A novel sensing matrix for cluster structured sparse signals

In Compressive Sensing (CS) technique, the original sparse signal is compressed in an adequate manner so as to ease its recovery from a reduced number of measurements. This depends potently on the sensing matrix. In this paper, we consider cluster structured sparse signals, and propose an enhanced Bernoulli sensing matrix. We show that the original data can be efficiently reconstructed by performing traditional signal recovery algorithms with the proposed sensing matrix. Moreover, the use of the new sensing matrix provides a considerable gain in terms of the rate of exact reconstruction.