two spatial dimensions. This results in an improved reconstruction quality and therefore allows greater scan time reductions as compared to subsampling along one dimension. In this work we present a new approach based on the generalized autocalibrating partially parallel acquisitions (GRAPPA) technique that allows Fourier-domain reconstructions of data sets that are subsampled along two dimensions. The method works by splitting the 2D reconstruction process into two separate 1D reconstructions. This approach is compared with an extension of the conventional GRAPPA method that directly regenerates missing data points of a 2D subsampled k-space by performing a linear combination of acquired data points. In this paper we describe the theoretical background and present computer simulations and in vivo experiments.