A fast geometric method for blind separation of sparse sources

In this paper, we introduce a new geometry-based approach for blind separation of sparse sources modeled by a linear instantaneous mixtures model. The algorithm assumes at least two mixtures of any number of sources, in addition to the sources being sparse in some representation. Formulating the problem as a clustering problem, the unknown mixing matrix is estimated from the transformed data up to the usual indeterminacies. An extraction method is then used for separation of the sources according to transform-space directions induced by the mixing-matrix estimation process, with an optional noise reduction scheme. Because of the geometric nature of the methods, they are extremely fast and are suitable for use in real-time systems. Simulation results demonstrate the effectiveness of the proposed algorithm for different signal-to-noise ratio (SNR) values.