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In this paper, a novel source extraction method is proposed for removing ballistocardiogram (BCG) artifact from EEG. BCG appears in EEG signals recorded simultaneously with functional magnetic resonance imaging. The proposed method is a semiblind source extraction algorithm based on linear prediction technique. We define a cost function according to a joint short- and long-term prediction strategy to extract the BCG sources. We call this method SLTP-BSE standing for short- and long-term prediction blind source extraction. The objective of this work is to 1) model the temporal structure of the sources using short-term prediction and 2) impose the prior information about the BCG sources using long-term prediction. These two procedures are simultaneously implemented to optimize the system. The performance of the proposed method is evaluated using both synthetic and real EEG data. The obtained results show that the proposed technique is able to remove the BCG artifact while preserving the task-related parts of the signal. The results of SLTP-BSE are compared with those of well-known BCG removal techniques confirming the superiority of the proposed method.