Underdetermined Blind Source Separation Based on Third-order Statistics

Blind Source Separation ( BSS) aims to separate the source signals from the mixed observations without any information about the mixing process and the source signals, which is a major area in the signal processing field. In Underdetermined Blind Source Separation ( UBSS), the number of observed signals is less than the number of source signals, and thus UBSS is much closer to reality than the determined/overdetermined BSS. However, the observations are always disturbed by noise, deteriorating the performance of traditional underdetermined blind source separation based on second-order statistics and signal sparsity. Taking the advantage of third-order statistics in dealing with symmetric noise, a novel mixing matrix estimation method based on the third- order statistics of the observations is proposed. Considering the autocorrelations of the sources, a sequence of third-order statistics of the observations corresponding to multiple delays are calculated and stacked into a fourth-order tensor. Then the mixing matrix is estimated via the canonical polyadic decomposition of the fourth-order tensor. Furthermore, the generalized Gaussian distribution is employed to characterize the sources and the expectation-maximum algorithm is utilized to recover the sources. The results from 1000 Monte Carlo experiments demonstrate that the proposed method is robust to the noise. The proposed method archives the normalized mean square error of -20.35 dB and the mean absolute correlation coefficient between the recovered sources and the real ones of 0.84 when the signal to noise ratios equal to 15 dB for the cases with 3x4 mixing matrices. Simulation results demonstrate that the proposed algorithm yields superior performances in comparing with state-of-the-art underdetermined blind source separation methods.