Eye blink artifacts and power line noise always disturb the electroencephalograms (EEG) recorded on the scalp and pose serious problems in its signal analysis and interpretation. In this paper, two Independent Component Analysis (ICA) algorithms-- Infomax-ICA and Extended-Infomax-ICA were applied to extract eye movements and power noise of 50Hz in several sets of EEG data. It is confirmed that Extended-Infomax-ICA method can isolate both superguassian artifacts (eye blinks) and subguassian interference (line noise), but original Infomax-ICA method is only limited to remove superguassian artifacts. In particular, Extended-Infomax-ICA has shown excellent performance on separating the original EEG signals from heavy line noise in an EEG data of very low SNR (-40dB), with a fine stability and robust. Meanwhile, by calculating the values of approximation entropy (ApEn) before and after ICA processing, it showed that ICA algorithms could well preserve the nonlinear characteristics of EEG after removing the artifacts. Experiment results show that ICA algorithm is a quite powerful technique and suitable for EEG data processing in clinical engineering.