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In this project, three different approaches were developed for the estimation of focal brain activity using EEG measurements.
The proposed approaches have been tested and found feasible using simulated data.
A. EEG focal source estimation using Convex Optimization
We developed a solver for the recovery of focal dipole sources. The solver is based on the truncated Newton interior point method
combined with a logarithmic barrier method for the approximation of the penalty term.
As a penalty term, we used the weighted dipole strength (also called weighted L1,2 norm) as prior information
in order to ensure that the sources are sparse and focal.
Further details can be found in https://spiral.imperial.ac.uk/handle/10044/1/25759 Chapter 3.
Here, I show an example of a single focal dipole source reconstruction using different regularization parameters.
The L1,2-norm regularization performs better than the simple weighted L1-norm penalty or the L2-norm regularization.
We compare the results using the Earth mover's distance (EMD), the distances are in mm.
In the second approach, vector field tomography (VFT), i.e. Radon Integral, was used for the estimation of underlying electric fields inside the brain from external EEG measurements. The electric field is reconstructed using a set of line integrals.
The benefit of this approach is that we do not need a mathematical model for the sources.
An example with reconstructions of dipole fields using line integral data is presented here (reconstructions in the presence of different noise levels when the source activity is deep in the domain).
C. Bayesian approximation error approach (BAE) in EEG inverse problem
When the precise knowledge of the tissue conductivities and head geometry are not available, then the Bayesian approximation error approach (BAE) can be used for the estimation of the source activity.
In this case, a coarse head model is used and the typical variations in the head geometry and tissue conductivities are taken into account statistically in the inverse model.
We demonstrate that the BAE results are comparable to those obtained with an accurate head model.
Reconstruction of dipole sources from EEG measurements using the BAE.
Comparison of the results obtained using different prior knowledge (e.g. known/unknown geometry and incorporation of the BAE statistics in the solver.)
For further details see:
Compensation of domain modelling errors in the inverse source problem of the Poisson equation: application in electroencephalographic imaging, Applied Numerical Mathematics, Vol. 106, Aug. 2016, P. 24-36
Presentation on model based learning for parameter selection
Presentation on model based learning for parameter selection
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