Déconvolution impulsionnelle par filtre de Hunt et seuillage

A new method of sparse spike train deconvolution is presented. It is based on the coupling of the Hunt filter with a thresholding (to obtain a sparse spike train signal). We show that a good model for the probability density function of the Hunt filter output is a Gaussian mixture, from which we derive the threshold that minimizes the probability of errors. Based on an interpretation of the method as a MAP estimator, the hyperparameters are estimated using a JMAP (joint MAP) approach. This method is applied successfully on partial discharge signals.