Cramer-Rao lower bounds for atomic decomposition

Abstract

In a previous paper [1] we presented a method for atomic decomposition with chirped, Gabor functions based on maximum likelihood estimation. In this paper we present the Cramér-Rao lower bounds for estimating the seven chirp parameters, and the results of a simulation showing that our sub-optimal, but computationally tractable, estimators perform well in comparison to the bound at low signal-to-noise ratios. We also show that methods based on signal dictionaries will require much higher computations to perform well in low signal-to-noise ratios.