[Mne_analysis] MNE method is invariant to the scale of noise

[Evgenii Kalenkovich]

Hi all,

I noticed that if I scale the noise covariance matrix, it does not change
the source estimates in any way. In this example
<https://martinos.org/mne/stable/auto_tutorials/plot_mne_dspm_source_localization.html#sphx-glr-auto-tutorials-plot-mne-dspm-source-localization-py>
from
the example gallery if I change  the method to "MNE" before the first stc
calculation and then do this:

inverse_operator = make_inverse_operator(info, fwd, noise_cov,
                                         loose=0.2, depth=0.8)
stc = apply_inverse(evoked, inverse_operator, lambda2,
                    method=method, pick_ori=None)

from copy import deepcopy
noise_cov_scaled = deepcopy(noise_cov)
noise_cov_scaled['data'] *= 1000000
inverse_operator_scaled = make_inverse_operator(info, fwd, noise_cov_scaled,
                                         loose=0.2, depth=0.8)
stc_scaled = apply_inverse(evoked, inverse_operator_scaled, lambda2,
                           method=method, pick_ori=None)


Then stc_scaled contains exactly the same data as stc. With "dSMP" and
"sLORETA" the result do differ. Why doesn't "MNE" care about the scale of
the covariance matrix?

Evgenii
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