wMNE method - mathematical formulation question

MNE source localization method includes “depth bias” so it is de facto wMNE method. How exactly wMNE algorithm is implemented? Standard way of doing this is to include weighting matrix in a regularization term i.e.: F(x) = |Lx - y|^2 + a|Wx|^2. However looking at source code it looks like a leadfield matrix is weighted?

If it is true it should lead to similar results (or maybe the same if weighted leadfield matrix L_W = LW^(-1)). However it would be good to clarify it in documentation.