Sensing Matrix Sensitivity to Random Gaussian Perturbations in Compressed Sensing

In compressed sensing, the choice of the sensing matrix plays a crucial role: it defines the required hardware effort and determines the achievable recovery performance. Recent studies indicate that by optimizing a sensing matrix, one can potentially improve system performance compared to random ensembles. In this work, we analyze the sensitivity of a sensing matrix design to random perturbations, e.g., caused by hardware imperfections, with respect to the total (average) matrix coherence. We derive an exact expression for the average deterioration of the total coherence in the presence of Gaussian perturbations as a function of the perturbations' variance and the sensing matrix itself. We then numerically evaluate the impact it has on the recovery performance.