In this last part of the tutorial we will attempt to solve the
EEG inverse problem. That is, given a distribution of scalp
potentials we will attempt to localize the underlying EEG sources. In fact
this is just one part of the inverse solution. The full solution involves also
the reconstruction of the temporal activation of the underlying EEG sources.
However, we will leave that for a future tutorial where
our EEG sources will have time-varying activation patterns.
In this part III of the tutorial you may use some the sources that you generated
in Part II or you may as well generate
new sources altogether. I will follow the latter approach. If you decide to use
new sources then you should first remove the old ones:
Now let's plot the scalp potentials that we would measure in such a
single dipole scenario:
plot_scalp_potentials(myHead, 'time', 1)
The result is shown below.
As we have single EEG source and no noise, the distribution of scalp potentials
(what we are measuring) is identical to the leadfield generated by the only
underlying EEG source (what we need for source localization). This is
obviously an ideal scenario and we would expect to be able to solve the inverse
problem accurately. Let's try:
The first command above will estimate the location of the source using a
Minimum Norm Estimate (MNE), which is the method employed, for instance, by
the MNE software.
The generated figure is shown below:
Although you can barely see it in the figure above, the inverse solver estimated
non-zero activation not only at the true location of the dipole, but also at
many other locations of the source grid. You can actually inspect the activation
values that were estimated at each source voxel with the command:
The latter command will use a higher weighting exponent for the plot so
that stronger voxel activations will appear even stronger and weak
activations will look even weaker. The resulting figures are shown
As you can see, the inverse estimate has deteriorated considerably and
it is now much more difficult to tell where the source of interest is located.
Still, if you would inspect myHead.InverseSolution.strength you would
discover that the strongest voxel is still 245, i.e. the true location of
the underlying EEG dipole.
Use the tools that I used above to determine how strong the noise should
be for the inverse solution to fail to identify the location of the EEG source.