  Nonlinear spatial encoding magnetic (SEM) fields have been studied to
complement multichannel RF encoding and accelerate MRI scans. Published schemes
include PatLoc, O-Space, Null Space, 4D-RIO, and others, but the large variety
of possible approaches to exploiting nonlinear SEMs remains mostly unexplored.
Before, we have presented a new approach, Fast ROtary Nonlinear Spatial
ACquisition (FRONSAC) imaging, where the nonlinear fields provide a small
rotating perturbation to standard linear trajectories. While FRONSAC encoding
greatly improves image quality, at the highest accelerations or weakest FRONSAC
fields, some undersampling artifacts remain. However, the under-sampling
artifacts that occur with FRONSAC encoding are relatively incoherent and well
suited to the compressed sensing (CS) reconstruction. CS provides a
sparsity-promoting convex strategy to reconstruct images from highly
undersampled datasets. The work presented here combines the benefits of FRONSAC
and CS. Simulations illustrate that this combination can further improve image
reconstruction with FRONSAC gradients of low amplitudes and frequencies.
