An instantaneous formulation of mixtures for blind separation of propagating waves

This paper deals with the modeling and the identification of mixtures of multiple propagating waves recorded by a compact set of sensors. These mixtures, depending on attenuation coefficients and propagating delays, are represented as instantaneous mixtures of different temporal derivatives of sources generating the waves. These derivatives act as new dependent sources, and the instantaneous mixtures are not directly identifiable. It is shown that separation can be achieved by a second-order statistical analysis of the recordings, when a sufficient number of sensors is available. The validity of this approach is illustrated by numerical simulations for mixtures of three audio sources. The results point out good performances (up to -30 dB of remaining crosstalk). Experimental validation of the theoretical model is also presented in the case of a two-source separation with an eight-microphone array.