[Mne_analysis] Depth prior

[Alexandre Gramfort]

hi Emily,

sorry for the slow answer.

> I generally use fixed orientation forward models, and I've just started
> experimenting with using a depth prior for my MNE solutions. I noticed that
> make_inverse_operator requires the input forward model to be in free
> orientation mode in order to use depth weighting, because
> compute_depth_prior uses all three orientations to calculate the weights.
>
> Actually, compute_depth_prior can work with either free or fixed
> orientations, but it seems that make_inverse_operator enforces free
> orientations because the resulting depth prior is better in some sense. That
> is, the first singular value of dot(Gk.T,Gk) for each source location is a
> better normalizing factor than sum(G**2, axis=0).

I convinced myself it the right approach by working on phantom data like here:

https://martinos.org/mne/dev/auto_tutorials/plot_brainstorm_phantom_elekta.html

one intuition is that dot(Gk.T,Gk) is only sensitive to depth while
sum(G**2, axis=0).
is sensitive also orientation. Basically with sparse solvers, using
sum(G**2, axis=0).
you don't recover the correct orientation.

> I don't think the original Fuchs et al 1999 or Lin et al 2006 papers
> describing depth weighting use the singular value trick -- is there another
> article that justifies its use?
> I'm concerned that in my case where I ultimately use fixed orientations, the
> singular-value based depth prior is introducing a systematic bias against
> frontal sources. This may be related to a systematic mismatch between the
> source direction chosen based on the cortical patch statistics and the
> direction of the first singular vector of dot(Gk.T,Gk). Is that possible?

can you show this with sensitivity maps?

> How would you normally quantify bias as a function of source location? I
> have been looking at a few things, including

position a source at every location and see where the peak is found
by solver.

I am also looking at things like this these days.

Alex

> the size of the rows of C^(-1/2)*G*R^(1/2), which I can reconstruct from the
> eigenfields, eigenleads, and singular values in the inverse operator
> the magnitudes of the rows and columns of the resolution matrix
>
>
> Thanks,
> Emily
>
>
>
>
>
>
>
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