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Recent dynamic source localization algorithms for the Magnetoencephalographic inverse problem use cortical spatio-temporal dynamics to enhance the quality of the estimation. However, these methods suffer from high computational complexity due to the large number of sources that must be estimated. In this work, we introduce a fast iterative greedy algorithm incorporating the class of subspace pursuit algorithms for sparse source localization. The algorithm employs a reduced order state-space model resulting in significant computational savings. Simulation studies on MEG source localization reveal substantial gains provided by the proposed method over the widely used minimum-norm estimate, in terms of localization accuracy, with a negligible increase in computational complexity.