  In this paper, a methodology is investigated for signal recovery in the
presence of non-Gaussian noise. In contrast with regularized minimization
approaches often adopted in the literature, in our algorithm the regularization
parameter is reliably estimated from the observations. As the posterior density
of the unknown parameters is analytically intractable, the estimation problem
is derived in a variational Bayesian framework where the goal is to provide a
good approximation to the posterior distribution in order to compute posterior
mean estimates. Moreover, a majorization technique is employed to circumvent
the difficulties raised by the intricate forms of the non-Gaussian likelihood
and of the prior density. We demonstrate the potential of the proposed approach
through comparisons with state-of-the-art techniques that are specifically
tailored to signal recovery in the presence of mixed Poisson-Gaussian noise.
Results show that the proposed approach is efficient and achieves performance
comparable with other methods where the regularization parameter is manually
tuned from the ground truth.
