Sparsity and adaptivity for the blind separation of partially correlated sources

TL;DR

This paper introduces AMCA, a novel sparsity-based blind source separation method that effectively retrieves partially correlated sources by adaptively re-weighting samples, outperforming standard techniques especially in astrophysical data analysis.

Contribution

The paper presents a new adaptive sparsity-enforcing BSS method called AMCA that handles partial source correlation, which standard methods struggle with.

Findings

AMCA outperforms standard BSS methods in partially correlated scenarios.

AMCA is robust to source correlation in numerical experiments.

Applied successfully to astrophysical microwave data separation.

Abstract

Blind source separation (BSS) is a very popular technique to analyze multichannel data. In this context, the data are modeled as the linear combination of sources to be retrieved. For that purpose, standard BSS methods all rely on some discrimination principle, whether it is statistical independence or morphological diversity, to distinguish between the sources. However, dealing with real-world data reveals that such assumptions are rarely valid in practice: the signals of interest are more likely partially correlated, which generally hampers the performances of standard BSS methods. In this article, we introduce a novel sparsity-enforcing BSS method coined Adaptive Morphological Component Analysis (AMCA), which is designed to retrieve sparse and partially correlated sources. More precisely, it makes profit of an adaptive re-weighting scheme to favor/penalize samples based on their level of correlation. Extensive numerical experiments have been carried out which show that the proposed method is robust to the partial correlation of sources while standard BSS techniques fail. The AMCA algorithm is evaluated in the field of astrophysics for the separation of physical components from microwave data.