  MRI data is acquired in Fourier space/k-space. Data acquisition is typically
performed on a Cartesian grid in this space to enable the use of a fast Fourier
transform algorithm to achieve fast and efficient reconstruction. However, it
has been shown that for multiple applications, non-Cartesian data acquisition
can improve the performance of MR imaging by providing fast and more efficient
data acquisition, and improving motion robustness. Nonetheless, the image
reconstruction process of non-Cartesian data is more involved and can be
time-consuming, even through the use of efficient algorithms such as
non-uniform FFT (NUFFT). Reconstruction complexity is further exacerbated when
imaging in the presence of field imperfections. This work (implicit GROG)
provides an efficient approach to transform the field corrupted non-Cartesian
data into clean Cartesian data, to achieve simpler and faster reconstruction
which should help enable non-Cartesian data sampling to be performed more
widely in MRI.
