A Markov Random Field Model for Medical Image Denoising

In this paper, we model the image prior using Markov random field. It is difficult to model image priors directly on the intensity value of each pixel, as the relationships between intensity values of pixels are extremely complicated. Instead, we model the probability by how likely we observe the filter responses. The filters of size 5times5 are learned from PCA on 5times5 patches. The distributions of filter responses are modeled by double exponential distributions with parameters obtained also from PCA. Based on this prior model, the denoising algorithm is carried out on the basis of Bayesian Analysis. The clean image is the most likely image given the observation and the previous knowledge (prior). We perform the gradient ascent method on the logarithm of the posterior probability to find the most likely image. We apply this denoising algorithm on fMRI images and ultrasound images and have very good denoising results.