Pseudo-cartesian GRAPPA reconstruction of undersampled non-cartesian data

Introduction: The application of the basic Cartesian GRAPPA [1] reconstruction algorithm requires regular, symmetric undersampled data. Non-Cartesian sampling schemes, such as radial or spiral trajectories, do not fulfill this requirement. Therefore, special reconstruction and/or data reordering procedures are necessary. In all previous methods, the GRAPPA reconstruction is performed first on the reordered data, followed by regridding of the reconstructed data onto a Cartesian grid [2-5]. However, if the undersampled non-Cartesian data are first regridded, the inherent symmetry of the acquisition scheme can be used to define several Cartesian patterns in the regridded data which can be used for reconstruction. Examining specifically the spiral case, the regridded undersampled k-space can be divided into several “sectors,” where each sector can be reconstructed with a specific Cartesian pattern. The reconstruction for each sector is then identical to a Cartesian GRAPPA reconstruction; the weights for each sector’s pattern are determined from low-resolution, fully-sampled data (ACS), and applied to the undersampled data to arrive at the full k-space.