Maximum a posteriori-based approach to blind nonlinear underdetermined mixture

A new learning algorithm is proposed to solve the separation problem of the blind nonlinear underdetermined mixtures. The mixing system is characterised by the post-nonlinear structure and concurrently the number of sensors is less than the number of sources. The proposed algorithm utilises the generalised Gaussian distribution to model the prior probability distribution of the source signals and the mixing variables. A novel iterative technique based on alternate optimisation within the Bayesian framework has been developed for estimating the source signals, mixing matrix and the nonlinear distortion. It is shown that through formal Bayesian derivation, the update of the mixing matrix can be decomposed into two separate constituents given by linear and nonlinear parts. Furthermore, the post-nonlinear distortion functions in the mixing model are approximated by a set of polynomials and the coefficients are found by solving a least square error problem. Simulations have been carried out to verify the effectiveness in separating signals under nonlinear and underdetermined conditions. An average margin of 130 improvement has been obtained when compared with the existing linear algorithm.