Cadzow Denoising Upgraded: A New Projection Method for the Recovery of Dirac Pulses from Noisy Linear Measurements
Résumé
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 reformulated as structured low rank approximation of an appropriate matrix. To solve this difficult, even 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. Thus, the estimation error is smaller than with the classical heuristic method of alternating projections, a.k.a. Cadzow denoising, while sharing its speed and easiness of implementation.
Origine : Fichiers produits par l'(les) auteur(s)