[Eeglablist] Should Average Reference Include Eye Channels?
Joseph Dien
jdien07 at mac.com
Mon Feb 20 16:24:13 PST 2012
Might as well throw in my several bits. Robin, thanks for citing my 1998 paper!
My own take is it depends on exactly what you're doing but here are some thoughts:
1) One question is whether you're re-referencing before or after dealing with the eye blinks etc. I definitely wouldn't drop the EOG channels until after you've dealt with the EOG artifacts in whatever manner. Keeping the EOG channels in there during the EOG artifact correction/rejection process can only help. I normally use ICA to remove eye blinks and deal with other types of artifacts and bad channels before going to average reference to avoid spreading the artifacts around to the other channels. The high amplitude of the EOG artifacts in the EOG channels can only help. Think of it as being especially high signal-to-noise (where signal is the blink activity that you're trying to characterize and then remove).
2) Once you've dealt with the major EOG artifacts, then it's less clear whether to keep them or not. I generally leave them in since with a high-density montage the distinction between an EOG channel and a regular channel is fairly arbitrary (assuming they are all referenced to a common reference channel(s), as you indicated yours are. I do usually leave the EOG channels out during source analysis since they are more susceptible to signal leakage out the optic tract, which distorts source analysis algorithms that don't account for the presence of the optic tract.
3) Regarding the average reference itself, keep in mind that some of the signal from the EOG activity is going to end up in the other channels anyway (which is why we record EOG channels in the first place) so as far as the average reference goes, the more completely you are characterizing the fields the better. The flip side is whether you might be keeping more noise than signal. That depends on how high quality the signal from the EOG channels is. In this context, "noise" means electrode noise due to poor contact with the skin and due to physical displacement of the electrode as opposed to unwanted but real electrical fields from either eye movements or from background EEG. The latter is also ending up in the other channels so characterizing that real electrical activity is good.
4) I can't see any way that operations like epoching and baseline correction can cause problems for average reference. Average reference is computed on a timepoint by timepoint basis. It makes no difference what is happening at other timepoints. In fact, informally, I've found that you get better results from data that are both epoched and baseline corrected prior to performing ICA for eyeblink correction (this is how my EP Toolkit does it). This seems to be the case because it helps deal with slow high amplitude variations in the EEG data that can otherwise swamp out the EEG and EOG activity. Whether this is an issue likely depends on the filter settings and the nature of the equipment (I observed this with an EGI system with a digital .1 high-pass setting). Been meaning to write up my automated artifact correction algorithm up. Hope to do so soon. If you'd like to try it out, it's at: http://sourceforge.net/projects/erppcatoolkit/
Not sure what you mean by baseline correcting and not epoching though, but agree that it sounds problematic.
5) If you rereference only the 128 channels and then add in the 4 EOG channels then the data will be badly distorted. Don't do it!
Cheers!
Joe
On Feb 19, 2012, at 11:26 PM, Scott Makeig wrote:
> Unlike Alejandro, I regard decently recorded EEG data as having rather little noise, e.g., Gaussian noise, though it does have some, of course -- plus many (non-Gaussian) non-brain 'artifact' sources contributing to it (some, including eye movement artifacts, large).
>
> Biophysically, referencing to the average field at the whole surface of a spherical head would be ideal in the sense that the resulting potentials would not be spatially biased by the reference. But an EEG montage cannot cover the whole head (when neck is attached...), and the head is not quite spherical, etc. ...
>
> Simply including biopolar channels in the average reference calculation does not make sense, because this will introduce additional bias in the reference:
>
> For example, if scalp channels (s_1 - r_1) and (s_2 - r_1) are both ref'd to r_1, and eye channel e_1 to e_2, then average reference for the common-reference (s) channels is, for s_1, ...
>
> (s_1-r_1) - [(s_1-r_1) + (s_2-r_1)]/2
> = s_1-r_1-s_1/2+r_1/2 - s_2/2+r_1/2
> = s_1 - (s_1+s_2)/2 <== this average reference channel contains no r_1...
>
> But including bipolar channel (e1-e2) and then taking average reference,
>
> (e_1-e_2) - [(s_1-r_1) + (s_2-r_1) + (e_1-e_2)]/3
> = e_1 - e_2 - s_1/3 +r_1/3 - s_2/3 +r_1/3 - e_1/3 + e_2/3
> = 2/3(e_1-e_2) + 2/3r_1 - (s_1 + s_2)/3 <== this has no simple interpretation
>
> However, performing average reference on the common reference channels, and then combining these with the bipolar channels into the ICA training matrix is possible -- since all the signals are linearly related to the independent source activations.
>
> However, in this case the IC scalp maps may have a discontinuity between the eye and scalp channels, since they do not share a reference. Removing the bipolar eye channels from these maps involves performing a pseudo-inverse on the IC map matrix, however, which may introduce some degree of inaccuracy ...
>
> In practice, ICA typically picks up eye activities very well from their frontal scalp channel projections -- so I'd recommend using the extra channels for any other common-reference channel positions of interest, and not for bipolar eye channels.
>
> Scott Makeig
>
>
> On Fri, Feb 17, 2012 at 2:40 PM, Matthew Stief <ms2272 at cornell.edu> wrote:
> Thank you very much for this Alejandro.
>
> Just to confirm I understand you correctly, you are saying that it does not matter that the eye movement artifacts in the EOG monopolar channels are larger than those present in scalp electrodes, because the assumption is that the overall average of the noise will still be gaussian and therefore sum to zero, regardless of whether it includes the higher magnitude activity in EOG channels?
>
>
>
>
> On Wed, Feb 15, 2012 at 4:50 AM, Alejandro <alejo.ojeda83 at gmail.com> wrote:
>
> Here I will address the question: should I include EOG monopolar channels in the average reference? After some years now trying this and that for pre-processing my EEG data, doing some reading, and asking to people more knowledgeable than me, I'll explain why I would answer YES to that question.
>
> The problem of referencing the data comes from the fact that physiological signals measured on the scalp are always contaminated by noise, which is several orders of magnitude bigger. For instance, let's suppose we recorded the voltage from three different places:
>
> x1 = x~1 + n1
> x2 = x~2 + n2
> x3 = x~3 + n3
>
>
> Where the signal we measure X is assumed to be a mixture of two components: 1) the electrical activity generated by physiological processes inside the brain, transmitted across several layers of tissue that finally reach the scalp , x~, and 2) the noise at that point, n. Because the noise itself is a signal formed by a contribution of many non-physiological processes from a different nature (instrumental, electromagnetic, thermal, etc.) is usually represented as a random variable assumed gaussian with zero mean.
>
> The purpose of the average reference is to minimize the contribution of the noise keeping the tiny variations inside it that represent the physiological activity. Let's do the math for one electrode:
>
> x1r = x~1 + n1 - ( x~1 + n1 + x~2 + n2 + x~3 + n3 ) / 3
>
> where x1r represents the signal in the electrode 1 after removing the average reference. Re-grouping terms we have:
>
> x1r = x~1 - ( x~1 + x~2 + x~3 ) / 3 - ( n1 - n1 + n2 + n3 ) / 3
>
> But because the sum of several gaussian processes ( as the noise is considered ) is also a gaussian process, then the contribution of the noise goes to zero, ending up with a signal x1r that is still a mixture of things but at least those things represent more closely the physiological precesses:
>
> x1r = x~1 - ( x~1 + x~2 + x~3 ) / 3
>
> Generalizing to n electrodes we could say that:
> X r = ( I n -1⋅1 T /n) X
>
> the average reference data X r is equal to the so called "average reference operator" H=( I n -1⋅1 T ) times the raw data X. To construct this operator in Matlab just type:
>
> >> H = eye(n) - ones(n)/n;
>
> where n represents the number of channels we include in the average.
>
> One interesting thing about H is that it is what the mathematicians call an idempotent matrix, this is a matrix where H*H*...H=H. This has the practical implication that removing the average reference of your data several times, without doing anything else in between, doesn't introduce additional modifications.
>
> However it's true that multiplying by H could be seen as a mixing process of "hopefully" physiological signals, and there is when ICA comes to play an important roll. ICA will find (as far as it can and its assumptions are close to the reality) those sources x~1 , x~2 , x~3 ... associated to the local space and temporal coherent electrical activity generated inside the tissue (I say "tissue" to be general because usually we have components representing brain signals, muscle, EKG, etc). Just for the record, I'm not saying that H is the mixing matrix per se, I'm just saying that it contributes to the mixing process that takes place in the scalp and the other layers of tissue.
>
> I hope these thoughts can give you some clues about your pre-processing. They represent part of my practical experience and reading, but this still remains as an open field so don't take my words as pure dogma.
>
> Regards,
> Alejandro
>
> --
> _________________________________________________________________
> Matthew Stief
> Human Development | Sex & Gender Lab | Cornell University
> http://www.human.cornell.edu/HD/sexgender
>
>
> Heterosexuality isn't normal, it's just common.
> -Dorothy Parker
>
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> --
> Scott Makeig, Research Scientist and Director, Swartz Center for Computational Neuroscience, Institute for Neural Computation; Prof. of Neurosciences (Adj.), University of California San Diego, La Jolla CA 92093-0559, http://sccn.ucsd.edu/~scott
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--------------------------------------------------------------------------------
Joseph Dien,
Senior Research Scientist
University of Maryland
E-mail: jdien07 at mac.com
Phone: 301-226-8848
Fax: 301-226-8811
http://homepage.mac.com/jdien07/
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