Hello everyone, I'm Greg working on inverse methods with Brainstorm.
I'm trying to understand the GLS method implemented in the code.
My question is about the GLS Kernel formula used in bst_inverse_linear_2018.m
% So L = [A.Ua] * blkdiag(A.Sa) * blkdiag(A.Va)'; % good for any subset too.
[...]
%Kernel(ndx,: ) = A(i).Va * (Lambda*A(i).Sa) * inv(Lambda * A(i).Sa + I) * A(i).Ua';
Kernel(ndx,: ) = A(i).Ua';
The first commented lines shows that Ua, Sa and Va correspond with the SVD of the whitened and weighted Lead field matrix (L).
The second commented line, seems to correspond with some regularized generalized inverse of L
But what about the third line and the formula really used? Why only using Ua ?
Is there any references ?
Thanks & regards.
Greg