Nonlinear underdetermined blind signal separation using Bayesian neural network approach

Nonlinear signal separation and underdetermined signal separation have received much attention in blind signal separation literature. However, neither of them can solve the situation where both nonlinear and underdetermined characteristics exist at the same time. In this paper, a new learning algorithm based on Bayesian statistics is proposed to solve the separation problem of the blind nonlinear underdetermined mixtures. We suppose that the observations are post-nonlinear mixtures of the sources and the number of observations is less than the number of sources. Due to the characteristics of Bayesian statistics, the generalized Gaussian distribution model is utilized to approximate the prior probability distribution of the source signals and the mixing variables. Formal derivation shows that the source signals, mixing matrix and nonlinear functions can be estimated through an iterative technique based on alternate optimization. The nonlinear mismatch problem is also considered by applying a multilayer perceptron with a typical least square error problem. Simulations have been given to demonstrate the effectiveness in separating signals under nonlinear and underdetermined conditions.