Sparsity and adaptivity for the blind separation of partially correlated sources
This addresses the limitation of BSS methods in real-world scenarios where sources are partially correlated, particularly in fields like astrophysics, though it appears incremental as it builds on existing sparsity-based approaches.
The authors tackled the problem of blind source separation (BSS) for partially correlated sources, which standard methods fail to handle, by introducing the Adaptive Morphological Component Analysis (AMCA) method, which showed robustness in numerical experiments and was successfully applied to astrophysical microwave data.
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.