Unsupervised deconvolution of sparse spike trains using stochastic approximation

This paper presents an unsupervised method for restoration of sparse spike trains. These signals are modeled as random Bernoulli-Gaussian processes, and their unsupervised restoration requires (i) estimation of the hyperparameters that control the stochastic models of the input and noise signals and (ii) deconvolution of the pulse process. Classically, the problem is solved iteratively using a maximum generalized likelihood approach despite questionable statistical properties. The contribution of the article is threefold. First, we present a new "core algorithm" for supervised deconvolution of spike trains, which exhibits enhanced numerical efficiency and reduced memory requirements. Second, we propose an original implementation of a hyperparameter estimation procedure that is based upon a stochastic version of the expectation-maximization (EM) algorithm. This procedure utilizes the same core algorithm as the supervised deconvolution method. Third, Monte Carlo simulations show that the proposed unsupervised restoration method exhibits satisfactory theoretical and practical behavior and that, in addition, good global numerical efficiency is achieved.