用于图像复原的二阶与四阶结合的偏微分方程滤波

崔学英; 张权; 刘祎; 付学敬; 桂志国

您当前的位置：

首页 >

文章列表页 >

用于图像复原的二阶与四阶结合的偏微分方程滤波

电子与电子信息 | 更新时间：2026-09-14

- 用于图像复原的二阶与四阶结合的偏微分方程滤波
- A Partial Differential Equation Filter Combining a Second-Order Filter and a Fourth-Order Filter for Image Restoration
- 中北大学学报（自然科学版） 2013年34卷第2期页码：183-187
- 作者机构：
  
  1. 中北大学电子测试技术国防重点实验室
  2. 太原科技大学应用科学学院
  3. 上海长安信息技术咨询开发中心
- 作者简介：
- 基金信息：
  
  国家自然科学基金资助项目(61071192,61271357);山西省自然科学基金资助项目(2009011020-2);山西省高等学校优秀青年学术带头人支持计划资助项目;太原科技大学青年基金资助项目(20113019)
- DOI：
  中图分类号：
- 纸质出版：2013
- 稿件说明：
移动端阅览
崔学英, 张权, 刘祎, 等. 用于图像复原的二阶与四阶结合的偏微分方程滤波[J]. 中北大学学报（自然科学版）, 2013,34(2):183-187.

崔学英, 张权, 刘祎, et al. A Partial Differential Equation Filter Combining a Second-Order Filter and a Fourth-Order Filter for Image Restoration[J]. 2013, 34(2): 183-187.
崔学英, 张权, 刘祎, 等. 用于图像复原的二阶与四阶结合的偏微分方程滤波[J]. 中北大学学报（自然科学版）, 2013,34(2):183-187. DOI：

崔学英, 张权, 刘祎, et al. A Partial Differential Equation Filter Combining a Second-Order Filter and a Fourth-Order Filter for Image Restoration[J]. 2013, 34(2): 183-187. DOI：

摘要

针对目前现有的用于图像复原的二阶偏微分方程滤波和四阶偏微分方程滤波的不足之处

提出了一个二阶偏微分方程滤波和四阶偏微分方程滤波相结合的非线性滤波.该滤波充分利用了二阶滤波保持边缘和四阶滤波在平滑区域去除阶梯效应的优点

能够在恢复的图像中保持边缘和避免阶梯效应.数值实现结果表明:该模型的去噪效果好

而且还具有较快的收敛速度.将实验结果与其他二阶和四阶模型相比

恢复的图像质量较高

体现了该模型在图像复原上的有效性.

Abstract

Aimed at the shortcomings of the existing second-order partial differential equation(PDE) filters and fourth-order PDE filters

a nonlinear PDE filter that combined a second-order PDE filter with a fourth-order PDE filter was proposed.The combined filter took the advantage of both filters since it was able to preserve edges while avoiding the staircase effect in smooth regions.Numerical experimental results show that the proposed filter denoising effect is ideal and could provide a significantly fast convergence rate.The proposed method provides a denoised image with higher quality in comparison with that of the existing methods and demonstrates the effectiveness of the proposed method in image restoration.

关键词

Keywords

references

Perona P,Malik J.Scale-space and edge detectionusing anisotropic diffusion[J].IEEE Trans.onPattern Anal.Machine Intell.,1990,12(7):629-639.

Catte F,Lions P L,Morel J M,et al.Image selectivesmoothing and edge detection by nonlinear diffusion[J].SIAM.J.Num.Anal.,1992,29(1):182-193.

Chao S M,Tsai D M.An improved anisotropicdiffusion model for detail and edge preservingsmoothing[J].Pattern Recognition Letters,2010,31:2012-2023.

Rudin L,Osher S,Fatema E.Nonlinear totalvariation based noise removal algorithms[J].Physica D,1992,60:259-268.

Marquina A,Osher S.Explicit algorithm for a newtime dependent model based on level set motion fornonlinear deblurring and noise removal[J].SIAM J.Sci.Comput.,2000,22:387-405.

Lysaker M,Lundervold A,Tai X C.Noise removalusing fourth-order partial differential equation withapplications to medical magnetic resonance images inspace and time[J].IEEE Transactions on ImageProcessing,2003,12(12):1579-1590.

Liu Xinwu,Huang Lihong,Guo Zhenyuan.Adaptivefourth-order pattial differential equation filter forimage denoising[J].Applied Mathematics Letters,2011,24:1282-1288.

You Y L,Kaveh M.Fourth-order partial differentialequations for noise removal[J].IEEE Transactions onImage Processing,2000,9(10):1723-1730.

Hajiaboli M R.A self-governing hybrid model fornoise removal[J].Lecture Notes in ComputerScience,2009,5414:295-305.

Li Fang,Shen Chaomin,Fan Jingsong,et al.Imagerestoration combing a total variational filter and afourth-order filter[J].J.Vis.Commun.Image R.,2007,18:322-330.

Chen Qiang,Montesinos P,Sun Quansen,et al.Adaptive total variation denoising based ondifference curvature[J].Image and VisionComputing,2010,28:298-306.

Kim S,Lim H.Fourth-order partial differentialequation for effective image denoising[J].ElectronJ.Differ.Equ.Conf.,2009,17:107-121.

Wunerli T.A partial regularity result for ananisotropic smoothing functional for imagerestoration in BV space[J].J.Math.Anal.Appl.,2008,339:1169-1178.

Liu Zhaoxia,Guo Boling.New numerical algorithmsfor the nonlinear diffusion model of image denoisingand segmentation[J].Applied Mathematics andComputation,2006,178:380-389.

浏览量

161

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

基于CEEMDAN和改进小波模极大值的高低频混合信号去噪算法

一类偏微分方程的解的Bernstein性质

一种改进的基于偏微分方程图像的降噪算法

脉冲作用下Holling-Ⅳ型捕食系统的研究

复模糊值函数级数的收敛及其推论