Blind noisy mixture separation for independent/dependent sources through a regularized criterion on copulas

M. El Rhabi (1) , H. Fenniri (2) , A. Ghazdali (3) , A. Hakim (4) , A. Keziou (2)

1 IMI - Département Ingénierie Mathématique et Informatique, École des Ponts ParisTech
2 CRESTIC - Centre de Recherche en Sciences et Technologies de l'Information et de la Communication - EA 3804
3 LIPOSI - Laboratoire Ingénierie des Procédés et Optimisation des Systèmes Industriels, Ecole Nationale des Sciences Appliquées, Université Hassan I
4 UCA - Université Cadi Ayyad [Marrakech]

The paper introduces a new method for Blind Source Separation (BSS) in noisy instantaneous mixtures of both independent or dependent source component signals. This approach is based on the minimization of a regularized criterion. Precisely, it consists in combining the total variation method for denoising with the Kullback–Leibler divergence between copula densities. The latter takes advantage of the copula to model the structure of the dependence between signal components. The obtained algorithm achieves separation in a noisy context where standard BSS methods fail. The efficiency and robustness of the proposed approach are illustrated by numerical simulations.

Keywords: Total variation; Noisy instantaneous mixtures; Blind source separation; Mutual information; Kullbak–Leibler divergence between; Copulas; Kullbak-Leibler divergence

Domains: Mathematics [math]; Statistics [math.ST]; Information Theory [cs.IT]; Signal and Image Processing

M. El Rhabi, H. Fenniri, A. Ghazdali, A. Hakim, A. Keziou. Blind noisy mixture separation for independent/dependent sources through a regularized criterion on copulas. Signal Processing, 2017, 131, pp.502 - 513. ⟨10.1016/j.sigpro.2016.09.006⟩. ⟨hal-01811736⟩