[Eeglablist] dipfit uses average reference?

[Jonathan R Folstein]

This thread is extremely useful, thank you.  Would a non-cephalic
reference at the base of the neck be a reasonable substitute for average
reference?

Jonathan Folstein
University of Arizona



On Mon, 27 Nov 2006, Robert Oostenveld wrote:

> On 23 Nov 2006, at 2:18, arno wrote:
> > David Groppe wrote:
> >> I'm using Dipfit 2 to localize independent components using the
> >> spherical head model.  Apparently the software requires the data
> >> to use the average reference.  Why is this?
> > Source localization assumes that the data is average reference (I
> > think it is because no current should get in or out). I do not
> > think it is really an option not to use average reference. Robert
> > might have more insight about that.
>
> Although the "no current leaving the body/head" argument is valid, we
> also have to account for the limited sampling of the head: only the
> upper half is sampled sparsely. In principle you could use an
> arbitrary reference in your source reconstruction. The practical
> reason to use an average reference over the sampled electrodes in
> source estimation is that this prevents the solution to be biassed
> due to forward modelling errors at the reference electrode. Let me
> give a partially intuitive, partially mathematical explanation. This
> follows on the idea of Joseph.
>
> Assume that you would use left mastoid as reference. That would mean
> that the measured value "V" at each electrode "x" is V_x, so the list
> of all measured values in the N channels is
>   V_C3-V_M1
>   V_Cz-V_M1
>   V_C4-V_M1
>   ...
>   V_M1-V_M1  (this is zero)
>   V_M2-V_M1
>
> Those values can be modeled using the source model and the volume
> condution model. Now, lets assume a spherical volume conduction
> model. That is especially inaccurate for low electrodes, and the bony
> structure of the mastoid is definitely not modelled appropriately in
> a spherical model. So for the model potential "P" we would have the
> value at each of the N electrode also referenced to the model mastoid
> electrode:
>   P_C3-P_M1
>   P_Cz-P_M1
>   P_C4-P_M1
>   ...
>   P_M1-P_M1  (this is zero)
>   P_M2-P_M1
>
> The source estimation algorithm tries to minimize the quadratic error
> between model potential distribution and the measurement, so the
> error term to be minimized is
>   Total_Error
>   = sum of quadratic error over all channels
>   = [(V_C3-V_M1)-(P_C3-P_M1)]^2 + ....
>   = [(V_C3-P_C3)-(V_M1-P_M1)]^2 + ....   (here the terms are re-ordered)
>
> So for each channel the error term consists of a part that
> corresponds to the potential at the electrode of interest, plus a
> part that corresponds to the reference electrode. The error term
> corresponding to the reference electrode is identical over all
> channels (i.e. repeats in each channel), hence for each channel you
> are adding some error term for the reference electrode. Therefore,
> the minimum error ("minimum norm") solution will be one that
> especially tries to minimize the model error at the reference
> electrode (since that is included N times). In the case of a mastoid
> reference we know that there is a large volume conductor model error
> at M1, hence the source solution would mainly try to minimize that
> error term. The result would be that the source solution would be
> biassed, because it tries to reduce the (systematic) error at the
> reference.
>
> The solution is to use an average reference (average over all
> measured electrodes). That implicitely assumes that the model error
> over all electrodes is on average zero, hence the minimum norm
> solution is not biassed towards a specific reference electrode.
>
> I hope that this clarifies it.
>
> best regards,
> Robert
>
> PS the maths in my explanation above are rather sloppy, but the
> argument still holds for a more elaborate mathematical derivation
> which would assume the forward model inaccuracies are uncorrelated
> over electrode sites.
>
>
>
>
>
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Jonathan Folstein, Doctoral Candidate
Cognitive Psychology
University of Arizona
email: folstein at u.arizona.edu
lab phone (520)-621-3265