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Algorithms based on sparsity hypotheses for robust estimation of the noise standard deviation in presence of signals with unknown distributions and concurrences

Dominique Pastor 1, 2, François-Xavier SOCHELEAU 1, 2

(2010)

Inmany applications, d-dimensional observations result fromthe randompresence or absence of randomsignals in independent and additivewhite Gaussian noise. An estimate of the noise standard deviation can then be very useful to detect or to estimate these signals, especially when standard likelihood theory cannot apply because of too little prior knowledge about the signal probability distributions. Recent results and algorithms have then emphasized the interest of sparsity hypotheses to design robust estimators of the noise standard deviation when signals have unknown distributions. As a continuation, the present paper introduces a new robust estimator for signals with probabilities of presence less than or equal to one half. In contrast to the standard MAD estimator, it applies whatever the value of d. This algorithm is applied to image denoising by wavelet shrinkage as well as to non-cooperative detection of radiocommunications.In both cases, the estimator proposed in the present paper outperforms the standard solutions used in such applications and based on the MAD estimator. The Matlab code corresponding to the proposed estimator is available at http://perso.telecom-bretagne.eu/pastor

1 :	Département Signal et Communications (SC)
	Institut Mines-Télécom – Télécom Bretagne – PRES Université Européenne de Bretagne [UEB]
2 :	Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC)
	CNRS : UMR3192 – Université de Bretagne Occidentale [UBO] – Université de Bretagne Sud – Institut Mines-Télécom – Télécom Bretagne – PRES Université Européenne de Bretagne [UEB] – Institut Supérieur des Sciences et Technologies de Brest (ISSTB)

Domaine

:

Statistiques/Théorie

Mots Clés : Sparsity – Robust statistics – Non parametric statistics – MAD estimation – Wavelet shrinkage – Soft thresholding – Image denoising – Communication Electronic Support – Cognitive radio

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Contributeur : Bibliothèque Télécom Bretagne <>

Déposé pour le compte de : Brest Bibliotheque TELECOM Bretagne <>

Soumis le : Vendredi 1 Juin 2012, 14:45:43

Dernière modification le : Vendredi 1 Juin 2012, 14:56:29