Generalized Wiener filtering for positive alpha-stable random variables

Filtrage de Wiener généralisé pour des variables aléatoires positives alpha-stables

Paul Magron (1, 2) , Roland Badeau (1, 2) , Antoine Liutkus (3)

1 Télécom ParisTech
2 LTCI - Laboratoire Traitement et Communication de l'Information
3 MULTISPEECH - Speech Modeling for Facilitating Oral-Based Communication

This report provides a mathematical proof of a result which is a generalization of Wiener filtering to Positive alpha-stable (PalphaS) distributions, a particular subclass of the alpha-stable distributions family whose support is [0;+inf[. PalphaS distributions are useful to model nonnegative data and since they are heavy-tailed, they present a natural robustness to outliers. In applications such as nonnegative source separation, it is paramount to have a way of estimating the isolated components that constitute a mixture. To address this issue, we derive an estimator of the sources which is given by the conditional expectation of the sources knowing the mixture. It extends the validity of the generalized Wiener filtering to PalphaS distributions. This allows us to extract the underlying PalphaS sources from their mixture.

Mots clés: nonnegative source separation; Wiener filtering; Stable distribution; Positive alpha-stable distributions

Domaines: Traitement du signal et de l'image [eess.SP]

Paul Magron, Roland Badeau, Antoine Liutkus. Generalized Wiener filtering for positive alpha-stable random variables. [Research Report] 2016D000, Télécom ParisTech. 2016. ⟨hal-01340797⟩