RLS-grappa: Reconstructing parallel MRI data with adaptive filters

GRAPPA is one of the predominant methods used to reconstruct accelerated parallel MRI data. In has been shown previously that spatially varying the GRAPPA reconstruction coefficients can be advantageous. A significant problem with these approaches, however, is an increase in computation time due to an increase in the number of linear system solves needed. Here, we leverage the fact that these systems vary slowly over the coordinate space and employ recursive adaptive filters in place of explicit system solves. This approach produces high quality spatially variant GRAPPA reconstructions with a computation time comparable to standard GRAPPA.