A Partially Collapsed Sampler for Unsupervised Nonnegative Spike Train Restoration

TL;DR

This paper introduces a Bayesian method with a new hierarchical prior based on the Generalized Hyperbolic distribution for restoring non-negative sparse signals, utilizing a partially collapsed Gibbs sampler for improved efficiency.

Contribution

The paper proposes a novel hierarchical prior and a partially collapsed Gibbs sampler for more efficient Bayesian sparse signal restoration.

Findings

The new prior effectively models non-negativity and sparsity.

The partially collapsed Gibbs sampler converges faster than classical methods.

The approach improves computational efficiency in sparse signal recovery.

Abstract

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.