Blind separation of speech and sub-Gaussian signals in underdetermined case

Conventional blind source separation (BSS) algorithms are applicable when the number of sources equals to that of observations; however, they are inapplicable when the number of sources is larger than that of observations. Most underdetermined BSS algorithms have been developed based on an assumption that all sources have sparse distributions. These algorithms are applicable to separate speech signals with super-Gaussian distribution in the underdetermined case. However, they fail to separate the underdetermined mixtures of speech signals and sub-Gaussian signals. In this paper, a novel method for separating the underdetermined mixtures of sources with both superand sub-Gaussian distributions is proposed. In the proposed method, underdetermined BSS problem is converted to conventional BSS problem by generating hidden observations so that the probability of estimated sources is maximized. Simulation results show that the proposed method can separate the underdetermined mixtures of speech signals and sub-Gaussian signals.