Don't trust the source power spectrum results

Would you not expect all vectors to be short(er), just like the vectors far away from channel 9 in the example on the right?

The size of the blue arrows is normalized, you can't make any interpretation about their length. What is meaningful is their relative length between different parts of the brain for one given sensor. All the arrows of similar length and orientation indicates that the all dipoles are influenced in a similar way by the selected electrode, which is expected for a distant electrode.
@tmedani Is this correct?

In addition, there seems to be a clear activation in the temporal poles with the OpenMEEG head model, which is not apparent in the topography or with the Spherical Head model.

This is mostly a matter of colormap setting. In all cases, these maps should be normalized, you shouldn't try to interpret these maps directly. After computing group-level statistics with many subjects, the results obtained with the two forward models might not be very important.

Secondly, the normalised maps (dSPM) show the main activation in the medial cortices, irrespective of the head model.

What clearly fails is the normalization of your minimum norm maps (both dSPM and sLORETA).
@Sylvain @John_Mosher: Could you please share your opinion on this?

But we're studying sleep disorders where we're interested in wake-like brain activity during sleep, so I guess we'd best use an identity matrix as noise estimates?

That's what we wrote in the noise covariance tutorial, indeed (https://neuroimage.usc.edu/brainstorm/Tutorials/NoiseCovariance#Variations_on_how_to_estimate_sample_noise_covariance), but it doesn't seem to work in your case.

Can you please post a screen capture illustrating what you obtain with a noise covariance estimated on a short segment of "calm" segments (early stages of sleep maybe)? Just to make sure that this is the problem for dSPM/sLORETA.

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