New constructions of Bernoulli and Gaussian sensing matrices for compressive sensing

Compressive Sensing (CS) is a new methodology to reconstruct sparse signals from a few number of measurements. These measurements are captured by a sensing matrix, which has a direct impact on the performance of the reconstruction algorithms. Among the sensing matrices proposed in the literature, Bernoulli and Gaussian random sensing matrices are the most prominent. In this work, we propose to improve these two sensing matrices following a trivial method to enhance their columns orthogonality property. Extensive theoretical comparisons with Bernoulli, Gaussian and partial Hadamard sensing matrices are carried out to show the power of the proposed sensing matrices. In that, the new sensing matrices provides a considerable gain in terms of the Rate of Exact Reconstruction (RER).