  Purpose: 3D Time-of-flight (TOF) MR Angiography (MRA) can accurately
visualize the intracranial vasculature, but is limited by long acquisition
times. Compressed sensing (CS) reconstruction can be used to substantially
accelerate acquisitions. The quality of those reconstructions depends on the
undersampling patterns used in the acquisitions. In this work, optimized sets
of undersampling parameters using various acceleration factors for Cartesian 3D
TOF-MRA are established.
  Methods: Fully-sampled datasets acquired at 7T were retrospectively
undersampled using variable-density Poisson-disk sampling with various
autocalibration region sizes, polynomial orders, and acceleration factors. The
accuracy of reconstructions from the different undersampled datasets was
assessed using the vessel-masked structural similarity index. Results were
compared for four imaging volumes, acquired from two different subjects.
Optimized undersampling parameters were validated using additional
prospectively undersampled datasets.
  Results: For all acceleration factors, using a fully-sampled calibration area
of 12x12 k-space lines and a polynomial order of around 2-2.4 resulted in the
highest image quality. The importance of sampling parameter optimization was
found to increase for higher acceleration factors. The results were consistent
across resolutions and regions of interest with vessels of varying sizes and
tortuosity. In prospectively undersampled acquisitions, using optimized
undersampling parameters resulted in a 7.2% increase in the number of visible
small vessels at R = 7.2.
  Conclusion: The image quality of CS TOF-MRA can be improved by appropriate
choice of undersampling parameters. The optimized sets of parameters are
independent of the acceleration factor.
