Underdetermined Joint Blind Source Separation for Two Datasets Based on Tensor Decomposition

In this letter, we aim to jointly separate the underdetermined mixtures of latent sources from two datasets, where the number of sources exceeds the number of observations in each dataset. Currently available blind source separation (BSS) methods, including joint blind source separation (JBSS) and underdetermined blind source separation (UBSS), cannot address this underdetermined problem effectively. We exploit the second-order statistics of observations and introduce a novel BSS method, termed as underdetermined joint blind source separation (UJBSS). Considering the dependence information between two datasets, the problem of jointly estimating the mixing matrices is tackled via canonical polyadic (CP) decomposition of a specialized tensor in which a set of spatial covariance matrices are stacked. Furthermore, the estimated mixing matrices are used to recover the sources from each dataset separately. Numerical results demonstrate the competitive performance of the proposed method when compared to a commonly used JBSS method, multiset canonical correlation analysis (MCCA), and the single-set UBSS method, UBSS with free active sources (UBSS-FAS).