Sampling signals with finite rate of innovation in the presence of noise

Recently, it has been shown that it is possible to sample non-bandlimited signals that possess a limited number of degrees of freedom and uniquely reconstruct them from a finite number of uniform samples. These signals include, amongst others, streams of Diracs. In this paper, we investigate the problem of estimating the innovation parameters of a stream of Diracs from its noisy samples taken with polynomial or exponential reproducing kernels. For the one-Dirac case, we provide exact expressions for the Cramer-Rao bounds of this estimation problem. Furthermore, we propose methods to reconstruct the location of a single Dirac that reach the optimal performance given by the unbiased CramerRao bounds down to noise levels of 5 dB.