Compressive detection of stochastic signals with the measurement matrix not necessarily orthonormal

We consider in this paper detecting stochastic signals with known probability density function (PDF) from their compressive measurements. We refer to it as the compressive detection problem. The Neyman-Pearson (NP) theorem is applied to derive the NP detectors for Gaussian signals. Our work is more general over the existing literature in the sense that we do not require that the measurement matrix is orthonormal. Theoretical performance results, namely the detection probability and the false alarm rate of the proposed NP detectors, are provided. They are verified via extensive computer experiments.