Unobtrusive mental state monitoring based on neurosphysiological signals has seen thriving developments over the past decade, with a wide area of applications, from rehabilitation to neuroergonomics and neuromarketing. Particularly, electroencephalography (EEG) and electrooculography (EOG) have been popular techniques to obtain cognitive-relevant biosignals. However, current wearable systems may still pose practical inconvenience, motivating further interest to integrate EOG+EEG recording into streamlined frontal-only sensor montages with sufficient signal fidelity. We propose, here, a spatial filtering approach to reliably extract EOG signals from a reduced set of frontal EEG electrodes, placed on non-hair-bearing (NHB) areas. Within a common signal analytic framework, two distinct schemes are examined. The one is based on standard linear least squares (LLS) and the other on Least Absolute Shrinkage and Selection Operator (LASSO). Both schemes are data-driven techniques, require a small amount of training data, and lead to reliable estimators of EOG activity from EEG signals. The LASSO-based technique, in addition, provides guidelines that generalize well across subjects. Using experimental data, we provide some empirical evidence that our estimators can replace the actual EOG signals in algorithmic pipelines that automatically detect oculographic events, like blinks and saccades.