Bayesian Image Restoration for Poisson Corrupted Image using a Latent Variational Method with Gaussian MRF

TL;DR

This paper presents a Bayesian image restoration method for Poisson noise using a latent variational approach with Gaussian MRF priors, employing EM and LBP for parameter inference, and demonstrates its effectiveness through simulations.

Contribution

It introduces a novel latent variable variational method for Poisson noise image restoration within a Bayesian framework, combining Gaussian MRF priors and EM-based inference.

Findings

The proposed algorithm effectively restores images corrupted by Poisson noise.

The method outperforms existing image restoration frameworks in simulations.

Abstract

We treat an image restoration problem with a Poisson noise chan- nel using a Bayesian framework. The Poisson randomness might be appeared in observation of low contrast object in the field of imaging. The noise observation is often hard to treat in a theo- retical analysis. In our formulation, we interpret the observation through the Poisson noise channel as a likelihood, and evaluate the bound of it with a Gaussian function using a latent variable method. We then introduce a Gaussian Markov random field (GMRF) as the prior for the Bayesian approach, and derive the posterior as a Gaussian distribution. The latent parameters in the likelihood and the hyperparameter in the GMRF prior could be treated as hid- den parameters, so that, we propose an algorithm to infer them in the expectation maximization (EM) framework using loopy belief propagation(LBP). We confirm the ability of our algorithm in the computer simulation, and compare it with the results of other im- age restoration frameworks.