Recovery of nonuniformdirac pulses from noisy linear measurements

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, bel...

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Bibliographic Details
Main Authors: Condat, L., Hirabayashi, A., Hironaga, Y.
Format: Conference Proceeding
Language:eng ; jpn
Subjects:
Approximation methods
Cadzow denoising
finite rate of innovation
Maximum likelihood estimation
Noise
Noise measurement
optimization
Recovery of Dirac pulses
structured low rank approximation
Technological innovation
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Summary: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.
ISSN:1520-6149
2379-190X
DOI:10.1109/ICASSP.2013.6638819