  In this paper the problem of restoration of non-negative sparse signals is
addressed in the Bayesian framework. We introduce a new probabilistic
hierarchical 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 the
decomposition of GH distributions as continuous Gaussian mean-variance mixture,
allows us to propose a partially collapsed Gibbs sampler (PCGS), which is shown
to be more efficient in terms of convergence time than the classical Gibbs
sampler.
