Most of the literature on the blind source separation problem only considers the case where the number of sensors and number of sources are equal. Algorithms developed for this "square" mixing case cannot be applied directly in the "tall" mixing case in which there are more sensors than sources. This thesis studies the problems of separating signals from tall mixtures. The approach taken here is to convert the tall mixture into square one by adding fake sources. This is termed dimension inflation. Adaptive natural gradient algorithms are unstable when the fake sources are taken to be Gaussian. The stability of the natural gradient algorithm is studied to find suitable probabilistic models for the fake sources that lead to stable adaptive algorithms. The Cramer-Rao bound of the dimension inflation algorithm and another algorithm termed dimension reduction are computed to show that dimension reduction has better results.
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