A BCI allows a person to communicate with the external world using artificial electronic or mechanical devices controlled by means of brain signals. Present-day BCIs can be divided into invasive and noninvasive. Prospective application of invasive BCIs to humans is debatable, since they require direct recording of electrical activity from the cortex with the inherent medical risks. Furthermore, the quality of the signals directly recorded on the brain deteriorates over time requiring new surgical interventions and implants in order to keep the functionality of the device. Non-invasive BCI basically rely on specific scalp EEG features. The main disadvantage of latter methods is that scalp EEG signals represent the noisy spatiotemporal overlapping of activity arising from very diverse brain regions, i.e., a single scalp electrode picks up and mixes the temporal activity of myriads of neurons at very different brain areas. Consequently, temporal and spectral features, specific to different processes arising at different areas, are intermixed on the same recording. Here we describe our approach to develop a direct noninvasive BCI system aimed to reproduce the excellent speed and prediction properties of the invasive systems while suppressing their risks. For doing that, we propose the non-invasive estimation of local field potentials in the whole human brain from the scalp measured EEG data using recently developed inverse solutions (LAURA and ELECTRA) to the neuroelectromagtic inverse problem. Recent studies have shown that the temporal and spectral features of the electric activity within the brain can be estimated from the surface signals with high precision. The goal of a linear inverse procedure is to de-convolve or un-mix the scalp signals attributing to each brain area its own temporal activity. By targeting on the particular temporal/spectral features at specific brain areas we expect to select a low number of features that capture information related to the state of the individual in a way that is relatively invariant to time. This avoids long training periods and increases the reliability and efficiency of the classifiers. For instances, in paralyzed patients the classification stage can be improved by focusing on the specific brain areas known to participate and code the different steps of voluntary or imagined motor action trough temporal and spectral features. For these reasons, a direct non invasive BCI system based on linear inverse solutions should combine the advantages of invasive and non invasive devices providing a safer and faster alternative to translate brain thoughts into actions.