Recovery of nonuniformdirac pulses from noisy linear measurements

Abstract

We consider the recovery of a finite stream of Dirac pulses at nonuniform locations, from noisy lowpass-filtered samples. We show that maximum-likelihood estimation of the unknown parameters can be formulated as structured low rank approximation of an appropriate matrix. To solve this difficult, believed NP-hard, problem, we propose a new heuristic iterative algorithm, based on a recently proposed splitting method for convex nonsmooth optimization. Although the algorithm comes, in absence of convexity, with no convergence proof, it converges in practice to a local solution, and even to the global solution of the problem, when the noise level is not too high. It is also fast and easy to implement.