Linear-Time Algorithm in Bayesian Image Denoising based on Gaussian Markov Random Field

Bayesian image processing [1] based on a probabilistic graphical model has a long and rich history [2]. In Bayesian image processing, one constructs a posterior distribution and then infers restored images based on the posterior distribution. The posterior distribution is derived from a prior distribution that captures the statistical properties of the images. One of the major challenges of Bayesian image processing is the construction of an effective prior for the images. For this purpose, a Gaussian Markov random field (GMRF) model (or Gaussian graphical model) is a possible choice.