Joint MEG-EEG signal decomposition using the coupled SECSI framework: Validation on a controlled experiment

Simultaneously recorded magnetoencephalography (MEG) and electroencephalography (EEG) signals can benefit from a joint analysis based on coupled Canonical Polyadic (CP) tensor decompositions. The coupled CP decomposition jointly decomposes tensors that have at least one factor matrix in common. The Coupled — Semi-Algebraic framework for approximate CP decomposition via SImultaneous matrix diagonalization framework (C-SECSI) efficiently estimates the factor matrices with adjustable complexity-accuracy trade-offs. Our objective is to decompose simultaneously recorded MEG and EEG signals above intact skull and above two conducting skull defects using C-SECSI in order to determine how such a tissue anomaly of the head is reflected in the tensor rank. The source of the MEG and EEG signals is a miniaturized electric dipole that is implanted into a rabbit's brain. The dipole is shifted along a line under the skull defects, and measurements are taken at regularly spaced points. The coupled SECSI analysis is conducted for MEG and EEG measurement series and ranks 1–3. This coupled decomposition produces meaningful components representing the three characteristic signal topographies for source positions under defect 1 and the positions on either side of defect 1. The rank estimation with respect to the complexity-accuracy trade-off of rank 3 reflects the three characteristic cases well and matches the dimensions spanned by the data set. The intact skull MEG signals show a higher complexity (rank 3) than the corresponding EEG signals (rank 1). The C-SECSI framework is a very promising method for blind signal separation in multidimensional data with coupled modalities, such as simultaneous MEG-EEG.

[1]  David B. Grayden,et al.  Skull Defects in Finite Element Head Models for Source Reconstruction from Magnetoencephalography Signals , 2016, Front. Neurosci..

[2]  Laurent Albera,et al.  Tensor-based preprocessing of combined EEG/MEG data , 2012, 2012 Proceedings of the 20th European Signal Processing Conference (EUSIPCO).

[3]  Martin Haardt,et al.  Analysis of the photic driving effect via joint EEG and MEG data processing based on the coupled CP decomposition , 2017, 2017 25th European Signal Processing Conference (EUSIPCO).

[4]  Tamara G. Kolda,et al.  All-at-once Optimization for Coupled Matrix and Tensor Factorizations , 2011, ArXiv.

[5]  Florian Roemer,et al.  A semi-algebraic framework for approximate CP decompositions via simultaneous matrix diagonalizations (SECSI) , 2013, Signal Process..

[6]  S. Khoshbin,et al.  Evaluation of Postoperative Sharp Waveforms Through EEG and Magnetoencephalography , 2010, Journal of clinical neurophysiology : official publication of the American Electroencephalographic Society.

[7]  Martin Haardt,et al.  Extension of the semi-algebraic framework for approximate CP decompositions via simultaneous matrix diagonalization to the efficient calculation of coupled CP decompositions , 2016, 2016 50th Asilomar Conference on Signals, Systems and Computers.

[8]  J. Haueisen,et al.  Magnetoencephalography signals are influenced by skull defects , 2014, Clinical Neurophysiology.

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

[10]  Pierre Comon,et al.  Joint tensor compression for coupled canonical polyadic decompositions , 2016, 2016 24th European Signal Processing Conference (EUSIPCO).

[11]  Andrzej Cichocki,et al.  Tensor Decompositions for Signal Processing Applications: From two-way to multiway component analysis , 2014, IEEE Signal Processing Magazine.

[12]  Rasmus Bro,et al.  Data Fusion in Metabolomics Using Coupled Matrix and Tensor Factorizations , 2015, Proceedings of the IEEE.

[13]  W A Cobb,et al.  Breach rhythm: the EEG related to skull defects. , 1979, Electroencephalography and clinical neurophysiology.