Post-nonlinear undercomplete blind signal separation: A Bayesian approach

The post-nonlinear undercomplete Blind Signal Separation problem is solved by a Bayesian approach in this paper. The proposed algorithm applies the Generalized Gaussian model to approximate the prior distribution probability and a Maximum a Posteriori (MAP) based learning algorithm to estimate the source signals, mixing matrix and the nonlinearity of the mixing process. The mixing nonlinearity is modeled by a Multilayer Perceptron (MLP) neural network. In our proposed algorithm, the source signals, mixing matrix and the parameters of the MLP are iteratively updated in an alternate manner until they converges to a fixed value. The noise variance is regarded as the hyper-parameter which is estimated in a closed form. Simulations based on real audio have been carried out to investigate the efficacy of the proposed algorithm. A performance gain of over 125% has been achieved when compared to linear approach.