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In this paper the problem of restoration of non-negative sparse signals isaddressed in the Bayesian framework. We introduce a new probabilistichierarchical prior, based on the Generalized Hyperbolic (GH) distribution,which explicitly accounts for sparsity. This new prior allows on the one hand,to take into account the non-negativity. And on the other hand, thanks to thedecomposition of GH distributions as continuous Gaussian mean-variance mixture,allows us to propose a partially collapsed Gibbs sampler (PCGS), which is shownto be more efficient in terms of convergence time than the classical Gibbssampler.

A Partially Collapsed Sampler for Unsupervised Nonnegative Spike Train Restoration