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Global Optimization for Recovery of Clipped Signals Corrupted With Poisson-Gaussian Noise

Abstract

We study a variational formulation for reconstructing nonlinearly distorted signals corrupted with a Poisson-Gaussian noise. In this situation, the data fidelity term consists of a sum of a weighted least squares term and a logarithmic one. Both of them are precomposed by a nonlinearity, modelling a clipping effect, which is assumed to be rational. A regularization term, being a piecewise rational approximation of the ℓ0 function provides a suitable sparsity measure with respect to a preset linear operator. We propose a global optimization approach for such a problem. More specifically, it is first transformed into a generalized moment problem by introducing some auxiliary variables. Then, a hierarchy of semidefinite programming relaxations is built. Numerical examples show the good performance of the proposed approach.

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Details

Category:
Articles
Type:
artykuły w czasopismach
Published in:
IEEE SIGNAL PROCESSING LETTERS no. 27, pages 970 - 974,
ISSN: 1070-9908
Language:
English
Publication year:
2020
Bibliographic description:
Marmin A., Węsierska A., Castella M., Pesquet J.: Global Optimization for Recovery of Clipped Signals Corrupted With Poisson-Gaussian Noise// IEEE SIGNAL PROCESSING LETTERS -Vol. 27, (2020), s.970-974
DOI:
Digital Object Identifier (open in new tab) 10.1109/lsp.2020.2998699
Verified by:
Gdańsk University of Technology

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