Variable density compressed sensing in MRI. Theoretical vs heuristic sampling strategies

The structure of Magnetic Resonance Images (MRI) and especially their compressibility in an appropriate representation basis enables the application of the compressive sensing theory, which guarantees exact image recovery from incomplete measurements. According to recent theoretical results on the reconstruction guarantees, a near optimal strategy is to down-sample the k-space using an independent drawing of the acquisition basis entries. Here, we first bring a novel answer to the synthesis problem, which amounts to deriving the optimal distribution (according to a given criterion) from which the data should be sampled. Then, given that the sparsity hypothesis is not fulfilled in the low frequency band in MRI, we extend this approach by densely sampling this center and drawing the remaining samples from the optimal distribution. We compare this theoretical approach to heuristic strategies, and show that the proposed two-stage process drastically improves reconstruction results on anatomical MRI.