New Approaches for EEG Source Localization and Dipole Moment Estimation. Shun Chi Wu, Yuchen Yao, A. Lee Swindlehurst University of California Irvine

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1 New Approaches for EEG Source Localization and Dipole Moment Estimation Shun Chi Wu, Yuchen Yao, A. Lee Swindlehurst University of California Irvine

2 Outline Motivation why EEG? Mathematical Model equivalent current dipoles w/ multiple sensors Prior Approaches maximum likelihood, MUSIC, beamforming, ICA Interference Suppression control (pre stimulus) and task (post stimulus) Our Contributions: spatial interference nulling noise subspace fitting Simulation Results Conclusions & Future Work

3 Motivation EEG provides direct measurement of neuronal activity w/ best temporal resolution, key to diagnosing many neurological impairments since measurements can be taken with behavioral activities in process, great interest in combining EEG with new measurement modalities (e.g., functional MRI) EEG signals are weak: must rely on measurements from multiple electrodes to more precisely localize and extract signal Classical approaches based on finding electrode with strongest signal, but they are too widely spaced, and this approach only provides position projected on brain surface sub cortical activity cannot be distinguished. Modern alternative: use data from multiple electrodes & detailed head models to calibrate electrode array for full 3D set of possible locations. Techniques borrowed from radar & communications statistical signal processing. Our contribution: apply new signal processing techniques for improved robustness and performance, especially for difficult applications involving highly correlated signals and strong interference.

4 Mathematical Model cortical neuron can be modeled as a current dipole key parameters of interest: dipole location, orientation, current waveform difficulty: brain is constantly buzzing with activity; how to single out sources of interest from the background direct measurement of energy from electrodes does not provide sufficient resolution Image courtesy of

5 Mathematical Model (cont.) stack outputs from electrode array into a vector using detailed head model and array calibration, determine array response to unit amplitude source ( lead field vector, LFV) LFV is broken down into its dipole moments output of electrode array for a superposition of multiple sources: goal is to determine high dimensional inverse problem

6 Prior Approaches Maximum Likelihood (ML): assume interference with known pdf (Gaussian) for temporally & spatially white noise, boils down to non linear least squares problem can handle highly correlated sources waveform can be separated from minimization still requires multi dimensional search for 6d parameters

7 Prior Approaches (cont.) MUSIC (MUltiple SIgnal Classification): technique borrowed from radar literature estimate signal and noise subspaces from eigendecomposition of spatial covariance matrix idea: locate EEG sources as those whose LFV is most orthogonal to noise subspace. Results in 3 dim generalized eigenvalue search: low dimensional search, provides visual EEG map, but cannot handle highly correlated sources

8 Prior Approaches (cont.) Constrained Beamforming (LCMV): also borrowed from radar/sonar community step through beams formed by providing unit gain at each possible source position and minimizing array output power from all other locations solution ends up being very similar to MUSIC: low dimensional search, provides visual EEG map, but cannot handle highly correlated sources also very sensitive to imprecise LFV model

9 Prior Approaches (cont.) Independent Components Analysis (ICA): statistical technique relying on assumption of sources with independent current waveforms first step: array data is factored into product of spatial and temporal principal components: second step: extract location/orientation information from provides waveforms without relying on LFV model unable to provide accurate location/orientation information for highly correlated sources

10 Interference Suppression None of the previous techniques provide good results without some attempt at interference cancellation Simulation example: 3 strong sources with 25 weak interferers strong sources move along tracks shown below

11 Interference Suppression None of the previous techniques provide good results without some attempt at interference cancellation

12 Interference Suppression (cont.) None of the previous techniques provide good results without some attempt at interference cancellation Common approach: measure quiescent brain activity during control state (pre stimulus), followed by measurement of brain activity during task state (post stimulus) Use control state measurements to learn statistical properties of the background interference, then try to cancel such components in task state data Most common implementation: control state data used to estimate spatial covariance of the interference, then algorithms are implemented using Pre Whitened (PW) data Requires assumption of spatial and temporal stationarity

13 Drawbacks of Existing Approaches Optimal methods (ML) cannot decouple estimation of location and dipole orientation, and require assumptions about interference distribution and covariance structure Methods that employ pre whitening require assumptions of both temporal and spatial stationarity, and estimation of covariance matrices, which takes large data sets Good performance for highly correlated sources requires use of expensive ML technique Our contributions: spatial interference nulling eliminates interference without estimation of covariance matrices, and without assumption of temporal stationarity noise subspace fitting achieves near optimal performance while allowing for decoupled location/orientation estimation, and good performance for highly correlated sources

14 Spatial Interference Nulling Use singular value decomposition (SVD) of control state data to find spatial signal subspace of background interference Instead of pre whitening, simply project out from task state data: Implement algorithms with clean task state data Allows statistical properties of interference waveforms to change from control to task state without performance penalty Following examples illustrate benefit of interference nulling (NP) over PW for MUSIC and LCMV. First example uses 3 uncorrelated sources, second involves 2 highly correlated sources

15 Spatial Interference Nulling Results

16 Spatial Interference Nulling Results (cont.)

17 Spatial Interference Nulling Results (cont.)

18 Spatial Interference Nulling Results (cont.)

19 Noise Subspace Fitting We show that ML criterion can be asymptotically approximated by a simpler function in the vicinity of the solution: NSF criterion depends quadratically on orientation parameters, which allows them to be decoupled from the estimation Thus, search is only over the 3d location parameters (for which prior information may be available) Choice of optimal weighting matrix is critical: requires initial estimation stage in which consistent parameter estimates can be obtained Performance of NSF is superior to MUSIC, LCMV for highly correlated sources

20 Noise Subspace Fitting Results

21 Noise Subspace Fitting Results (cont.)

22 Noise Subspace Fitting Results (cont.)

23 Noise Subspace Fitting Results (cont.)

24 Future Work Looking for partner for help with experimental aspects: head models, live data (while simulations used real data, they were not real experiments) Developing alternative near ML cost functions that allow for more flexible noise model Developing methods that are robust to imprecise LFV models How to exploit prior information? Estimating of sources which move rapidly or whose dipole moment is time varying Connections with MEG models, function MRI, etc.