[FieldTrip] Beamformers: SAM vs LCMV vs LCMV fixedori

[Max Cantor]

Thanks Marc,

Hopefully this can explain some of the differences I'm seeing between the
beamformers with our data and help me determine if they are significant for
our purposes. Good luck with the poster! I'm not sure if this is what you
were getting at, but if it is made publicly available online I would
certainly be interested in reading it, thank you.


On Wed, Jul 9, 2014 at 11:50 AM, Marc Lalancette <
marc.lalancette at sickkids.ca> wrote:

> 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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> q_pm9wFB5FZ-_L0A at mail.gmail.com>
> Content-Type: text/plain; charset="utf-8"
>
> 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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-- 
Max Cantor
Lab Manager
Computational Neurolinguistics Lab
University of Michigan
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