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Generalized Wiener filtering for positive alpha-stable random variables

Paul Magron 1, 2 Roland Badeau 1, 2 Antoine Liutkus 3
3 MULTISPEECH - Speech Modeling for Facilitating Oral-Based Communication
Inria Nancy - Grand Est, LORIA - NLPKD - Department of Natural Language Processing & Knowledge Discovery
Abstract : 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.
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Submitted on : Friday, July 1, 2016 - 6:05:03 PM
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  • HAL Id : hal-01340797, version 1

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

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