Distributed covariance estimation for compressive signal processing

In this paper we present a novel technique for the distributed estimation of the covariance matrix of an additive colored noise process affecting Compressed Sensing (CS) measurements. The main application is in wireless sensor networks, where nodes sense signals in CS format in order to save energy in the computation and transmission stages. The proposed technique enables a variety of compressive signal processing operations to be performed at each node directly on the linear measurements, such as detection, exploiting the knowledge of the noise statistics, thereby achieving improved performance. The parametric approach we introduce promises to yield good results while keeping the communication cost low. Hence, we validate our technique by evaluating the error on the estimated covariance matrix, and by including it in a compressive detection task.