Tensor decomposition meets blind source separation.

In this paper, we investigate the problem of blind source separation (BSS) through the lens of tensor decomposition (TD). Two fundamental connections between TD and BSS are established, forming the basis for two novel tensor-based BSS methods, namely TenSOFO and TCBSS. The former is designed for a joint individual differences in scaling (INDSCAL) decomposition, addressing instantaneous (linear) BSS tasks; while the latter efficiently performs a constrained block term decomposition (BTD), aligning with the design of convolutive BSS. Leveraging the benefits of the alternating direction method of multipliers and the strengths of tensor representations, both TenSOFO and TCBSS prove to be effective in BSS. Our experimental results demonstrate the effectiveness of these two proposed methods in addressing both TD and BSS tasks, particularly when compared to state-of-the-art algorithms. • Blind source separation (BSS) is addressed through the lens of tensor decomposition. • Two connections between BSS models and tensor decompositions are established. • The proposed TenSOFO method integrates both second-order and fourth-order statistics. • The proposed TCBSS method is designed for convolutive BSS tasks. • We demonstrate their effectiveness on both synthetic and real data. [ABSTRACT FROM AUTHOR]