A novel blind signal extraction (BSE) scheme for the removal of eye-blink artifact from electroencephalogram (EEG) signals is proposed. In this method, in order to remove the artifact, the source extraction algorithm is provided with an estimation of the column of the mixing matrix corresponding to the point source eye-blink artifact. The eye-blink source is first extracted and then cleaned, artifact-removed EEGs are subsequently reconstructed by a deflation method. The a priori knowledge, namely, the vector, corresponding to the spatial distribution of the eye-blink factor, is identified by fitting a space-time-frequency (STF) model to the EEG measurements using the parallel factor (PARAFAC) analysis method. Hence, we call the BSE approach semiblind signal extraction (SBSE). This approach introduces the possibility of incorporating PARAFAC within the blind source extraction framework for single trial EEG processing applications and the respected formulations. Moreover, aiming at extracting the eye-blink artifact, it exploits the spatial as well as temporal prior information during the extraction procedure. Experiments on synthetic data and real EEG measurements confirm that the proposed algorithm effectively identifies and removes the eye-blink artifact from raw EEG measurements.