Relating measures of electroencephalography (EEG) back to the underlying sources is a long-standing inverse problem. Here we propose a new method to estimate the EEG sources of identified electrophysiological states that represent spontaneous activity, or are evoked by a stimulus, or caused by disease or disorder. Our method has the unique advantage of seamlessly integrating a statistical significance of the source estimate while efficiently eliminating artifacts (e.g., due to eye blinks, eye movements, bad electrodes). After determining the electrophysiological states in terms of stable topographies using established methods (e.g.: ICA, PCA, k-means, epoch average), we propose to estimate these states' time courses through spatial regression of a General Linear Model (GLM). These time courses are then used to find EEG sources that have a similar time-course (using temporal regression of a second GLM). We validate our method using both simulated and experimental data. Simulated data allows us to assess the difference between source maps obtained by the proposed method and those obtained by applying conventional source imaging of the state topographies. Moreover, we use data from 7 epileptic patients (9 distinct epileptic foci localized by intracranial EEG) and 2 healthy subjects performing an eyes-open/eyes-closed task to elicit activity in the alpha frequency range. Our results indicate that the proposed EEG source imaging method accurately localizes the sources for each of the electrical brain states. Furthermore, our method is particularly suited for estimating the sources of EEG resting states or otherwise weak spontaneous activity states, a problem not adequately solved before.