Blind source separation of underdetermined mixtures of event-related sources

• DOI: 10.1016/j.sigpro.2014.01.031
• Publication Date: 2014-02-06T19:01:46Z
• Authors: Mohammad Niknazar; Hanna Becker; Bertrand Rivet; Christian Jutten; Pierre Comon
• Keywords: Underdetermined system; Source Separation; Robustness; Identifiability; Signal subspace

This paper addresses the problem of blind source separation for underdetermined mixtures (i.e., more sources than sensors) of event-related sources that include quasi-periodic sources (e.g., electrocardiogram (ECG)), sources with synchronized trials (e.g., event-related potentials (ERP)), and amplitude-variant sources. The proposed method is based on two steps: (i) tensor decomposition for underdetermined source separation and (ii) signal extraction by Kalman filtering to recover the source dynamics. A tensor is constructed for each source by synchronizing on the "event" period of the corresponding signal and stacking different periods along the second dimension of the tensor. To cope with the interference from other sources that impede on the extraction of weak signals, two robust tensor decomposition methods are proposed and compared. Then, the state parameters used within a nonlinear dynamic model for the extraction of event-related sources from noisy mixtures are estimated from the loading matrices provided by the first step.The influence of different parameters on the robustness to outliers of the proposed method is examined by numerical simulations. Applied to clinical electroencephalogram (EEG), ECG and magnetocardiogram (MCG), the proposed method exhibits a significantly higher performance in terms of expected signal shape than classical source separation methods such as π CA and FastICA. HighlightsWeak sources are extracted from underdetermined mixtures.Synchronization of repetitive events allows arranging data in tensor format.Robust criteria are proposed to fit the tensor CP model.Dynamics of sources are recovered via a Kalman filtering framework.The proposed method is applicable for ERP and fetal ECG and MCG extraction.