Morphological diversity and sparsity in blind source separation

J. Bobin (1) , Yassir Moudden (1) , Jalal M. Fadili (2) , Jean-Luc Starck (1)

1 DEDIP - Département d'Electronique, des Détecteurs et d'Informatique pour la Physique (ex SEDI)
2 Equipe Image - Laboratoire GREYC - UMR6072

This paper describes a new blind source separation method for instantaneous linear mixtures. This new method coined GMCA (Generalized Morphological Component Analysis) relies on morphological diversity. It provides new insights on the use of sparsity for blind source separation in a noisy environment. GMCA takes advantage of the sparse representation of structured data in large overcomplete signal dictionaries to separate sources based on their morphology. In this paper, we define morphological diversity and focus on its ability to be a helpful source of diversity between the signals we wish to separate. We introduce the blind GMCA algorithm and we show that it leads to good results in the overdetermined blind source separation problem from noisy mixtures. Both theoretical and algorithmic comparisons between morphological diversity and independence-based separation techniques are given. The effectiveness of the proposed scheme is confirmed in several numerical experiments.

Domaines: Algorithme et structure de données [cs.DS]; Traitement des images [eess.IV]

J. Bobin, Yassir Moudden, Jalal M. Fadili, Jean-Luc Starck. Morphological diversity and sparsity in blind source separation. 7th International Conference on Independent Component Analysis and Signal Separation ICA'07, 2007, London, United Kingdom. pp.349-356, ⟨10.1007/978-3-540-74494-8_44⟩. ⟨hal-00196328⟩