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

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.