Blind Separation of Independent Sources Using Gaussian Mixture Model

In this paper, two novel algorithms for blind separation of noiseless instantaneous linear mixture of independent sources are presented. The proposed algorithms exploit nonGaussianity of the independent sources by modeling their distribution using the Gaussian mixture model (GMM). The first proposed method is based on the maximum-likelihood (ML) estimator. According to this method, the sensors distribution parameters are estimated via the expectation-maximization (EM) algorithm for GMM parameter estimation and the separation matrix is estimated by applying nonorthogonal joint diagonalization of the estimated GMM covariance matrices. The second proposed method is also a ML-based approach. According to this method, the distribution parameters of the prewhitened sensors are estimated via the EM algorithm for GMM parameter estimation and a unitary separation matrix is estimated by applying orthogonal joint diagonalization of the estimated GMM covariance matrices. It is shown that estimation of the sensors distribution parameters amounts to obtaining a tight lower bound on the log-likelihood of the separation matrix, and that the joint diagonalization of the estimated GMM covariance matrices amounts to maximization of the obtained tight lower bound. Simulations demonstrate that the proposed methods outperform state-of-the-art blind source separation techniques in terms of interference-to-signal ratio.