Parameter estimation and restoration of noisy images using Gibbs distributions in hidden Markov models

A noisy image model is formulated by integrating the image and noise models into the hidden and observation layers of a hidden Markov model (HMM). The true image is modeled by a Markov random field (MRF), and the noise is a flip error that changes the gray level of image pixels according to a stochastic matrix. An algorithm for parameter estimation is developed on the basis of the reestimation formulation in HMM. At each iteration of the reestimation, the Gibbs distribution (GD) parameters are estimated using gradient ascent, and the noise parameter is estimated as the percentage of pixels in the unobserved image having the same gray levels as the observed image, where the percentage is the posterior expectation over all possible configurations of the unobserved image. Gibbs samplers are used to generate the samples of MRFs, and sample averages are taken to approximate the expectation terms. Images are restored using the minimum misclassification technique. Experiments on binary images contaminated by 20-30% noise showed good restoration results