Finite rate of innovation with non-uniform samples

In this paper, we investigate the problem of retrieving the innovation parameters (time and amplitude) of a stream of Diracs from non-uniform samples taken with a novel kernel (a hyperbolic secant). We devise a non-iterative, exact algorithm that allows perfect reconstruction of 2K innovations from as few as 2K non-uniform samples. We also investigate noise issues and compute the Cramér-Rao lower bounds for this problem. A simple total least-squares extension of the algorithm proves to be efficient in reconstructing the location of a single Dirac from noisy measurements.