基于高斯马尔可夫随机场的MAP估计在高斯噪声滤波中的应用

提出了基于高斯马尔可夫随机场(GMRF)的最大后验概率(MAP)估计在图像高斯噪声滤波中的应用方法。根据高斯噪声的先验特点，建立基于高斯马尔可夫随机场的退化图像恢复模型，从而将图像高斯噪声滤波问题转化为求解最大后验概率问题。先验概率可以根据马尔可夫随机场(MRF)和吉布斯分布(GD)的等效性, 用GD的概率估计。为了求解最大后验概率，第一，通过期望最大化(EM）算法对GMRF模型进行参数估计。第二，用共轭梯度法将目标函数最小化。实验结果表明，与其他滤波器（如高斯滤波、维纳滤波等）相比，本文所阐述的方法在滤除高斯噪声、保持图像原有结构方面效果更好。

Application of MAP estimation based on Gaussian Markov random field in gaussian noise filter

The application of a Gaussian Markov Random Fields (GMRF) based Maximum A Posteriori Probability (MAP) estimation for image Gaussian noise filter was presented. According to the characteristics of the Gaussian noise, the restoration model of the degenerated image based on GMRF was built, and then the problem of image Gaussian noise filter was transformed to MAP estimation. The prior probability can be estimated by using the equivalence of the Markov random fields and the Gibbs Distribution (GD). In order to get the MAP estimation, first, the GMRF parameters were estimated by means of the Expectation-Maximization (EM) algorithm. Second, objective function was minimized with conjugate gradient technique. The experimental results demonstrate that the proposed method outperforms other filters (the Gaussian filter, the Wiener filter, etc.) in suppressing Gaussian noise and maintaining the original composition of images.