A Gaussian Mixture MRF for Model-Based Iterative Reconstruction with Applications to Low-Dose X-ray CT

摘要

Markov random fields (MRFs) have been widely used as prior models in variousinverse problems such as tomographic reconstruction. While MRFs provide asimple and often effective way to model the spatial dependencies in images,they suffer from the fact that parameter estimation is difficult. In practice,this means that MRFs typically have very simple structure that cannotcompletely 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 problemssuch as denoising and reconstruction. The GM-MRF forms a global image model bymerging together individual Gaussian-mixture models (GMMs) for image patches.In addition, we present a novel analytical framework for computing MAPestimates using the GM-MRF prior model through the construction of surrogatefunctions that result in a sequence of quadratic optimizations. We alsointroduce a simple but effective method to adjust the GM-MRF so as to controlthe sharpness in low- and high-contrast regions of the reconstructionseparately. We demonstrate the value of the model with experiments includingimage denoising and low-dose CT reconstruction.