Transient brain oscillatory activities recorded with Eelectroencephalography (EEG) or magnetoencephalography (MEG) are characteristic features in physiological and pathological processes. This study is aimed at describing, evaluating, and illustrating with clinical data a new method for localizing the sources of oscillatory cortical activity recorded by MEG. The method combines time-frequency representation and an entropic regularization technique in a common framework, assuming that brain activity is sparse in time and space. Spatial sparsity relies on the assumption that brain activity is organized among cortical parcels. Sparsity in time is achieved by transposing the inverse problem in the wavelet representation, for both data and sources. We propose an estimator of the wavelet coefficients of the sources based on the maximum entropy on the mean (MEM) principle. The full dynamics of the sources is obtained from the inverse wavelet transform, and principal component analysis of the reconstructed time courses is applied to extract oscillatory components. This methodology is evaluated using realistic simulations of single-trial signals, combining fast and sudden discharges (spike) along with bursts of oscillating activity. The method is finally illustrated with a clinical application using MEG data acquired on a patient with a right orbitofrontal epilepsy.