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Integration of electroencephalography (EEG) and functional magnetic imaging (fMRI) resonance will allow analysis of the brain activities at superior temporal and spatial resolution. However simultaneous acquisition of EEG and fMRI is hindered by the enhancement of artifacts in EEG, the most prominent of which are ballistocardiogram (BCG) and electro-oculogram (EOG) artifacts. The situation gets even worse if the evoked potentials are measured inside MRI for their minute responses in comparison to the spontaneous brain responses. In this study, we propose a new method of attenuating these artifacts from the spontaneous and evoked EEG data acquired inside an MRI scanner using constrained independent component analysis with a priori information about the artifacts as constraints. With the proposed techniques of reference function generation for the BCG and EOG artifacts as constraints, our new approach performs significantly better than the averaged artifact subtraction (AAS) method. The proposed method could be an alternative to the conventional ICA method for artifact attenuation, with some advantages. As a performance measure we have achieved much improved normalized power spectrum ratios (INPS) for continuous EEG and correlation coefficient (cc) values with outside MRI visual evoked potentials for visual evoked EEG, as compared to those obtained with the AAS method. The results show that our new approach is more effective than the conventional methods, almost fully automatic, and no extra ECG signal measurements are involved.