"Electroencephalography (EEG) from scalp potentials has affirmed itself as one of the primary non-invasive techniques to map and study the brain electric activity. EEG imaging is of crucial importance in the electric characterization of epileptic seizures. This is especially true for patients affected by focal epilepsy, when source characterization and localization is a key step of a pre-surgical protocol that precedes the removal of the patient’s brain area that shows an abnormal electric activity.This project will investigate innovative tools for solving the EEG neuroimaging problem that will sensibly advance the EEG’s state of the art by: (i) Investigating a new Boundary Element solver for the direct EEG problem that will combine the benefits of Finite and Boundary Element approaches, currently used in literature, without sharing their deficiencies. (ii) Developing the first EEG direct problem solution tool providing non-iterative (direct inverse) solutions in linear time. (iii) Interfacing the new solver with the most advanced inverse scattering algorithms and designing the complete neuroimaging tool in order to efficiently work on low-cost GPU hardware accelerators. This will make available very high definition and potentially real-time EEGs even in low-budget medical environments. (iv) Pursuing an optimization study (made possible by the new technology developed in i-iii) of the density and placement of EEG electrodes with high electrode numbers and in the presence of very high resolution head models.The impact of the novel technology developed in this project will be demonstrated by a thorough analysis in both canonical and real case scenarios rising from the medical practice. After the completion of this project the newly developed EEG neuroimaging tool will be made available for the benefit of the scientific community and of the EU citizenship."