If you use this code, please cite the following paper: Puy et al., "On Variable Density Compressive Sampling," in IEEE Signal Processing Letters, vol. 18(10), pp. 595-598, 2011.

• Link to preprint

• Link to published paper

Abstract: 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.

Acknowledgement: This code make use of the function "oneProjectorMex" of the spgl1 toolbox. The SPGL1 toolbox is available at http://www.cs.ubc.ca/~mpf/spgl1/. The description of the theory of the SPGL1 algorithm is outlined in E. van den Berg and M. P. Friedlander, "Probing the Pareto frontier for basis pursuit solutions," SIAM J. on Scientific Computing, 31(2):890-912, 2008.