A Partial Differential Equation Filter Combining a Second-Order Filter and a Fourth-Order Filter for Image Restoration

崔学英; 张权; 刘祎; 付学敬; 桂志国

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A Partial Differential Equation Filter Combining a Second-Order Filter and a Fourth-Order Filter for Image Restoration

更新时间：2026-09-14

- A Partial Differential Equation Filter Combining a Second-Order Filter and a Fourth-Order Filter for Image Restoration
- 用于图像复原的二阶与四阶结合的偏微分方程滤波
- Vol. 34, Issue 2, Pages: 183-187(2013)
- 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：
- DOI：
  CLC：
- Published：2013
- 稿件说明：
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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：

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.

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references

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