I know the data from the sensor will be either under-determined or over-determined.(structure-wise), meaning its an inverse problem.
Why do we calculate the noise covariance?
Conceptually I know source localization helps in estimating source locations, so calculating for the noise covariance will help determining the true activity in that location. This is me guessing. I don’t know if I am right with what I said.
Also, why use empty room measurements for the estimation of sensor noise? Is it to find the true measurement from a particular sensor?
There is often depth bias in the source localization (MNE tends to bias superficially and beamformer tends to bias deep). To remove the depth bias, there are a few strategies and one is to project the noise covariance through the same localization weights. Dividing the depth biased source activity by the depth biased noise helps to remove the depth bias. A standard MNE solution will result in an estimate of neural current, but dividing by the noise leaves you with a statistic (dSPM (T or F stat) and lcmv (psuedo-T)). Other depth bias reducing techniques are contrasting two conditions (at least in beamformer this works) and I think there is a way to modify the forward model to correct bias.
Why emptyroom? — You can often use the prestimulus baseline time to estimate a noise covariance and use this as your noise covariance. This however is a problem if you have ongoing brain activity that is related to your task. An example is a demanding cognitive task where the subject may still be thinking of the last answer during the prestim to the next trial. If this is the case, you would be dividing your active source estimate by the “semi-active” baseline - resulting in a weird/biased result.
There may be other reasons for the empty room. And there are some groups that do not use it.
And regarding the evoked response, that just means the average of the trials - it doesn’t need to be source localized. And an alternative to evoked response is induced response which is the squared power response (generally in a frequency band).
