The ballistocardiogram (BCG) is a major artifact in electroencephalographic (EEG) data acquired inside a magnetic resonance imaging (MRI) scanner, and is several times larger in magnitude than the actual EEG signals. Removing the BCG artifacts remains an unresolved challenge, especially in studies of continuous EEG recordings. In this work, we propose a Direct Recording-Joint Incoherent Basis (DRJIB) method to decompose the observed noisy EEG measurements into BCG and underlying EEG components. We compare its preliminary performance quantitatively with that of the benchmark Optimal Basis Set (OBS) method. Without assuming orthogonality or independence of the BCG and EEG subspaces, as in conventional methods, our approach learns the bases faithfully from BCG-only and EEG-only signals acquired from our new experimental setup. Specifically, to promote subspace separability, a paired set of low-dimensional and semi-orthogonal (BCG, EEG) basis representations is obtained by minimizing a cost function consisting of group sparsity penalties for automatic dimension selection and an energy term for encouraging incoherence. Reconstruction is subsequently obtained by fitting the contaminated data to a generative model using the learned bases subject to regularization. In the challenging non-event-related EEG studies, our DRJIB method outperforms the OBS method by nearly 12-fold in separating and preserving the continuous BCG and EEG signals.