Elimination of intra-artifacts in EEG has been overlooked in most of the existing sleep staging systems, especially in deep learning-based approaches. Whether intra-artifacts, originated from the eye movement, chin muscle firing, or heart beating, etc., in EEG signals would lead to a positive or a negative masking effect on deep learning-based sleep staging systems was investigated in this paper. We systematically analyzed several traditional pre-processing methods involving fast Independent Component Analysis (FastICA), Information Maximization (Infomax), and Second-order Blind Source Separation (SOBI). On top of these methods, a SOBI-WT method based on the joint use of the SOBI and Wavelet Transform (WT) is proposed. It offered an effective solution for suppressing artifact components while retaining residual informative  data. To provide a comprehensive comparative analysis, these pre-processing methods were applied to eliminate the intra-artifacts and the processed signals were fed to two ready-to-use deep learning models, namely two-step hierarchical neural network (THNN) and SimpleSleepNet for automatic sleep staging. The evaluation was performed on two widely used public datasets, Montreal Archive of Sleep Studies (MASS) and Sleep-EDF Expanded, and a clinical dataset that was collected in Huashan Hospital of Fudan University, Shanghai, China (HSFU). The proposed SOBI-WT method increased the accuracy from 79.0% to 81.3% on MASS, 83.3% to 85.7% on Sleep-EDF Expanded, and 75.5% to 77.1% on HSFU compared with the raw EEG signal, respectively. Experimental results demonstrate that the intra-artifacts bring out a masking negative impact on the deep learning-based sleep staging systems and the proposed SOBI-WT method has the best performance in diminishing this negative impact compared with other artifact elimination methods.