[FieldTrip] Beamformers: SAM vs LCMV vs LCMV fixedori

[Marc Lalancette]

Hi Max,

The formulae are different even when using LCMV with the same fixed orientation as the one found by SAM.
For example, the power formulae, with hopefully clear enough notation (o is orientation vector), and assuming unit-gain weight normalization for simplicity:
scalar: w(o)' R w(o) = 1 / [o' L' R^-1 L o]
1-d vector: o' W' R W o = o' [L' R^-1 L]^-1 o

Of course, if using different software, there might also be differences in what weight normalization is used, how the data is filtered, whether or not a baseline or "DC offset" is subtracted, etc.

Note of potential interest: I'm preparing a poster for Biomag with information on scalar and vector beamformers, with emphasis on the issue of rotational invariance since it is a common issue in the literature and in some software: that some formulae are not rotationally invariant, i.e. the results depend on how the coordinate system is defined/oriented.  This is obviously not acceptable for any physically significant measure.  Regarding Fieldtrip itself, the only such issue I found is the (mostly hidden, thus probably not typically used) option to normalize lead fields by column.

Cheers,

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


Date: Wed, 2 Jul 2014 10:10:02 -0400
From: Max Cantor <mcantor at umich.edu>
To: FieldTrip discussion list <fieldtrip at science.ru.nl>
Subject: [FieldTrip] Beamformers: SAM vs LCMV vs LCMV fixedori
Message-ID:
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Hi Fieldtrip,

We are currently using the SAM beamformer for source localization, but are
thinking of switching to LCMV. Given the research I've read, the vector
beamformer approach should, for our purposes, be more efficient and be as,
if not more accurate than scalar.

However, other than the vector/scalar difference, I don't have a great
understanding of what other differences exist between the two beamformers.
To test the differences, I've run SAM, LCMV, and LCMV with fixed
orientation (making it scalar), with both our real data and with simulated
data, and while SAM and LCMV fixedori are more similar to each other than
either are when compared to LCMV without fixedori (particularly with the
simulation, less so with our real data), they are still visibly different
from each other. This suggests to me that there are other potentially
meaningful differences between SAM and LCMV besides the scalar/vector
difference, and I want to make sure I have at least some idea of what those
differences are before I commit to the change.

That being said, I get the feeling that these differences may be more
nuanced than I can decipher on my own, so if anyone can explain to me what
these differences are and if they are important, I would greatly appreciate
it.

Thanks,

Max

--
Max Cantor
Lab Manager
Computational Neurolinguistics Lab
University of Michigan

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