Model Selection for Convolutive ICA with an Application to Spatiotemporal Analysis of EEG

We present a new algorithm for maximum likelihood convolutive independent component analysis (ICA) in which components are unmixed using stable autoregressive filters determined implicitly by estimating a convolutive model of the mixing process. By introducing a convolutive mixing model for the components, we show how the order of the filters in the model can be correctly detected using Bayesian model selection. We demonstrate a framework for deconvolving a subspace of independent components in electroencephalography (EEG). Initial results suggest that in some cases, convolutive mixing may be a more realistic model for EEG signals than the instantaneous ICA model.

[1]  Lars Kai Hansen,et al.  Model Structure Selection in Convolutive Mixtures , 2006, ICA.

[2]  S Makeig,et al.  A natural basis for efficient brain-actuated control. , 2000, IEEE transactions on rehabilitation engineering : a publication of the IEEE Engineering in Medicine and Biology Society.

[3]  Arnold Neumaier,et al.  Estimation of parameters and eigenmodes of multivariate autoregressive models , 2001, TOMS.

[4]  Nikolaos Mitianoudis,et al.  Audio source separation of convolutive mixtures , 2003, IEEE Trans. Speech Audio Process..

[5]  Ah Chung Tsoi,et al.  A variational Bayesian approach to number of sources estimation for multichannel blind deconvolution , 2008, Signal Image Video Process..

[6]  Terrence J. Sejnowski,et al.  From single-trial EEG to brain area dynamics , 2002, Neurocomputing.

[7]  M. Kenward,et al.  An Introduction to the Bootstrap , 2007 .

[8]  Tzyy-Ping Jung,et al.  Imaging brain dynamics using independent component analysis , 2001, Proc. IEEE.

[9]  Te-Won Lee,et al.  Blind Separation of Delayed and Convolved Sources , 1996, NIPS.

[10]  Pierre Comon,et al.  BLIND SEPARATION OF CONVOLUTIVE MIXTURES A CONTRAST-BASED JOINT DIAGONALIZATION APPROACH , 2001 .

[11]  Eric Moulines,et al.  A blind source separation technique using second-order statistics , 1997, IEEE Trans. Signal Process..

[12]  Lucas C. Parra,et al.  Convolutive blind separation of non-stationary sources , 2000, IEEE Trans. Speech Audio Process..

[13]  Terrence J. Sejnowski,et al.  Independent Component Analysis Using an Extended Infomax Algorithm for Mixed Subgaussian and Supergaussian Sources , 1999, Neural Computation.

[14]  Terrence J. Sejnowski,et al.  An Information-Maximization Approach to Blind Separation and Blind Deconvolution , 1995, Neural Computation.

[15]  Birger Kollmeier,et al.  Adaptive separation of acoustic sources for anechoic conditions: A constrained frequency domain approach , 2003, Speech Commun..

[16]  Kari Torkkola,et al.  Blind separation of convolved sources based on information maximization , 1996, Neural Networks for Signal Processing VI. Proceedings of the 1996 IEEE Signal Processing Society Workshop.

[17]  Lars Kai Hansen,et al.  Convolutive ICA (c-ICA) captures complex spatio-temporal EEG activity , 2004 .

[18]  P. Sajda,et al.  Spatiotemporal Linear Decoding of Brain State , 2008, IEEE Signal Processing Magazine.

[19]  Hans Bruun Nielsen,et al.  UCMINF - an Algorithm for Unconstrained, Nonlinear Optimization , 2000 .

[20]  Christian Jutten,et al.  On the blind source separation of human electroencephalogram by approximate joint diagonalization of second order statistics , 2008, Clinical Neurophysiology.

[21]  A. Cichocki,et al.  Blind signal deconvolution by spatio-temporal decorrelation and demixing , 1997, Neural Networks for Signal Processing VII. Proceedings of the 1997 IEEE Signal Processing Society Workshop.

[22]  Xiaoan Sun,et al.  A NATURAL GRADIENT CONVOLUTIVE BLIND SOURCE SEPARATION ALGORITHM FOR SPEECH MIXTURES , 2001 .

[23]  L. Parra,et al.  Convolutive blind source separation based on multiple decorrelation , 1998, Neural Networks for Signal Processing VIII. Proceedings of the 1998 IEEE Signal Processing Society Workshop (Cat. No.98TH8378).

[24]  Ramesh A. Gopinath,et al.  An EM algorithm for convolutive independent component analysis , 2002, Neurocomputing.

[25]  Lucas C. Parra,et al.  Convolutive Source Separation and Signal Modeling with ML , 2007 .

[26]  Tzyy-Ping Jung,et al.  Independent Component Analysis of Electroencephalographic Data , 1995, NIPS.

[27]  Dorothea Kolossa,et al.  REAL TIME SEPARATION OF CONVOLUTIVE MIXTURES , 2001 .

[28]  Tzyy-Ping Jung,et al.  Extended ICA Removes Artifacts from Electroencephalographic Recordings , 1997, NIPS.

[29]  Ying Tang.  A New Algorithm of ICA: Using the Parametrized Orthogonal Matrixes of Any Dimensions: A New Algorithm of ICA: Using the Parametrized Orthogonal Matrixes of Any Dimensions , 2008 .

[30]  Eric Moulines,et al.  Maximum likelihood for blind separation and deconvolution of noisy signals using mixture models , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[31]  Terrence J. Sejnowski,et al.  Independent Component Analysis Using an Extended Infomax Algorithm for Mixed Sub-Gaussian and Super-Gaussian Sources , 1999, Neural Comput..

[32]  Reinhold Orglmeister,et al.  Blind source separation of real world signals , 1997, Proceedings of International Conference on Neural Networks (ICNN'97).

[33]  Per Christian Hansen,et al.  Deconvolution and Regularization with Toeplitz Matrices , 2002, Numerical Algorithms.

[34]  Dinh-Tuan Pham,et al.  Optimization Issues in Noisy Gaussian ICA , 2004, ICA.

[35]  Hagai Attias,et al.  Blind Source Separation and Deconvolution: The Dynamic Component Analysis Algorithm , 1998, Neural Computation.

[36]  T. Sejnowski,et al.  Removing electroencephalographic artifacts by blind source separation. , 2000, Psychophysiology.

[37]  Barak A. Pearlmutter,et al.  Maximum Likelihood Blind Source Separation: A Context-Sensitive Generalization of ICA , 1996, NIPS.

[38]  Terrence J. Sejnowski,et al.  Complex Independent Component Analysis of Frequency-Domain Electroencephalographic Data , 2003, Neural Networks.

[39]  James P. Reilly,et al.  A frequency domain approach to blind identification of MIMO FIR systems driven by quasi-stationary signals , 2002, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[40]  Lars Kai Hansen,et al.  CICAAR: Convolutive ICA with an Auto-regressive Inverse Model , 2004, ICA.

[41]  T. Sejnowski,et al.  Dynamic Brain Sources of Visual Evoked Responses , 2002, Science.

[42]  Thomas G. Dietterich,et al.  Editors. Advances in Neural Information Processing Systems , 2002 .

[43]  Terrence J. Sejnowski,et al.  Unraveling Spatio-temporal Dynamics in fMRI Recordings Using Complex ICA , 2004, ICA.

[44]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[45]  Arnaud Delorme,et al.  EEGLAB: an open source toolbox for analysis of single-trial EEG dynamics including independent component analysis , 2004, Journal of Neuroscience Methods.

[46]  S. Makeig,et al.  Mining event-related brain dynamics , 2004, Trends in Cognitive Sciences.

[47]  T. Sejnowski,et al.  Electroencephalographic Brain Dynamics Following Manually Responded Visual Targets , 2004, PLoS biology.

[48]  Arnaud Delorme,et al.  Frontal midline EEG dynamics during working memory , 2005, NeuroImage.

[49]  James P. Reilly,et al.  Blind source separation of convolved sources by joint approximate diagonalization of cross-spectral density matrices , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[50]  T. Sejnowski,et al.  Electroencephalographic brain dynamics following visual targets requiring manual responses , 2022 .

[51]  Andrzej Cichocki,et al.  Self-whitening algorithms for adaptive equalization and deconvolution , 1999, IEEE Trans. Signal Process..

[52]  Shun-ichi AMARIyy,et al.  NATURAL GRADIENT LEARNING WITH A NONHOLONOMIC CONSTRAINT FOR BLIND DECONVOLUTION OF MULTIPLE CHANNELS , 1999 .