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 estimation 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. The GM-MRF forms a global image model by merging together individual Gaussian-mixture models (GMMs) for image patches. In addition, we present a novel analytical framework for computing MAP estimates using the GM-MRF prior model through the construction of surrogate functions that result in a sequence of quadratic optimizations. We also introduce a simple but effective method to adjust the GM-MRF so as to control the sharpness in low- and high-contrast regions of the reconstruction separately. We demonstrate the value of the model with experiments including image denoising and low-dose CT reconstruction.

本文介绍了一种高效的先验模型——高斯混合Markov随机场模型(GM-MRF)，以及通过构建替代函数的新型分析框架，在低对比度和高对比度区域分别控制图像重建锐度的方法。实验证明了该模型在图像去噪和低剂量CT重建方面的价值。

基于高斯混合的MRF的模型迭代重建算法及其在低剂量X射线CT上的应用