基于偏微分方程的变分去噪模型  

Improved variational model to remove multiplicative noise based on partial differential equation

作　　者：胡学刚[1,2] 张龙涛[1] 蒋伟[3] 

机构地区：[1]重庆邮电大学计算机科学与技术学院,重庆400065 [2]重庆邮电大学系统理论及应用研究中心,重庆400065 [3]重庆交通大学理学院,重庆400074

出　　处：《计算机应用》2012年第7期1879-1881,1901,共4页journal of Computer Applications

基　　金：国家自然科学基金资助项目(11071266);重庆市教委科研基金资助项目(KJ100505)

摘　　要：针对现有去除图像乘性噪声的变分模型的保真项中存在病态条件的问题,结合全变分方法和对数变换的相关理论对保真项进行分析,提出一种新的基于偏微分方程(PDE)的去除图像乘性噪声的变分模型,导出了该模型对应的偏微分方程初边值问题,并给出了相应的数值计算方法。从数值实验结果可以看出,所提模型的均方误差(MSE)明显下降,峰值信噪比(PSNR)明显提升,同时很好地避免了模型的病态情形,对去除图像乘性噪声的变分模型中保真项存在的病态条件提供了很好的解决办法,减小了离散化过程中可能存在的误差。数值实验结果表明,所提模型具有良好的去噪效果,能够较好地抑制图像中的"阶梯效应"现象。In this paper,a new variational model based on Partial Differential Equation（PDE） was proposed to solve the ill-posed problems in the data-fidelity item of the existing key variational approaches to remove multiplicative noise with the theories of total variation and logarithmic transformation.The initial boundary value problem of the PDE associated with the new variational problem was derived and discreted numerically.The numerical experimental results show that the values of Mean Square Error（MSE） are decreased and Peak Signal to Noise Ratio（PSNR） are increased obviously.The ill-posed problem in the data-fidelity item is avoided well at the same time.It makes a good method to solve this problem,and avoids the errors which may appear in the discretization process.The quality of the images restored by the proposed method is not only more favorable,but the new model also eliminates the ＂step-casing effect＂.

关 键 词：变分方法 偏微分方程 图像去噪 保真项 乘性噪声 

分 类 号：TP391[自动化与计算机技术—计算机应用技术] TN911[自动化与计算机技术—计算机科学与技术]