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Theses

Mesures de dépendance pour la séparation aveugle de sources. Application aux mélanges post non linéaires

Abstract : This thesis deals with statistical methods applied to signal processing. In order to solve the problem of blind source separation using an independent component analysis, we define two measures of dependence, the well-known mutual information and a new one : the quadratic dependence measure. We show some properties of the latter related to characteristic functions and propose a simple estimation, whose asymptotic properties are obtained thanks to the U-statistics of Hoeffding. This leads to measure the effect of the choice of a kernel and a bandwidth. Finally, the resolution of the blind source separation problem in post nonlinear mixtures is achieved through the minimization of the dependence measures. We describe three different approaches, including one based on the derivatives of the nonlinearities. Plots of the objective-function exhibit the obstacles to overcome the minimisation.
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https://tel.archives-ouvertes.fr/tel-00004629
Contributor : Sophie Achard <>
Submitted on : Wednesday, February 11, 2004 - 3:29:03 PM
Last modification on : Wednesday, March 10, 2021 - 1:50:03 PM
Long-term archiving on: : Friday, April 2, 2010 - 7:23:10 PM

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  • HAL Id : tel-00004629, version 1

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Sophie Achard. Mesures de dépendance pour la séparation aveugle de sources. Application aux mélanges post non linéaires. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2003. Français. ⟨tel-00004629⟩

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