# [FieldTrip] unit gain for Fieldtrip's LCMV beamformer - unit

Marc Lalancette marc.lalancette at sickkids.ca
Fri Sep 11 18:40:20 CEST 2015

```Hi Russ,

There are lots of options in Fieldtrip, in particular various normalization options.  First the theory: careful not to confuse "unit gain" and "unit noise-gain".  I suppose these names may be defined differently in different places, but I'll use them as defined by Sekihara (great book for understanding beamforming).  Thus the latter has unit length weights, not the former and a scalar beamformer with unit gain would have Am units.  However, see a previous thread about Fieldtrip's leadfield units: http://mailman.science.ru.nl/pipermail/fieldtrip/2014-September/008438.html which would possibly also affect unit gain beamformer results.  I would double check if using that to confirm units.  For vector beamforming, power would be returned so units should be (Am)^2.  If the power is normalized by the estimated projected noise power, we get an estimate of output SNR (pseudo-Z^2, no units, sometimes called neural activity index, though not same formula as the original NAI by Van Veen).  This is often how unit noise-gain is used, by also dividing the result by an estimate of sensor noise power (assumed uniform across sensors).

That being said, I think Fieldtrip's LCMV by default will use a 2-d vector beamformer (2 "tangential" source orientations, those corresponding to the 2 largest eigenvalue of the leadfield eigendecomposition).  It does not however use unit noise-gain as defined by Sekihara (which is good by the way because that solution is not rotationally invariant - I had a poster on that last Biomag).  Instead it does a slightly different normalization dividing the summed power by the summed projected noise power (summed over the 2 orientations).  That is a rotationally invariant solution but may not be as sharp as other options.  There would be more to say about these different normalization options.

But to answer your question, yes in some cases there would be no units for the beamformer time course, though of course even then the quantity should still be properly identified.  My personal preference however is to get time courses in physical units (Am or squared for power).  I find it makes interpretation easier and comparisons more meaningful than comparing say SNR between groups.

Cheers,

Marc Lalancette
Lab Research Project Manager, Research MEG lab
Department of Diagnostic Imaging, Program in Neurosciences and Mental Health
The Hospital for Sick Children, 555 University Avenue, Room S742, Toronto, ON, M5G 1X8
416-813-7654 x201535

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Subject: fieldtrip Digest, Vol 58, Issue 10

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Today's Topics:

1. unit gain for Fieldtrip's LCMV beam former - unit for     LCMV
derived timecourse (russ port)

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Message: 1
Date: Thu, 10 Sep 2015 12:31:28 -0400
From: russ port <russgport at gmail.com>
To: fieldtrip at science.ru.nl
Subject: [FieldTrip] unit gain for Fieldtrip's LCMV beam former - unit
for     LCMV derived timecourse
Content-Type: text/plain; charset="utf-8"

Hi All,

Sorry to bother you, but I have a question that I would just like to bounce of the list (to make sure I understand what I?m talking about). The fieldtrip version of LCMV beamforming use a unit-gain (AKA unit length) normalization for the analysis. As such (according to http://cheynelab.utoronto.ca/httpdoc/Introduction_to_beamforming_part2.pdf <http://cheynelab.utoronto.ca/httpdoc/Introduction_to_beamforming_part2.pdf>), the output unit of the beamformer derived time course (shown on previous discussion list post as making sensor weights (involving the lead fields for the dipole position AND covariance matrix) and multiplying the data per trial by the result), would be IF we had not used unit gain, A-m, but since we add the normalization, the unit of the output is arbitrary units. As such, when I plot an example time course of the data, there is no unit for the y axis.

Sorry for checking this, but I figure its safer to ask, and hopefully someone else is also wondering the same thing.

Best ,
Russ
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