Separation of Alpha-Stable Random Vectors - Archive ouverte HAL Access content directly
Journal Articles Signal Processing Year : 2020

Separation of Alpha-Stable Random Vectors

(1) , (2) , (3)
1
2
3

Abstract

Source separation aims at decomposing a vector into additive components. This is often done by first estimating source parameters before feeding them into a filtering method, often based on ratios of covariances. The whole pipeline is traditionally rooted in some probabilistic framework providing both the likelihood for parameter estimation and the separation method. While Gaussians are ubiquitous for this purpose, many studies showed the benefit of heavy-tailed models for estimation. However, there is no counterpart filtering method to date exploiting such formalism, so that related studies revert to covariance-based filtering after estimation is finished. Here, we introduce a new multivariate separation technique, that fully exploits the flexibility of α-stable heavy-tailed distributions. We show how a spatial representation can be exploited, which decomposes the observation as an infinite sum of contributions originating from all directions. Two methods for separation are derived. The first one is non-linear and similar to a beamforming technique, while the second one is linear, but minimizes a covariation criterion, which is the counterpart of the covariance for α-stable vectors. We evaluate the proposed techniques in a large number of challenging and adverse situations on synthetic experiments, demonstrating their performance for the extraction of signals from strong interferences.
Fichier principal
Vignette du fichier
AlphaStableVector_final.pdf (1.72 Mo) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-02433213 , version 1 (09-01-2020)

Identifiers

Cite

Mathieu Fontaine, Roland Badeau, Antoine Liutkus. Separation of Alpha-Stable Random Vectors. Signal Processing, 2020, pp.107465. ⟨10.1016/j.sigpro.2020.107465⟩. ⟨hal-02433213⟩
180 View
296 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More