Blind Separation of Parametric Nonlinear Mixtures of Possibly Autocorrelated and Non-Stationary Sources

In this paper, we present a new method, formulated in a maximum-likelihood framework, for blindly separating nonlinear mixtures of statistically independent signals. Our method exploits, on the one hand, the knowledge of the parametric model of the mixing transformation (with unknown parameter values), and on the other hand, the possible structure of source signals, i.e., their autocorrelation and/or nonstationarity. One of the main advantages of the proposed method is that it can be implemented even if the analytical expression of the inverse model is unknown. The method is first addressed in a general configuration, then detailed for two special cases, i.e., a simple bijective “toy” model and a linear-quadratic model. The study of the toy model is interesting because of its simplicity and its global bijectivity, which allows us to focus our efforts on parameter estimation. The linear-quadratic model is chosen due to its capacity to describe real-world mixing phenomena. Simulation results, using the toy model and using a subclass of the linear-quadratic model (i.e., the bilinear model), show that taking into account the nonlinearity of the mixing transformations and the structure of signals considerably improves separation performance.