# How is the problem of uniform weights for different dipoles addressed for wMNE?

Hi Brainstormers!

I used the wMNE method (with default settings in Brainstorm) for source localization in a study (BEM head model). One reviewer raised some concerns about the wMNE: how was the problem of uniform weights for different dipoles addressed for the wMNE method? For example, how were the weights for each dipole in a specific layer determined to minimize bias from uniform hyperparameter settings?
From my understanding of the wMNE solution, it seems to not involve "uniform weights" or "uniform hyperparameters" for different dipoles.

S_wMNE = WL'(LWL'+λI)^-1
where W is a weight matrix (source covariance matrix) built from the leadfield matrix L with non-zero terms inversely proportional to the norm of the lead field vectors.
Instead, the MNE solution makes a uniform estimate of source covariance: W = I.

I'm wondering if I've missed something or if there's a misunderstanding on my part.

Thanks in advance for helping me!

Best,
Milton

You got it right. The W weights also include a form of compensation against decreasing SNR with depth. Something along the lines of:

https://doi.org/10.1016/j.neuroimage.2005.11.054

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Weighted minimum norm is a technique used in source localization to account for the depth bias in the estimation of neural activity. In the context of Brainstorm software, weighted minimum norm refers to the use of depth weighting options (--depth, --weightexp, and --weightlimit) during the computation of minimum norm estimates.

By modifying the source covariance model at each point in the source grid, deeper sources are "boosted" to increase their signal strength relative to shallower dipoles. This is done to prevent the resulting minimum norm current density maps from being dominated by shallower sources.

However, it's important to note that the use of depth weighting was more debated in the 1990s. With the introduction of normalization methods like dSPM and sLORETA, the effects of depth weighting are mostly canceled out. After normalization, minimum norm results tend to look quite similar whether depth weighting is used or not.

If you have specific questions about the implementation or settings of weighted minimum norm in Brainstorm, I recommend referring to the MNE manual (https://mne.tools/mne-c-manual/MNE-manual-2.7.3.pdf) for a detailed understanding of these parameters.

Hi Sylvain,

Thank you so much for the help!

Best regards,
Milton