Underdetermined joint blind source separation based on tensor decomposition

Abstract

In this paper, we propose a simple and effective scheme to jointly estimate the mixing matrices from multiple datasets for the underdetermined case, where the number of sources exceeds that 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 for multiple datasets. We first introduce a novel BSS method, termed as underdetermined joint blind source separation (UJBSS), to estimate the mixing matrices of two datasets. The problem of jointly estimating the mixing matrices is reformulated as canonical polyadic (CP) decomposition of a specialized tensor in which a set of spatial covariance matrices are stacked. Furthermore, exploring the dependence information between multiple datasets, we generalize the idea of UJBSS for two datasets to UJBSS for multiple datasets. Numerical results demonstrate the competitive performance of the proposed UJBSS method when compared to SOBIUM, a commonly-used single-set UBSS method.