This paper proposes an automatic method for artefact removal and noise elimination from scalp electroencephalogram recordings (EEG). The method is based on blind source separation (BSS) and supervised classification and proposes a combination of classical and news features and classes to improve artefact elimination (ocular, high frequency muscle and ECG artefacts). The role of a supplementary step of wavelet denoising (WD) is explored and the interactions between BSS, denoising and classification are analyzed. The results are validated on simulated signals by quantitative evaluation criteria and on real EEG by medical expertise. The proposed methodology successfully rejected a good percentage of artefacts and noise, while preserving almost all the cerebral activity. The "denoised artefact-free" EEG presents a very good improvement compared with recorded raw EEG: 96% of the EEGs are easier to interpret.