A convolutive source separation method with self-optimizing non-linearities

This paper deals with the separation of two convolutively mixed signals. The proposed approach uses a recurrent structure adapted by a generic rule involving arbitrary separating functions. These functions should ideally be set so as to minimize the asymptotic error variance of the structure. However, these optimal functions are often unknown in practice. The proposed alternative is based on a selfadaptive (sub-)optimization of the separating functions, performed by estimating the projection of the optimal functions on a predehned set of elementary functions. The equilibrium and stability conditions of this rule and its asymptotic error variance are studied. Simulations are performed for real mixtures of speech signals. They show that the proposed approach yields much better performance than classical rules. 1. PROBLEM STATEMENT AND CLASSICAL RESULTS Multichannel blind (or self-adaptive) source separation is a basic topic in signal processing. It aims at extracting unknown independent signals (the so-called sources) from sensor observations that are unknown linear mixtures of these sources. A commonly used model corresponds to a two-dimensional mixing system defined by the following source-observation relationship: YI(z) = S,(t) + An(r)&(z) (1) Yz(z) = Ax(z)Xl(z) + X,(z), (2) where Xc(z) and Y, (2) are respectively the Z-transforms of the source z,(n) and observation y,(n). A,, (2) is the unknown transfer function of the channel that links source i to sensor i. The corresponding impulse response is denoted (at, (k))&Z hereafter. The mixing system is assumed to be minimum-phase (i.e. to be causal and stable and to have a This work was partly performed when the authors were with the Laboratoires d’Electronique Philips S.A.S (LEP), at LimeilBrivannes, France. Yannick Deville Laboratoire d’Acoustique, de Metrologie; d’Instrumentation (LAMI) Universite Paul Sabatier 38 Rue des 36 Ponts 31400 Toulouse France. [email protected]