We propose a novel approach for compressive sampling of the neonatal electro-encefalogram (EEG) data. The method assumes that the set of EEG data is generated by linearly mixing a fewer number of source signals. Another assumption is that the sources are nearly-sparse in Gabor dictionary. The presented method, instead of compressing original EEG channels, first performs a data-reduction, and then compresses the obtained sources. With this approach we showed that the gain in reconstruction speed is 33%–50%, whereas the compression rate is enhanced by 33%.