Gaussian mixture Markov random field for image denoising and reconstruction

Markov random fields (MRFs) have been widely used as prior models in various inverse problems such as tomographic reconstruction. While MRFs provide a simple and often effective way to model the spatial dependencies in images, they suffer from the fact that parameter estimate is difficult. In practice, this means that MRFs typically have very simple structure that cannot completely capture the subtle characteristics of complex images. In this paper, we present a novel Gaussian mixture Markov random field model (GM-MRF) that can be used as a very expressive prior model for inverse problems such as denoising and reconstruction. This method forms a global image model by merging together individual Gaussian-mixture models for image patches. Moreover, we present a novel analytical framework for computing MAP estimates with the GM-MRF prior model through the construction of exact surrogate functions that result in a sequence of quadratic optimizations. We demonstrate the value of the approach with some simple applications to denoising of dual-energy CT images.