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We present a novel approach to the spatio-temporal decomposition of evoked brain responses in magnetoencephalography (MEG) aiming at a sparse representation of the underlying brain activity in terms of spatio-temporal atoms. Our approach is characterized by three attributes which constitute significant improvements with respect to existing approaches: (1) the spatial and temporal decomposition is addressed simultaneously rather than sequentially, with the benefit that source loci and corresponding waveforms can be unequivocally allocated to each other, and, hence, allow a plausible physiological interpretation of the parametrized data; (2) it is free from severe a priori assumptions about the solution space; (3) it comprises an optimization technique for the use of very large spatial and temporal subdirectories to greatly reduce the otherwise enormous computational cost by making use of the Cauchy-Schwarz inequality. We demonstrate the efficiency of the approach with simulations and real MEG data obtained from a subject exposed to a simple auditory stimulus.

Simultaneous spatio-temporal matching pursuit decomposition of evoked brain responses in MEG