Blind source separation of underdetermined mixtures of event-related sources

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.

[1]  Joos Vandewalle,et al.  Fetal electrocardiogram extraction by blind source subspace separation , 2000, IEEE Transactions on Biomedical Engineering.

[2]  Nikos D. Sidiropoulos,et al.  Robust iterative fitting of multilinear models , 2005, IEEE Transactions on Signal Processing.

[3]  Hamid Reza Mohseni,et al.  Preprocrssing of Event-Related Potential Signals via Kalman Filtering and Smoothing , 2007, 2007 15th International Conference on Digital Signal Processing.

[4]  S. Huffel,et al.  Neonatal seizure localization using PARAFAC decomposition , 2009, Clinical Neurophysiology.

[5]  Joachim Möcks,et al.  Decomposing event-related potentials: A new topographic components model , 1988, Biological Psychology.

[6]  Alexey Ozerov,et al.  Multichannel Nonnegative Matrix Factorization in Convolutive Mixtures for Audio Source Separation , 2010, IEEE Transactions on Audio, Speech, and Language Processing.

[7]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[8]  Tom Eichele,et al.  Tracking pattern learning with single-trial event-related potentials , 2006, Clinical Neurophysiology.

[9]  Mika P. Tarvainen,et al.  Single-trial dynamical estimation of event-related potentials: a Kalman filter-based approach , 2005, IEEE Transactions on Biomedical Engineering.

[10]  Mohinder S. Grewal,et al.  Kalman Filtering: Theory and Practice Using MATLAB , 2001 .

[11]  Daniel Graupe,et al.  Topographic component (Parallel Factor) analysis of multichannel evoked potentials: Practical issues in trilinear spatiotemporal decomposition , 2005, Brain Topography.

[12]  Nikos D. Sidiropoulos,et al.  Blind PARAFAC receivers for DS-CDMA systems , 2000, IEEE Trans. Signal Process..

[13]  Salah Bourennane,et al.  Nonorthogonal Tensor Matricization for Hyperspectral Image Filtering , 2008, IEEE Geoscience and Remote Sensing Letters.

[14]  Andrew G. Favret,et al.  Computer matched filter location of fetalR-waves , 1968, Medical and biological engineering.

[15]  Aapo Hyvärinen,et al.  Fast and robust fixed-point algorithms for independent component analysis , 1999, IEEE Trans. Neural Networks.

[16]  Andrzej Cichocki,et al.  Nonnegative Matrix and Tensor Factorization T , 2007 .

[17]  Andrzej Cichocki,et al.  Nonnegative Tensor Factorization for Continuous EEG Classification , 2007, Int. J. Neural Syst..

[18]  Tamara G. Kolda,et al.  Tensor Decompositions and Applications , 2009, SIAM Rev..

[19]  Andrzej Cichocki,et al.  Canonical Polyadic Decomposition Based on a Single Mode Blind Source Separation , 2012, IEEE Signal Processing Letters.

[20]  D. T. Kaplan,et al.  Fetal ECG extraction with nonlinear state-space projections , 1998, IEEE Transactions on Biomedical Engineering.

[21]  P. Comon.  Contrasts, independent component analysis, and blind deconvolution , 2004 .

[22]  Christian Jutten,et al.  Multichannel Electrocardiogram Decomposition Using Periodic Component Analysis , 2008, IEEE Transactions on Biomedical Engineering.

[23]  Zbynek Koldovský,et al.  Weight Adjusted Tensor Method for Blind Separation of Underdetermined Mixtures of Nonstationary Sources , 2011, IEEE Transactions on Signal Processing.

[24]  Bart De Schutter,et al.  DAISY : A database for identification of systems , 1997 .

[26]  P. Comon,et al.  Tensor decompositions, alternating least squares and other tales , 2009 .

[27]  Laurent Albera,et al.  On the behavior of current second order blind source separation methods for first and second order cyclostationary sources-application to CPFSK sources , 2002, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[28]  Jean-François Cardoso,et al.  Multidimensional independent component analysis , 1998, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).

[29]  Pierre Comon,et al.  Handbook of Blind Source Separation: Independent Component Analysis and Applications , 2010 .

[30]  Pierre Comon,et al.  Deterministic Blind Separation of Sources Having Different Symbol Rates Using Tensor-Based Parallel Deflation , 2010, LVA/ICA.

[31]  E Donchin,et al.  Brain-computer interface technology: a review of the first international meeting. , 2000, IEEE transactions on rehabilitation engineering : a publication of the IEEE Engineering in Medicine and Biology Society.

[32]  P. Comon,et al.  Blind identification and source separation in 2/spl times/3 under-determined mixtures , 2004, IEEE Transactions on Signal Processing.

[33]  Fabian J. Theis,et al.  Sparse component analysis and blind source separation of underdetermined mixtures , 2005, IEEE Transactions on Neural Networks.

[34]  Rasmus Bro,et al.  MULTI-WAY ANALYSIS IN THE FOOD INDUSTRY Models, Algorithms & Applications , 1998 .

[35]  J. Kruskal.  Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics , 1977 .

[36]  Rémi Gribonval,et al.  A survey of Sparse Component Analysis for blind source separation: principles, perspectives, and new challenges , 2006, ESANN.

[37]  J. Mocks,et al.  Topographic components model for event-related potentials and some biophysical considerations , 1988, IEEE Transactions on Biomedical Engineering.

[38]  B. Widrow,et al.  Adaptive noise cancelling: Principles and applications , 1975 .

[39]  Zhaoshui He,et al.  Convolutive Blind Source Separation in the Frequency Domain Based on Sparse Representation , 2007, IEEE Transactions on Audio, Speech, and Language Processing.

[40]  Linda Cardozo,et al.  Contrasts , 2003, BMJ : British Medical Journal.

[41]  Gérard Favier,et al.  Blind equalization of nonlinear channels using a tensor decomposition with code/space/time diversities , 2009, Signal Process..