Blind source extraction: Standard approaches and extensions to noisy and post-nonlinear mixing

We provide an overview of blind source extraction (BSE) algorithms whereby only one source of interest is separated at the time. First, BSE approaches for linear instantaneous mixtures are reviewed with a particular focus on the “linear predictor” based approach. A rigorous proof of the existence BSE paradigm is provided, and the mean-square prediction error (MSPE) is identified as a unique source feature. Both the approaches based on second-order statistics (SOS) and higher-order statistics (HOS) are included, together with extensions for BSE in the presence of noise. To help circumvent some of the problems associated with the assumption of linear mixing, an extension in the form of post-nonlinear mixing system is further addressed. Simulation results are provided which confirm the validity of the theoretical results and demonstrate the performance of the derived algorithms in noiseless, noisy and nonlinear mixing environments.