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Iterative enhancement of event related potentials through sparsity constraints

In this paper we propose an iterative technique that enhances the average event related potential (ERP) by correcting the delay associated with the ERP in each trial. This correction is done in three steps: in the first step a sparse template function is estimated. In the second step, this template is utilized in estimating the inter-trial ERP delays. The ERPs fromeach trial are time-aligned using the estimated delays. In the third step, a new estimate of the ERP waveform is obtained by averaging these time-aligned signals over the trials. The algorithm iterates through these three steps until convergence. The sparse template is estimated in each iteration through the minimization of a convex objective function which compromises between the fit of the estimated ERP waveform to the template, and the sparsity of the estimated ERP waveform.