Fast recovery of non-negative sparse signals under heterogeneous noise

In this paper we consider recovering non-negative sparse signals under heterogeneous noise from a Bayesian inference perspective. To induce sparsity and non-negativity simultaneously, we assign a rectified Gaussian scale mixture prior to the signal of interest. With such a prior, the signal posterior is analytically intractable. To handle this, we employ an approximate approach to simplify the inference process and obtain the marginal posteriors approximately. Moreover, to reduce the high computational cost, we use a conjugate gradient based scheme to implement the above process. Based on these efforts, we develop a novel recovery algorithm for the problem of interest. Results of numerical experiments demonstrate that the algorithm can achieve high recovery accuracy as well as low computational cost.