计算机应用 ›› 2012, Vol. 32 ›› Issue (07): 1879-1881.DOI: 10.3724/SP.J.1087.2012.01879

• 图形图像技术 • 上一篇    下一篇

基于偏微分方程的变分去噪模型

胡学刚1,2,张龙涛1,蒋伟3   

  1. 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
  • 收稿日期:2012-01-18 修回日期:2012-03-15 发布日期:2012-07-05 出版日期:2012-07-01
  • 通讯作者: 胡学刚
  • 作者简介:胡学刚(1965-),男,重庆人,教授,博士,主要研究方向:偏微分方程、数字图像处理;张龙涛(1988-),男,重庆人,硕士研究生,主要研究方向:数字图像处理;蒋伟(1982-),男,重庆人,讲师,硕士研究生,主要研究方向:偏微分方程、数字图像处理。
  • 基金资助:

    福建高校产学合作科技重大项目(2010H6007);重庆市教委科研基金资助项目(KJ100505)

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

HU Xue-gang1,2,ZHANG Long-tao1,JIANG Wei3   

  1. 1. College of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
    2. Research Center of System Theory and Application, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
    3. School of Science, Chongqing Jiaotong University, Chongqing 400074, China
  • Received:2012-01-18 Revised:2012-03-15 Online:2012-07-05 Published:2012-07-01
  • Contact: HU Xue-gang

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。

关键词: 变分方法, 偏微分方程, 图像去噪, 保真项, 乘性噪声

Abstract: 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”.

Key words: variation approach, Partial Differential Equation (PDE), image denoising, data-fidelity item, multiplicative noise

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