<div dir="ltr">Dear colleagues,<div><br></div><div>Update--</div><div>I discussed this method with the colleague who taught me about this trick because I got an inquiry about it off the list.</div><div>He said that he would use it only to draw a scalp topography, and performing signal processing using the 'recovered' full-channel signal is not recommended.</div><div><br></div><div>Again, let X be the (single-channel referenced) original EEG data and Xb the bipolar-montage version of it.</div><div>Using a bipolar-referencing transform matrix M, the relation of X and Xb can be written as</div><div><br></div><div>Xb = M * X</div><div><br></div><div>Suppose X has 6 channels F1, F2, C1, C2, P1, P2, and bipolar-referencing was done with F1-F2, C1-C2, P1-P2.</div><div>Then, Xb is 3*t, M is 3*6, and X is 6*t (t is time).</div><div>The matrix M is </div><div><br></div><div>1 -1 0 0 0 0 </div><div>0 0 1 -1 0 0 </div><div>0 0 0 0 1 -1</div><div><br></div><div>(sorry but I don't have code)</div><div>To compute M^-1, one should use pinv() (i.e. pseudo-inverse) and the recovered full-channel data are NOT full-ranked (and this is NOT the only solution)</div><div>To recover full channel data, you also need to have something like F1-C1, C2-P1, P2-F2 so that the matrix is full-ranked and square, but such data are not usually available (as far as I know, Paul Sajda presented such a complicated reference system to address high-amplitude artifact in simultaneous fMRI-EEG recording).</div><div><br></div><div>So the recommended use of this solution is just to draw scalp topography for convenience.</div><div><br></div><div>Accordingly, let me correct my previous statement.</div><div><br></div><div><div style="font-size:12.8px">> Thus, by multiplying the inverse matrix of the known <span class="gmail-il">bipolar</span>-referencing transform matrix M, you obtain the original signal.</div></div><div><br></div><div>This is true ONLY IF you have redundantly referenced channels (which is very rare). Otherwise, it does NOT properly convert standard bipolar montage to a single-referenced data (because M is not square), therefore analyzing the 'recovered' data should be limited to specific purposes only.</div><div><br></div><div>Sorry if my previous writing was misleading.<br></div><div><br></div><div>Makoto</div></div><div class="gmail_extra"><br><div class="gmail_quote">On Fri, May 12, 2017 at 4:26 PM, Makoto Miyakoshi <span dir="ltr"><<a href="mailto:mmiyakoshi@ucsd.edu" target="_blank">mmiyakoshi@ucsd.edu</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr">Dear Mubaraki,<div><br></div><div>Ok this is the solution I learned from my colleague.</div><div>Let X be the (single-channel referenced) original EEG data and Xb be the bipolar-montage version of it.</div><div>Using a bipolar-referencing transform matrix M, the relation of X and Xb can be written as</div><div><br></div><div>Xb = M * X</div><div><br></div><div>Now M is a known matrix: if your bipolar montage is referenced as F1 - F3 for example, then F1 is 1 and F3 is -1. I guess the directions of the signs do not matter as long as they are consistent with other pairs, such as C1-C3 etc.</div><div>After making M, you multiply M^-1 from left, you obtain</div><div><br></div><div>X = M^-1 * Xb</div><div><br></div><div>Thus, by multiplying the inverse matrix of the known bipolar-referencing transform matrix M, you obtain the original signal.</div><div><br></div><div>What a smart solution! I'm proud of him.</div><span class="HOEnZb"><font color="#888888"><div><br></div><div>Makoto</div><div><br></div></font></span></div><div class="HOEnZb"><div class="h5"><div class="gmail_extra"><br><div class="gmail_quote">On Wed, May 10, 2017 at 1:45 PM, Makoto Miyakoshi <span dir="ltr"><<a href="mailto:mmiyakoshi@ucsd.edu" target="_blank">mmiyakoshi@ucsd.edu</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr">Dear Mubaraki,<div><br></div><div>I've recently seen a solution (and a surprisingly simple solution) one of my colleague used in SCCN. I'll ask him about it and will get back to you.</div><div><br></div><div>Makoto</div><div class="gmail_extra"><div><div class="m_5441762608284345862h5"><br><div class="gmail_quote">On Tue, Feb 14, 2017 at 7:12 PM, Ibtissem KHOUAJA <span dir="ltr"><<a href="mailto:ibtissem.Khouaja@live.fr" target="_blank">ibtissem.Khouaja@live.fr</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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<p><span id="m_5441762608284345862m_619213183448054737m_-495868527338532545m_-6629393656618825139x_result_box" lang="en"><span>Dear Mubaraki,</span></span></p>
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<p><span id="m_5441762608284345862m_619213183448054737m_-495868527338532545m_-6629393656618825139x_result_box" lang="en"><span>I think it will be not the same.<br>
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<p><span id="m_5441762608284345862m_619213183448054737m_-495868527338532545m_-6629393656618825139x_result_box" lang="en"><span>The EEG, in this case, records the potential difference between two active electrodes.</span></span></p>
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<p>Yours, Ibtissem<br>
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<font color="#666666" face="Comic Sans MS" size="2" style="background-color:rgb(255,255,255)">Ibtissem KHOUAJA BENFRADJ</font>
<div><span style="background-color:rgb(255,255,255)"><font color="#666666" face="Comic Sans MS" size="2">PhD in computer science</font></span></div>
<div><span style="background-color:rgb(255,255,255)"><font color="#666666" face="Comic Sans MS" size="2">Speciality: Biomedical Signal Processing</font></span></div>
<div><span style="background-color:rgb(255,255,255)"><font color="#666666" face="Comic Sans MS" size="2">Laboratory: LTIM, University of Monastir, Tunisia</font></span></div>
<div><a href="http://www.labtim.org/accueil.php" id="m_5441762608284345862m_619213183448054737m_-495868527338532545m_-6629393656618825139LPNoLP" target="_blank"><font color="#666666" face="Comic Sans MS" size="2" style="background-color:rgb(255,255,255)">http://www.labtim.org/accueil.<wbr>php</font></a></div>
<div><span style="background-color:rgb(255,255,255)"><font color="#666666" face="Comic Sans MS" size="2">Laboratory: LIGM, Univerisity of Paris-East, France </font></span></div>
<div><a href="http://ligm.u-pem.fr/" id="m_5441762608284345862m_619213183448054737m_-495868527338532545m_-6629393656618825139LPNoLP" target="_blank"><font color="#666666" face="Comic Sans MS" size="2" style="background-color:rgb(255,255,255)">http://ligm.u-pem.fr/</font></a></div>
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<div id="m_5441762608284345862m_619213183448054737m_-495868527338532545m_-6629393656618825139x_divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" color="#000000" style="font-size:11pt"><b>De :</b> <a href="mailto:eeglablist-bounces@sccn.ucsd.edu" target="_blank">eeglablist-bounces@sccn.ucsd.e<wbr>du</a> <<a href="mailto:eeglablist-bounces@sccn.ucsd.edu" target="_blank">eeglablist-bounces@sccn.ucsd.<wbr>edu</a>> de la part de Mubaraki A.A.H. <<a href="mailto:aahm1v15@soton.ac.uk" target="_blank">aahm1v15@soton.ac.uk</a>><br>
<b>Envoyé :</b> lundi 13 février 2017 12:06:13<br>
<b>À :</b> EEGLAB List [<a href="mailto:eeglablist@sccn.ucsd.edu" target="_blank">eeglablist@sccn.ucsd.edu</a>]<br>
<b>Objet :</b> [Eeglablist] convert EEG montage from bipolar to unipolar</font>
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<div class="m_5441762608284345862m_619213183448054737m_-495868527338532545m_-6629393656618825139PlainText">I am using data from <a href="https://physionet.org/pn6/chbmit/" target="_blank">
https://physionet.org/pn6/chbm<wbr>it/</a> for EEG research on EEGLAB. The channels here are provided in terms of a bipolar montage (ex: FP1-F7 instead of FP1). How can I convert this bipolar montage to the standard, unipolar channel data<br>
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</blockquote></div><br><br clear="all"><div><br></div>-- <br><div class="m_5441762608284345862gmail_signature" data-smartmail="gmail_signature"><div dir="ltr">Makoto Miyakoshi<br>Swartz Center for Computational Neuroscience<br>Institute for Neural Computation, University of California San Diego<br></div></div>
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</div></div></blockquote></div><br><br clear="all"><div><br></div>-- <br><div class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr">Makoto Miyakoshi<br>Swartz Center for Computational Neuroscience<br>Institute for Neural Computation, University of California San Diego<br></div></div>
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