This work considers the problem of brain imaging using simultaneously recorded electroencephalography (EEG) and functional magnetic resonance imaging (fMRI). To this end, we introduce a linear coupling model that links the electrical EEG signal to the hemodynamic response from the blood-oxygen level dependent (BOLD) signal. Both modalities are then symmetrically integrated, to achieve a high resolution in time and space while allowing some robustness against potential decoupling of the BOLD effect. The novelty of the approach consists in expressing the joint imaging problem as a linear inverse problem, which is addressed using sparse regularization. We consider several sparsity-enforcing penalties, which naturally reflect the fact that only few areas of the brain are activated at a certain time, and allow for a fast optimization through proximal algorithms. The significance of the method and the effectiveness of the algorithms are demonstrated through numerical investigations on a spherical head model.