Recent experiments have shown the possibility to use the brain electrical activity to directly control the movement of robots or prosthetic devices in real time. Such neuroprostheses can be invasive or non-invasive, depending on how the brain signals are recorded. In principle, invasive approaches will provide a more natural and flexible control of neuroprostheses, but their use in humans is debatable given the inherent medical risks. Non-invasive approaches mainly use scalp electroencephalogram (EEG) signals and their main disadvantage is that these 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. In order to combine the benefits of both approaches, we propose to rely on the non-invasive estimation of local field potentials (eLFP) in the whole human brain from the scalp measured EEG data using a recently developed inverse solution (ELECTRA) to the EEG inverse problem. The goal of a linear inverse procedure is to deconvolve or unmix the scalp signals attributing to each brain area its own temporal activity. To illustrate the advantage of this approach we compare, using identical set of spectral features, classification of rapid voluntary finger self-tapping with left and right hands based on scalp EEG and eLFP on three subjects using different number of electrodes. It is shown that the eLFP-based Gaussian classifier outperforms the EEG-based Gaussian classifier for the three subjects.