SSP projection and the forward gain matrix

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1

Hi MNE community,

I have a question about the SSP projection.
According to Page 86 of the MNE manual,

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)

So I thought when applying the SSP to the sensor data, the forward matrix
should also be multiplied by the operator.
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?
If the latter is true, why is it true?

Thanks so much.

Best,
Ying
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2

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

3

Thanks, Alex. It is very helpful!

Best,
Ying