Spread Spectrum for Universal Compressive Sampling

We propose a universal and efficient compressive sampling strategy based on the use of a spread spectrum technique. The method essentially consists in a random pre-modulation of the signal of interest followed by projections onto randomly selected vectors of an orthonormal basis. The effectiveness of the technique is induced by a decrease of coherence between the sparsity and the sensing bases. The sensing scheme is universal for a family of sensing bases in the sense that the number of measurements needed for accurate recovery is optimal and independent of the sparsity matrix. It is also efficient as sensing matrices with fast matrix multiplication algorithms can be used. These results are confirmed experimentally through analyses of the phase transition of the l1-minimization problem.