# Fast Bayesian Restoration of Poisson Corrupted Images with INLA

## TL;DR

This paper introduces a fast Bayesian image restoration technique for Poisson noise using INLA, significantly improving computational speed while maintaining accuracy, especially for images modeled as ICAR.

## Contribution

The paper presents a novel application of INLA for Poisson noise removal in images, offering faster computation compared to existing methods like MCMC and belief propagation.

## Key findings

- INLA-based method is faster than MCMC and belief propagation.
- The approach maintains high accuracy in restoring Poisson-corrupted images.
- Effective for images modeled as ICAR.

## Abstract

Photon-limited images are often seen in fields such as medical imaging. Although the number of collected photons on an image sensor statistically follows Poisson distribution, this type of noise is intractable, unlike Gaussian noise. In this study, we propose a Bayesian restoration method of Poisson corrupted image using Integrated Nested Laplace Approximation (INLA), which is a computational method to evaluate marginalized posterior distributions of latent Gaussian models (LGMs). When the original image can be regarded as ICAR (intrinsic conditional auto-regressive) model reasonably, our method performs very faster than well-known ones such as loopy belief propagation-based method and Markov chain Monte Carlo (MCMC) without decreasing the accuracy.