Evaluating sparsity penalty functions for combined compressed sensing and parallel MRI

The combination of compressed sensing (CS) and parallel magnetic resonance (MR) imaging enables further scan acceleration via undersampling than previously feasible. While many of these methods incorporate similar styles of CS, there remains significant variation in the particular choice of function used to promote sparsity. Having developed SpRING, a framework for combining CS and GRAPPA, a parallel MR image reconstruction method, we view the choice of penalty function as a design choice rather than a defining feature of the algorithm. For both simulated and real data, we compare different sparsity penalty functions to the empirical distribution of the reference images. Then, we perform reconstructions on uniformly undersampled data using a variety of penalty functions to illustrate the impact appropriately choosing the penalty function has on the performance of SpRING. These experiments demonstrate the importance of choosing an appropriate penalty function and how such a choice may differ between simulated data and real data.