  We advocate an optimization procedure for variable density sampling in the
context of compressed sensing. In this perspective, we introduce a minimization
problem for the coherence between the sparsity and sensing bases, whose
solution provides an optimized sampling profile. This minimization problem is
solved with the 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 magnetic
resonance imaging.
