On variable density compressive sampling

Incoherence between sparsity basis and sensing basis is an essential concept for compressive sampling. In this context, we advocate a coherence-driven optimization procedure for variable density sampling. The associated minimization problem is solved by use of convex optimization algorithms. We also propose a refinement of our technique when prior information is available on the signal support in the sparsity basis. The effectiveness of the method is confirmed by numerical experiments. Our results also provide a theoretical underpinning to state-of-the-art variable density Fourier sampling procedures used in MRI.