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<DIV><FONT face=Arial size=2>Hi Jim,</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>I've gone down a path investing your idea a couple
years ago, "<FONT face="Times New Roman" size=3>to observe the signal arising
from a particular spatial location, so that the starting point is the location
and the result is the signal generated there". Unfortunately, I hit a
technical barrier. If anyone knows a way around this, or can cite a paper
on the topic, please let me know.</FONT></FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>My understanding and experience with beamforming is
that it uses a head model (a lead field matrix, often characterized by BERG
parameters) and the time-course activities of a set of electrodes
(multiple, spatially distinct observations, uniformly sampled) to
'unmix' a mixture of signals detected by the observing electrodes.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>The signals are 'unmixed' by mapping variance at
the electrodes to variance in the head model (a uniform volumetric grid of
sampling points within the head model). The Linearly Constrained Minimum
Variance (LCMV) method of beamforming for example maps the scalp variance
to the volumetric head model grid using a measure of covariance between the
electrodes at the scalp. The covariance matrix is calculated via the
time-varying scalp field at the electrodes (the EEG data). The LCMV method
uses the inverse of the covariance matrix to determine the mapping of scalp
variance to variance at grid points in the volume domain.</FONT></DIV><FONT
face=Arial size=2>
<DIV><BR>Here is the key point. Beamforming creates a spatial filter to
separate the mixture of signal originating from inside the head by placing nulls
(canceling) on interfering signals and letting the signal of interest pass
through. Imagine this as a spatial version of a typical
time-frequency filter. In an ideal world, you would place nulls on all
locations in the head except those that you are interested in 'listening
to'. However, one is typically limited to 1/3 as many nulls as there are
EEG channels. My headmodels usually have about 5000 grid points and 124
EEG channels. Thus, it is necessary to know all of the location of
all of the interfering signals. </DIV>
<DIV> </DIV>
<DIV>Assuming you know the location of all the interfering signals, then you can
construct a spatial filter to NULL the interferers and pass the signal of
interest, i.e., the waveform activity of interest. I've played around with
beamforming quite a bit and found that even when you know the location of
interfering signals, because we are dealing with a head model, the NULLs that
are placed (which are restricted to grid locations) are exactly on the locations
of interferers in real brain activity. This is where ICA does a
better job of source separation because there is no 'grid' or head
model limiting ICA.</DIV>
<DIV> </DIV>
<DIV>Personally, I would like to have a method such that you have envisioned,
where one simply places poles (or emphasis) on the brain locations of interest
and does not need to know about interfering signals. However, I'm not sure
if that is technically feasible.</DIV>
<DIV> </DIV>
<DIV>Hope that is makes sense and is informative.</DIV>
<DIV> </DIV>
<DIV>~Phil</DIV>
<DIV> </DIV>
<DIV>=-=-=-=-=-=</DIV>
<DIV> </DIV>
<DIV>Philip Michael Zeman</DIV>
<DIV>Formally with the University of Victoria Brain-Computer Interface
Project</DIV>
<DIV>Interdisciplinary Studies: Engineering, Biology, Neuropsychology</DIV>
<DIV>(Currently publishing Ph.D. material and looking for work ;) )</DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV> </FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<BLOCKQUOTE dir=ltr
style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV style="FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV
style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: black"><B>From:</B>
<A title=jkk251@gmail.com href="mailto:jkk251@gmail.com">jkk251</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A title=pzeman@alumni.uvic.ca
href="mailto:pzeman@alumni.uvic.ca">Philip Michael Zeman</A> ; <A
title=conny_kranczioch@yahoo.de
href="mailto:conny_kranczioch@yahoo.de">conny_kranczioch@yahoo.de</A> ; <A
title=eeglablist@sccn.ucsd.edu
href="mailto:eeglablist@sccn.ucsd.edu">eeglablist@sccn.ucsd.edu</A> ; <A
title=jkroger@nmsu.edu href="mailto:jkroger@nmsu.edu">Jim Kroger</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Thursday, March 05, 2009 12:37
PM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> Re: [Eeglablist]
Beamformer?</DIV>
<DIV><BR></DIV>HI Phil, thanks for the response. My limited understanding is
that a beamformer allows one to observe the signal arising from a particular
spatial location, so that the starting point is the location and the result is
the signal generated there. I know this is sometimes extended to use as a
source localization tool if it is applied to many or all locations in the
head. This seems different than the ability of ICA to separate the signals
resulting from multiple sources or generators, without prior specification of
the physical location of the generators, and that the isolated signals
(components) may then be submitted to a localization algorithm. <BR><BR>In as
much as these are different, I want to do the
former.<BR><BR>Thanks,<BR>Jim<BR><BR><BR><BR>At 06:01 PM 3/4/2009, Philip
Michael Zeman wrote:<BR>
<BLOCKQUOTE class=cite cite="" type="cite">Jim,<BR><BR>is your objective to
use the beamformer characteristics of source sepration (instead of ICA) or
is your objective to identify the locations of ICA-derived sources using a
beamformer?<BR><BR><BR>~Phil Zeman<BR><BR>----- Original Message ----- From:
"Jim Kroger" <jkroger@nmsu.edu><BR>To:
<conny_kranczioch@yahoo.de>; <eeglablist@sccn.ucsd.edu><BR>Sent:
Tuesday, March 03, 2009 3:17 PM<BR>Subject: [Eeglablist]
Beamformer?<BR><BR><BR>
<BLOCKQUOTE class=cite cite="" type="cite"><BR>
<BLOCKQUOTE class=cite cite="" type="cite">Does anybody know of any
beamformer algorithms that have been<BR>implemented to work with
EEGLAB?</BLOCKQUOTE><BR>Thanks,<BR>Jim Kroger<BR><BR><BR><BR>
<BLOCKQUOTE class=cite cite=""
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</BLOCKQUOTE></BLOCKQUOTE><X-SIGSEP>
<P></X-SIGSEP><FONT
size=2>_________________________________________________<BR></FONT><FONT
color=#008000 size=2><B>New cell number: 575-571-8274<BR></FONT><FONT
color=#800080 size=2>New email address: jkk251@gmail.com <BR></B></FONT><FONT
size=2>Mail sent to my old email address will still reach
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