[Mne_analysis] Tuning Lambda^2 in High Noise Systems

[Eric Larson]

        External Email - Use Caution        

>
> I’ve been analyzing dipole localization error (DLE) and spatial dispersion
> (SD) on a resolution matrix with sensor noise injected in the middle (M @ N
> @ G, for M: inverse operator matrix, G: forward operator matrix, N: sensor
> noise matrix). I’m using MNE-Python to create my inverse and forward
> matrix.
>

You might consider using the same measures implemented in MNE directly
nowadays, which will also give you some possibly complementary information:

https://mne.tools/dev/generated/mne.minimum_norm.resolution_metrics.html#mne.minimum_norm.resolution_metrics

For a given system at a given sensor noise level, my measurements of DLE
> and SD are predictably quite sensitive to choice of lambda^2. It seems that
> the recommended choice of lambda^2 = 1/avg_snr (where avg_snr is the
> average power snr of the system) is not close to the best choice for
> lambda^2 found through tuning.
>
>
> As I sweep lambda^2 values, there is a clear minimum in the SD function
> that coincides with a knee of the curve for DLE. This seems like the right
> value to choose for optimal overall system performance. Most often, the
> tuned lambda^2 ends up being one or more orders of magnitude higher than
> the recommended value, with the scale factor increasing with more noise in
> the system.
>

In addition to testing some other metrics (above), you could also try
looking to see if there is any relationship to the estimated SNR like in:

https://mne.tools/dev/auto_examples/inverse/plot_snr_estimate.hhttps://mne.tools/dev/auto_examples/inverse/plot_snr_estimate.htmltml
<https://mne.tools/dev/auto_examples/inverse/plot_snr_estimate.html>

And you could follow related citations for these functions/methods:

https://mne.tools/dev/generated/mne.minimum_norm.estimate_snr.html#mne.minimum_norm.estimate_snr
https://mne.tools/dev/generated/mne.SourceEstimate.html#mne.SourceEstimate.estimate_snr

Does using a large lambda^2 value lead to simulation results that are
> valid, or is this a numerical exercise that introduces some bias that I
> don’t yet understand? Does it make sense that the tuned value for lambda^2
> would be much larger than 1/avg_snr for high noise systems, or is this
> likely indicating a bug somewhere?
>

I am not sure. It might also be worth (reading this and) pinging the
authors of this paper separately as they might have ideas, and I'm not sure
how actively they monitor the list:

https://link.springer.com/referenceworkentry/10.1007%2F978-3-030-00087-5_85

Best,
Eric
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