Understanding Source Localization of bst_inverse_linear[2018]

The lead field matrix is another name for the gain matrix produced by the forward model.

It is a computationally optimized version of the MNE equation you are quoting in #3. @jcmosher can tell you more about how it is derived more specifically.

The kernel is not an image, it is a matrix operator applied to the sensor data to produce an estimate of source time series at every cortical location. It is the large matrix multiplication to the left of M (the sensor data) in the equation in your point #3.

Hope this clarifies.

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