Reconstruction of undersampled non‐Cartesian data sets using pseudo‐Cartesian GRAPPA in conjunction with GROG

Most k‐space‐based parallel imaging reconstruction techniques, such as Generalized Autocalibrating Partially Parallel Acquisitions (GRAPPA), necessitate the acquisition of regularly sampled Cartesian k‐space data to reconstruct a nonaliased image efficiently. However, non‐Cartesian sampling schemes offer some inherent advantages to the user due to their better coverage of the center of k‐space and faster acquisition times. On the other hand, these sampling schemes have the disadvantage that the points acquired generally do not lie on a grid and have complex k‐space sampling patterns. Thus, the extension of Cartesian GRAPPA to non‐Cartesian sequences is nontrivial. This study introduces a simple, novel method for performing Cartesian GRAPPA reconstructions on undersampled non‐Cartesian k‐space data gridded using GROG (GRAPPA Operator Gridding) to arrive at a nonaliased image. Because the undersampled non‐Cartesian data cannot be reconstructed using a single GRAPPA kernel, several Cartesian patterns are selected for the reconstruction. This flexibility in terms of both the appearance and number of patterns allows this pseudo‐Cartesian GRAPPA to be used with undersampled data sets acquired with any non‐Cartesian trajectory. The successful implementation of the reconstruction algorithm using several different trajectories, including radial, rosette, spiral, one‐dimensional non‐Cartesian, and zig–zag trajectories, is demonstrated. Magn Reson Med 59:1127–1137, 2008. © 2008 Wiley‐Liss, Inc.