Maximum Likelihood Hyperparameter Estimation for solvable Markov Random Field Model in Image Restoration

摘要

We propose a new solvable Markov random field model for Bayesian image processing and give the exact expres- sions of the marginal likelihood and the restored image by using the multi-dimensional Gaussian formula and the discrete Fourier transform. The proposed Markov random field model includes the conditional autoregressive model and the simultaneous au- to regressive model as a special case. The estimates off hyper- parameters are obtained by maximizing the marginal likelihood. We study some statistical properties of the solvable markov ran- Dom field model.