Data Denoise with Partial Differential Equation Method

数据降噪的偏微分方程方法

余昕(Xin Yu) ； 田东风(Dong-Feng Tian) ； 田田(Tian Tian)

《Journal of Data Analysis》 4卷5期 (2009/10) Pp. 213-222

https://doi.org/10.6338/JDA.200910_4(5).0009

摘要

本文利用新定义的边界检测算子，改进了基于偏微分方程方法的数据降噪的Alvarez模型。作者利用有限差分法，给出了本文模型的数值实现算法，并针对带噪图像数据进行了降噪的对比数值实验。实验结果表明，本文方法在不降低去噪效果的同时能更好地保持图像边界等重要特征。

關鍵字

数据降噪 ； 偏微分方程 ； 锐度算子 ； 有限差分法

並列摘要

Firstly, a new edge operator is proposed in defining the boundary of a 2-dimensional domain. Comparing this operator with others in some known denoising models shows that the boundary operator established in this paper is more efficient than the preceeding ones in detecting the edge of the domain. Secondly, based on the new edge operator and a new designed edge-stopping function, we improve the Alvarez equation and establish a new nonlinear isotropic diffusion image-denoising equation and we prove that the problems can be dealt with more efficiently with the newly established model than with others. Finally, the emulating numerical result obtained in this paper with the newly established model shows that the new model is indeed better than those gotten with the previous ones.

並列關鍵字

Denoising Models

參考文獻

Wang, Dakai、Hou, Yuqing、Peng, Jinye(2008)。The Partial Differential Equation Method in Image Processing。Beijing:Science Press。

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Zhang, dan、Chen, Gang(2004)。The Image Processing Based on Partial Differential Equation。Beijing:Higher Education Press。

Fang, Shaomei、Zhong, penghong(2008)。A hybrid method of partial differential equations and region homogeneity measure for image edge detection。Journal of Foshan University。26(1)

Alvarez, L, Lions, P. L.,Morel, J. M.(1992).Image selective Image selective smoothing and edge detection by nonlinear diffusion II.SLAM J Num Anal.29(3),845-866.