The Electroencephalography (EEG)-based motor imagery (MI) paradigm is one of the most studied technologies for Brain-Computer Interface (BCI) development. Still, the low Signal-to-Noise Ratio (SNR) poses a challenge when constructing EEG-based BCI systems. Moreover, the non-stationary and nonlinear signal issues, the low-spatial data resolution, and the inter- and intra-subject variability hamper the extraction of discriminant features. Indeed, subjects with poor motor skills have difficulties in practicing MI tasks against low SNR scenarios. Here, we propose a subject-dependent preprocessing approach that includes the well-known Surface Laplacian Filtering and Independent Component Analysis algorithms to remove signal artifacts based on the MI performance. In addition, power- and phase-based functional connectivity measures are studied to extract relevant and interpretable patterns and identify subjects of inefficency. As a result, our proposal, Subject-dependent Artifact Removal (SD-AR), improves the MI classification performance in subjects with poor motor skills. Consequently, electrooculography and volume-conduction EEG artifacts are mitigated within a functional connectivity feature-extraction strategy, which favors the classification performance of a straightforward linear classifier.