Detecting artifacts produced in electroencephalographic (EEG) data by muscle activity, eye blinks and electrical noise, etc., is an important problem in EEG signal processing research. These artifacts must be corrected before further analysis because it renders subsequent analysis very error-prone. One solution is to reject the data segment if artifact is present during the observation interval, however, the rejected data segment could contain important information masked by the artifact. It has already been demonstrated that independent component analysis (ICA) can be an effective and applicable method for EEG de-noising. The goal of this paper is to propose a framework, based on ICA and wavelet denoising (WD), to improve the pre-processing of EEG signals. In particular we employ the concept of spatially-constrained ICA (SCICA) to extract artifact-only independent components (ICs) from the given EEG data, use WD to remove any brain activity from extracted artifacts, and finally project back the artifacts to be subtracted from EEG signals to get clean EEG data. The main advantage of the proposed approach is faster computation, as all ICs are not identified in the usual manner due to the square mixing assumption. Simulation results demonstrate the effectiveness of the proposed approach in removing focal artifacts that can be well separated by SCICA.