基于马尔可夫随机场的图像去噪复原方法  

An Image Restoration Method Based on Markov Random Field

作　　者：张川[1] 赵蓝飞[2] ZHANG Chuan;ZHAO Lan-fei(Luoyang Institute of Electro-Optical Equipment, AVIC, Luoyang 471000, China;The Higher Educational Key Laboratory for Measuring ＆ Control Technology and Instrumentations of Heilongjiang Province, Harbin University of Science and Technology, Harbin 150080, China)

机构地区：[1]中国航空工业集团公司洛阳电光设备研究所,河南洛阳471000 [2]哈尔滨理工大学测控技术与仪器黑龙江省高校重点实验室,哈尔滨150080

出　　处：《电光与控制》2018年第7期96-100,共5页Electronics Optics & Control

摘　　要：由于样本空间的多样性,势函数模型难以计算,因此无法得到马尔可夫随机场模型的参数估计。针对该问题,提出基于麦克劳林级数的马尔可夫随机场参数估计算法。通过二阶麦克劳林级数的展开式得到了势函数的近似值和似然函数的表示式,推导出极大似然估计对应的非线性方程组,通过牛顿迭代法得到方程组的解即是马尔可夫随机场的极大似然估计。提出了一种改进的Gibbs采样方法,加快了模拟退火的速度。实验分别从视觉效果、峰值信噪比和稳态迭代次数三方面验证了算法的有效性。Due to the diversity of sample space,it is difficult to calculate the model of the potential function,and therefore difficult to obtain the parameter estimation of Markov random field model. To solve the problem,a parameter estimation algorithm for Markov random field is presented based on Maclaurin series. This algorithm employs a second-order expansion of Maclaurin series to derive the approximate expressions of the potential function and the likelihood function. The system of nonlinear equations corresponding to the Maximum Likelihood Estimation（ MLE） is derived,which is calculated by Newton iteration method,and its solution is the MLE for Markov random field. An updated approach is presented and used to calculate the optimal observed value of the degradation model for noisy images based on Gibbs sampling for accelerating the simulation annealing. Tests have verified the effectiveness of the algorithm from three aspects of visual effect,peak signal to noise ratio,and iteration times.

关 键 词：图像去噪 马尔可夫随机场 麦克劳林级数 极大似然估计 GIBBS采样 

分 类 号：V271.4[航空宇航科学与技术—飞行器设计] TP391.41[自动化与计算机技术—计算机应用技术]