Fundamental performance bounds for a compressive sampling system

In this paper we explore several fundamental bounds for a compressive sampling system which uses the Fourier sampling algorithm of Gilbert et al. Beginning with the theoretical bounds on the number of samples necessary to reconstruct high fidelity approximations of input signals, we refine those theoretical bounds with empirical values in several practical input models. We show that the performance is consistent with traditional sampling systems, and, in certain cases, much better.