Fast Bayesian Restoration of Poisson Corrupted Images with INLA
This work addresses the challenge of efficient image restoration in fields like medical imaging, where Poisson noise is common, offering a faster alternative to established methods.
The authors tackled the problem of restoring photon-limited images corrupted by Poisson noise, which is intractable compared to Gaussian noise, by proposing a Bayesian restoration method using Integrated Nested Laplace Approximation (INLA). Their method achieves significantly faster performance than existing approaches like loopy belief propagation and Markov chain Monte Carlo, without compromising accuracy.
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.