UNSUPERVISED DECONVOLUTION OF SPARSE SPIKE TRAINS USING STOCHASTIC-APPROXIMATION

This paper presents an unsupervised method for restoration of sparse s pike trains, These signals are modeled as random Bernoulli-Gaussian pr ocesses, and their unsupervised restoration requires (i) estimation of the hyperparameters that control the stochastic models of the input a nd noise signals and (ii) deconvolution of the pulse process, Classica lly, the problem is solved iteratively using a maximum generalized lik elihood approach despite questionable statistical properties, The cont ribution of the article is threefold, First, we present a new ''core a lgorithm'' for supervised deconvolution of spike trains, which exhibit s enhanced numerical efficiency and reduced memory requirements, Secon d, we propose an original implementation of a hyperparameter estimatio n procedure that is based upon a stochastic version of the expectation -maximization (EM) algorithm. This procedure utilizes the same core al gorithm as the supervised deconvolution method, Third, Monte Carlo sim ulations show that the proposed unsupervised restoration method exhibi ts satisfactory theoretical and practical behaviors and that, in addit ion, good global numerical efficiency is achieved.