[Mne_analysis] SSP projection and the forward gain matrix

[Alexandre Gramfort]

hi Ying,

> The noise is decomposed to
> bn(t) = U * cn(t) + e(t),
>  where e(t) is white noise.
> Let y(t) be the sensor signal and x(t) be the source signal
>
> y(t) = G x(t) + bn(t)
> so if we apply the SSP operator  (I - UU'),
>
> (I-UU') y(t) = (I-UU')G x(t) + (I-UU') bn(t)
>                    = (I-UU')G x(t) + (I-UU') e(t)

this is correct.

> So I thought when applying the SSP to the sensor data, the forward matrix
> should also be multiplied by the operator.

yes

> But when I tried to read through  the python code in
> "mne.minimum_norm.inverse", I did not find this kind of operation.
> Am I missing something or is it the case that  the operator should not be
> applied to G?

it is applied to G but via the whitening matrix to which has been applied
the SSPs.

hope this helps,

Alex

> If the latter is true, why is it true?
>
> Thanks so much.
>
> Best,
> Ying
>
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