Can quality of analysis be estimated with resolution matrix?

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1

Dear colleges,
i m trying to find out what actually is resolution matrix, but the description havent clarify anything for me : |

Resolution matrix (inverse operator times forward operator).
        The result of applying the inverse operator to the forward operator.
        If source orientations are not fixed, all source components will be
        computed (i.e. for n_orient_inv > 1 or n_orient_fwd > 1).
        The columns of the resolution matrix are the point-spread functions
        (PSFs) and the rows are the cross-talk functions (CTFs).

If anyone can briefly explain what is it for or if it can be used for estimating the precision of analysis i ll highly appreciate that

2

Assume we place a source somewhere in the brain and calculate the EEG response for this source. Now, when we apply the inverse operator on this simulated EEG response, we would hope that the found source is exactly at the location that we placed it in.

However, due to the ill-posedness of the inverse problem , this will never happen. The most likely result is a blob of activation in the neighborhood of the real source location. This blob is a column of the resolution matrix (which ideally would be the identity matrix).

This is a fundamental limit of the precision of your source analysis method because in practice, also noise would be added to the EEG and the model might not be perfect.

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