Robust adaptive blind signal estimation algorithm for underdetermined mixture

In general, existing blind source separation (BSS) algorithms have been designed based on assumptions that there are at least an equal number of sources and sensors and/or there is no noise present. These ideal situations rarely exist and hence the algorithms do not produce optimum results where either one or both of the assumptions have been violated. Underdetermined mixtures where the number of source signals is greater than the number of observed signals are encountered in neural signal detection from a small number of sensors, image modelling, EEG data and biomedical applications. A new algorithm to estimate unknown source signals from fewer observed signals and simultaneously reduce noise is proposed. The proposed algorithm is based upon a model that addresses the issue of noise and offers greater accuracy with standard assumptions relaxed. It offers an attractive solution with no pre-requisites on the nature of the signals and noise for the algorithm to be applicable. Most BSS algorithms adopt batch processing and are only applicable to orthogonal mixtures. The proposed algorithm does not require the mixing matrix to be orthogonal and can be implemented in an adaptive format to track time-varying mixtures. Results supporting the algorithm's superiority and comparisons with results from other algorithms are also presented to prove the tracking capability of our adaptive algorithm. Synthetic and realtime simulations demonstrate the improvement in convergence and accuracy of estimated signals with fewer restrictions in terms of its applicability.