[Eeglablist] Comments on EEG and ERP reference

Mon Dec 29 06:17:42 PST 2025

Dear Ramesh,
Thanks a lot for your comments.

About the head model effect on REST, the following message may be helpgful 
(mainly from my book: Yao D. The Physics and Mathematics of Electroencephalogram. CRC, 2024 )

 (1) V0=AX=A'X'=A''X''
 where, X are the true sources, X' are the equivalent sources, A /A' is the lead array of the true head model corresponding to sources X/X' respectively (sources positions diferent).
 If we have an approximate head model, then we have the approximate lead array A'', and the corresonding X''. 
  In (1), the reference is zero (at infinity).
 As each of X, X'(many forms), X''(many forms) may generate the same true scalp recordings V0, we say that the EEG inverse is nonuniqueness. And it is this nonuniqueness that provides the theoretical base of the "equivalent sources principle" in electromagnetism, and give us chance to develope REST.

  (2) Vr=ArX=Ar'X'=Ar''X''
 it is a modified version of equation(1) with a non-zero reference r, which may be any a concrete reference,such AR, linked mastoids. Ar/Ar' still is the lead array of the true head model, Ar'' is the approximate lead array (the approximate head model), and the corresponding equivalent sources X'' which working together with Ar'' can (approximately) generating the  actual recordings Vr. 
Equation（2） means that, if we have the correct model-Ar', we definitely can have the equivalent sources X' (it may be dipole or charge or their combination, etc ). If we do not have the correct model-Ar',  or say if we only have an approximate head model-Ar'', then we still may have an approximate X'', which,  with Ar'',  may (approximately) generate the actual recordings Vr, too. It means the error of the head model (Ar''- Ar') may be partially (or numerically) compensated by an approximated equivalent sources. 
 Whether these guesses are true? or how about the final performance of REST with approximate head model?  there are many simulation studies concerning this issues, and the results are positive, in a word, the head model error may reduce the REST performance, but it is still usaully better than AR in general. 

 from equation (2),we have 
 (3) X'=Ar'(+)Vr
     X''=Ar''(+)Vr
here we see ,if the head model is approximate （Ar''- Ar'）, the equivalent sources may be a little different for the same scalp potential recordings Vr  （ X'-X"）.

from equation (3),we have
 (4)  V0=AX=A'X'=A'Ar'(+)Vr=T'Vr
   or V0=AX=A'X'=A''X''=A''Ar''(+)Vr=T''Vr

here we see, the equivalent sources only act as a "bridge", we do not really need to know it.  we only use T' and T'' which depends on the head  model and the correspondings equivalent sources positions (A, A', A''). In REST practice, we may assume that the equivalent sources are located on a closed surfce encovering the all actual sources (or a 3D distribution overlaying the all actual sources), then we have A'/A'' and their generalized inverse  A'(+)/A''(+） .

In REST practice, if you have individual head model, then you may take V0=T'Vr, with T'=A'Ar'(+)
for general case, without personal true head model, we recommend to use the three-spheres head model or the averged realistic head model, then we have V0=T''Vr, with T''=A''Ar''(+), here the T'' is provded by the REST software, Vr is your eeg data, and V0 is the final with zero reference.

In general,  both REST and  AR are based on "physical fact", the difference is :
  REST utilizes the "nonuniqueness' of EEG inverse in the EEG related 3D space, 3D physics involved.
  while, AR based on the scalp surface potential integral being zero ( assume the surface recordings are over a whole spherical head surface), 2D physics involved.
 That's why these two references are usually much better than Linked-ears or other unpolar references, and in general, REST is better than AR, as it utilize more "physics" to constrain the estimate.

best wishes

> -----原始邮件-----
> 发件人: "Richards, John" <RICHARDS at mailbox.sc.edu>
> 发送时间:2025-12-29 07:12:35 (星期一)
> 收件人: "Ramesh Srinivasan" <srinivar at uci.edu>, "dyao at uestc.edu.cn" <dyao at uestc.edu.cn>
> 抄送: eeglablist <eeglablist at sccn.ucsd.edu>
> 主题: RE: [Eeglablist] Comments on EEG and ERP reference
> 
> I have wondered about the head model used in the REST reference.  In addition to any other issue, if the head model is "incorrect" then are the calculations of the reference also incorrect?  Using an average template for a head model has some issues in source reconstruction, and might have some here also.  Using a participant-defined, individual-based, realistic head model, is better than an average MRI template head model in several ways in source modeling.  Might be so here also?
> 
> John
> 
> ***********************************************
> John E. Richards
> Carolina Distinguished Professor
> Department of Psychology
> University of South Carolina
> Columbia, SC  29208
> Dept Phone: 803 777 2079
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> 
> -----Original Message-----
> From: eeglablist <eeglablist-bounces at sccn.ucsd.edu> On Behalf Of Ramesh Srinivasan via eeglablist
> Sent: Sunday, December 28, 2025 1:25 AM
> To: dyao at uestc.edu.cn
> Cc: eeglablist <eeglablist at sccn.ucsd.edu>
> Subject: Re: [Eeglablist] Comments on EEG and ERP reference
> 
> Hi Dezhong,
> 
> Id like to comment first on your quote from Luck's book and then about your method REST.
> 
> First, Luck is apparently unaware of the argument for the average reference, or of the physical principles underlying them and is intellectually lazy by focusing on whether the models used to test these ideas are spherical or realistic.  That has nothing to do with it.
> 
> The critical issue is whether the head is a closed object, not whether it
> is a sphere.   In other words, is there evidence that current flows out of
> head into neck and vice versa.  The preponderance of  evidence suggests that very little current generated by sources in the brain travels down the neck into the body.  How do we know this?  Well, the simplest evidence is that we can record EEG at all.  If there was a significant current path through the neck, EEG recordings would be overwhelmed by EKG which is orders of magnitude larger signal.  Hence it is reasonable to assume that the neck is like a giant resistor limiting current flow in both directions.
> From the point of view of current flow from brain sources the head is mostly a closed object.  Indeed your REST method hinges on this being true because you dont use a volume conduction model of the whole body, just the
> head.   So, this quotation from Luck is just wrong, and is inconsistent
> with your views and methods.
> 
> If current is contained with the head, then the potentials on the head should sum to zero.  But we can never measure the underside of the head, so the average of the potentials we measure indeed must have some error.
> Thus, your papers make a good argument for REST.  I would only caution that the head model is approximate and not exact and is thus a potential source of error as well.
> 
> Ramesh Srinivasan
> Professor
> Department of Cognitive Sciences
> Department of Biomedical Engineering
> 
> 
> 
> On Sat, Dec 27, 2025 at 7:55 PM dyao--- via eeglablist < eeglablist at sccn.ucsd.edu> wrote:
> 
> > Hello everyone,
> >     Since the discover of EEG in 1924, EEG reference is continuously a
> > debate issue,  which one is the best?
> >     1. Prof Arnaud Delorme, the first author of the EEGLAb, has a
> > video on "What is the best EEG reference?"
> >
> > https://urldefense.com/v3/__https://urld/__;!!Mih3wA!B_y6AojvL8UK_viRzlNr2q7Xqoiu0WDu3k3h_W18Ou0WCZt0Lyr5WvORKF3yOahNTzBBsuIZRyMhupG00uO9bA$ 
> > efense.com%2Fv3%2F__https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DioIETU
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> > ox.sc.edu%7Cd8b0ceab7e034c20d0c108de464f8a78%7C4b2a4b19d135420e8bb2b1c
> > d238998cc%7C0%7C0%7C639025504614617191%7CUnknown%7CTWFpbGZsb3d8eyJFbXB
> > 0eU1hcGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIsI
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> > FlGO2UPFJg%3D&reserved=0
> > , the answer is REST
> >     2. Prof Steven Luck, in his new textbook(Applied Event-Related
> > Potential Data Analysis,2022), in section 6.1 "I’d like to point out
> > using the average across sites as the reference in order to
> > approximate the absolute voltage assumes that the surface of the head
> > sums to zero, but this is only true for spheres. I have yet to meet
> > someone with a spherical head. And no neck. Fortunately, there is a
> > way to estimate the true zero, called the Reference Electrode
> > Standardization Technique (REST), and there is an EEGLAB plugin that
> > implements it (Dong et al., 2017). I haven’t tried it myself or looked
> > at the math, so I don’t have an opinion about whether it’s useful and
> > robust. But if you really want to get an estimate of the absolute voltage, REST seems like the best current approach"
> >     3. in 2014, Lepage etal annouanced that they designed an updated
> > average reference (robust common average reference(rCAR))being better
> > than REST, and since then rCAR were adopted by a few following work.
> > however, a recent comment on rCAR,attached here, confirmed that rCAR
> > is not an EEG reference method but an "noise removement method on
> > various artificial data" as the all illustrative examples adopted in
> > rCAR paper were not EEG data (assumed, not generated by sources inside
> > a brain). In this comment paper, on Data generated by sources inside a
> > head model, REST is much better than rCAR. (Lepage, K.Q., Kramer,
> > M.A., Chu, C.J., 2014. A statistically robust EEG re-referencing
> > procedure to mitigate reference effect. J. Neurosci. Methods 235, 101–116).
> >     In general, REST and average reference(AR) are the best two as
> > both of them are based on EEG physics. REST is based on the equivalent
> > distributed-sources principle of the scalp potential, it depends on
> > the 'equivalence between the unknown neural sources in the brain and
> > the reconstructed equivalent sources in the brain', various
> > simulations confirmed the equivalence depends on the cover range and
> > density of the scalp electrode array. AR is based that the whole
> > surface potential integral is zero if the head a sphere, apparently, the weakness is that "
> > our head is not a sphere, and the measurment is usually limited to the
> > uper surface, not and impossible being the whole surface as we have
> > the neck", various simulations confirmed AR depends on the cover range
> > and density of the scalp electrode array,too. The conducted
> > comparative studies showed that REST is usually better than AR especially when electrode number>20.
> > For both methods, the most important factor is the cover range, then
> > is the density of the electrode density ,or say, the number and
> > distribution of electrodes.
> >    wish the above message is meaningful for your work in EEG and ERP.
> >    Best wishes
> > -----------------------------
> > Dezhong Yao, PhD, CheungKong Professor AIMBE Fellow，Cuba Academico
> > Correspondiente，CSBME Fellow Director, Brain-Apparatus Communication
> > Institute
> > Editor-in-Chief，Brain-Apparatus Communication, Taylor & Francis Group
> > University of Electronic Science and technology of China, 611731,
> > Chengdu, China _______________________________________________
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------------------------------
Dezhong Yao, PhD, CheungKong Professor
AIMBE Fellow，Cuba Academico Correspondiente，CSBME Fellow
Director, Brain-Apparatus Communication Institute
Editor-in-Chief，Brain-Apparatus Communication, Taylor & Francis Group  
University of Electronic Science and technology of China, 611731, Chengdu, China