Smooth sampling trajectories for sparse recovery in MRI

Recent attempts to apply compressed sensing to MRI have resulted in pseudo-random k-space sampling trajectories which, if applied naïvely, may do little to decrease data acquisition time. This paper shows how an important indicator of CS performance guarantees, the Restricted Isometry Property, holds for deterministic sampling trajectories corresponding to radial and spiral sampling patterns in common use. These theoretical results support several empirical studies in the literature on compressed sensing in MRI. A combination of Geršgorin´s Disc Theory and Weyl´s sums lead to performance bounds on sparse recovery algorithms applied to MRI data collected along short and smooth sampling trajectories.