[Mne_analysis] Tuning Lambda^2 in High Noise Systems

[Taylor Williams]

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Hi All,


I have some questions about good choices for the regularization parameter
lambda^2 in high noise systems. I’m using MNE-Python to run simulations of
theoretical high-density solid-state MEG arrays that operate with much
higher sensor noise than low-Tc SQUID sensors. These arrays contain a small
number of sensors with SNRs > 1, but the average SNR is usually << 1.


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.


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.


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?


Thanks,

Taylor Williams
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