Cramer-Rao bound for a sparse complex model

Complex-valued data play a prominent role in a number of signal and image processing applications. The aim of this paper is to establish some theoretical results concerning the Cramer-Rao bound for estimating a sparse complex-valued vector. Instead of considering a countable dictionary of vectors, we address the more challenging case of an uncountable set of vectors parameterized by a real variable. We also present a proximal forward-backward algorithm to minimize an ℓ₀ penalized cost, which allows us to approach the derived bounds. These results are illustrated on a spectrum analysis problem in the case of irregularly sampled observations.