[Eeglablist] Beamformer?

[Philip Michael Zeman]

Hi Jim,

I've gone down a path investing your idea a couple years ago, "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.

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.

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.

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.  

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.

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.

Hope that is makes sense and is informative.

~Phil

=-=-=-=-=-=

Philip Michael Zeman
Formally with the University of Victoria Brain-Computer Interface Project
Interdisciplinary Studies: Engineering, Biology, Neuropsychology
(Currently publishing Ph.D. material and looking for work ;) )



 

  ----- Original Message ----- 
  From: jkk251 
  To: Philip Michael Zeman ; conny_kranczioch at yahoo.de ; eeglablist at sccn.ucsd.edu ; Jim Kroger 
  Sent: Thursday, March 05, 2009 12:37 PM
  Subject: Re: [Eeglablist] Beamformer?


  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. 

  In as much as these are different, I want to do the former.

  Thanks,
  Jim



  At 06:01 PM 3/4/2009, Philip Michael Zeman wrote:

    Jim,

    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?


    ~Phil Zeman

    ----- Original Message ----- From: "Jim Kroger" <jkroger at nmsu.edu>
    To: <conny_kranczioch at yahoo.de>; <eeglablist at sccn.ucsd.edu>
    Sent: Tuesday, March 03, 2009 3:17 PM
    Subject: [Eeglablist] Beamformer?





        Does anybody know of any beamformer algorithms that have been
        implemented to work with EEGLAB?

      Thanks,
      Jim Kroger







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