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Reconstructing neural activities using non-invasive sensor arrays outside the brain is an ill-posed inverse problem since the observed sensor measurements could result from an infinite number of possible neuronal sources. The sensor covariance-based beamformer mapping represents one of popular and simple solutions to the above problem. We propose a family of beamformers by using covariance thresholding. A general theory is developed on how their spatial and temporal dimensions determine their performance. Conditions are provided for the convergence rate of the associated beamformer estimation. The implications of the theory are illustrated by simulation and a real data analysis.
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