Tensorial Convolutive Blind Source Separation

In this paper, we investigate the problem of convolutive blind source separation (BSS) via tensor decomposition. A fundamental link between convolutive BSS and block-term decomposition (BTD) is established, forming the basis for our novel tensor-based convolutive BSS method, namely TCBSS. Specifically, the proposed method offers a new effective approach for factorizing tensors under the BTD format where the loading factors are constrained to be identical. By leveraging second-order statistics of data observations, we construct a third-order tensor by stacking covariance matrices at different time lags, and then, apply TCBSS to identify the mixing process. Experimental results demonstrate the robust performance of TCBSS in addressing both BTD and convolutive BSS tasks, particularly when dealing with electromyography (EMG) signal decomposition.