Reconstruction of Arbitrary Non-Cartesian Trajectories using Pseudo-Cartesian GRAPPA in Conjunction with GRAPPA Operator Gridding (GROG)

Introduction: The recently introduced GRAPPA Operator Gridder (GROG) [1] has been shown to be useful for the regridding of fully-sampled non-Cartesian data. However, GROG can also be used to properly regrid undersampled non-Cartesian data, which cannot be performed with other common regridding schemes, such as the gold-standard convolution-based gridding [2]. GROG has the advantage that single non-Cartesian points are shifted to the nearest Cartesian point using the GRAPPA Operator, leaving empty spaces in k-space where data must be reconstructed; convolution gridders assume that the Nyquist criterion is fulfilled, and any “holes” in k-space lead to gridding errors, but not missing k-space points. After regridding the undersampled non-Cartesian data with GROG, Pseudo-Cartesian GRAPPA [3] can be performed, thereby reconstructing the missing points in k-space. This method eliminates the need for specialized non-Cartesian reconstruction algorithms, as the data can first be regridded and then reconstructed using a small number of simple Cartesian GRAPPA patterns. In addition, trajectories for which no non-Cartesian GRAPPA reconstruction currently exists, such as the rosette [4] trajectory, can be accelerated and reconstructed using Pseudo-Cartesian GRAPPA.