Correlation tuning in compressive sensing based on rakeness: A case study

Abstract

In this paper we take into account the rakeness approach in the design of Compressed Sensing (CS) based system, which allows, by means of the matching of some statistical properties of the CS sampling functions with statistical features of the input signal, to greatly increase system performance in terms of either a reduction of resources (hardware, energy, etc) required for the signal acquisition or an increase in the acquisition quality. In particular, with respect to the general formulation, we make two additional and non-restrictive hypotheses to ensure a good behavior of the system. With these, we can compute an upper and a lower bound for the parameter r used to control the statistical matching level, and we show with some numerical examples that the choice of r is not critical. In particular, any r value taken from the computed interval ensures almost optimal performance, making the rakeness approach robust and worthwhile

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“…Its solution, that is offline computed, is given by a correlation matrix C φ , that identifies the stochastic process to be used for generating sensing vectors. The tuning of τ on a proper range is not critical since it does not appreciably alter the overall system performance [24,25]. Note that this approach is perfectly compatible with the generation of a binary antipodal sensing matrix 2 .…”

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“…Compared to full random matrices, SBM reconstruction performance is not as good [63]. The authors in [64], [65] introduce Rakeness-based CS. This method aims to maximize the projection's ability to collect the signal energy while maintaining randomly sufficient paths to limit the signal space.…”

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“…where e represents the energy of each φ j , and r is a noncritical parameter ensuring that the φ j are random enough to preserve RIP [6]. The outcome of ( 4) is the correlation matrix R φ of the stochastic process φ to be used to generate the φ j .…”