Brain-Computer Interfaces (BCIs) are systems that translate their user's mental state, typically recorded via electroencephalography (EEG), into commands for a computer without any muscular activity being involved. They have been widely adopted in the medical community, for instance to allow patients suffering from locked-in syndrome to interact with their environment or for prosthesis control. In a recent incarnation, BCI algorithms leverage non-invasive neuroimaging techniques to better discriminate between users' mental states. One of the main challenges of these approaches is to ensure that the reconstruction of the intracranial brain activity from the external EEG measurements at the art of the neuroimaging procedure is accurate, without resorting to invasive measurements.