# A Variational Bayesian Approach for Image Restoration. Application to Image Deblurring with Poisson-Gaussian Noise

arXiv: https://arxiv.org/abs/1610.07519 · HTML: https://mlsanity.com/paper/1610.07519/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Oct 2016.

## Built on by (most cited first, 6 of 6)

- [Monte Carlo guided Diffusion for Bayesian linear inverse problems](https://mlsanity.com/paper/2308.07983/) (2023)
- [Unrolled Variational Bayesian Algorithm for Image Blind Deconvolution](https://mlsanity.com/paper/2110.07202/) (2021)
- [Adaptive importance sampling for heavy-tailed distributions via α-divergence minimization](https://mlsanity.com/paper/2310.16653/) (2023)
- [Self-supervised conformal prediction for uncertainty quantification in Poisson imaging problems](https://mlsanity.com/paper/2502.19194/) (2025)
- [Robust Filtering and Learning in State-Space Models: Skewness and Heavy Tails Via Asymmetric Laplace Distribution](https://mlsanity.com/paper/2507.22343/) (2025)
- [Adaptive regularization parameter selection for high-dimensional inverse problems: A Bayesian approach with Tucker low-rank constraints](https://mlsanity.com/paper/2603.16066/) (2026)

## Abstract (arXiv)

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.