Sparse blind source separation for partially correlated sources

J. Bobin (1) , J. Starck (1) , J. Rapin (2) , A. Larue (2)

1 IRFU - Institut de Recherches sur les lois Fondamentales de l'Univers
2 LADIS - Laboratoire d'analyse des données et d'intelligence des systèmes

Blind source separation (BSS) is a very popular technique to analyze data which can be modeled as linear mixtures of elementary sources. Standard approaches generally make the assumption that such sources are statistically independent or at least uncorrelated. However, this is barely the case for real-world sources which are very often partially correlated. We present a new sparsity-enforcing BSS method coined Adaptive Morphological Component Analysis (AMCA) designed to retrieve sparse and partially correlated sources based on an adaptive weighting scheme. Numerical experiments have been carried out which show that the proposed method is robust to the partial correlation of the sources while standard BSS techniques fail. The performances of the proposed algorithm are further illustrated with simulations in the context of astrophysics.

Keywords: Sparsity; wavelets; blind source separation; morphological diversity; Correlation; Standards; Algorithm design and analysis; RNA; Sparse matrices; statistical analysis; partially correlated sources; sparsity-enforcing BSS method; adaptive morphological component analysis; AMCA; adaptive weighting scheme

Domains: Signal and Image Processing; Numerical Analysis [math.NA]; Astrophysics [astro-ph]; Applications [stat.AP]

J. Bobin, J. Starck, J. Rapin, A. Larue. Sparse blind source separation for partially correlated sources. 2014 IEEE International Conference on Image Processing (ICIP), Oct 2014, Paris, France. pp.7026215, ⟨10.1109/ICIP.2014.7026215⟩. ⟨cea-01887796⟩