运用拓扑优化和分数阶扩散的图像去噪方法  

Image Denoising Based on Topological Optimization and Fractional Diffusion

作　　者：张文娟[1,2] 王艳红[1] 

机构地区：[1]西安工业大学理学院,西安710032 [2]西安电子科技大学理学院,西安710071

出　　处：《西安工业大学学报》2012年第1期31-34,共4页Journal of Xi’an Technological University

基　　金：国家自然科学基金(60872138);西安工业大学校长基金(XAGDXJJ-0931)

摘　　要：针对目前经典的图像去噪方法去掉图像噪声的同时使边缘变得模糊这一局限性,提出了一种利用拓扑导数和分数阶扩散的图像去噪方法.基于拓扑优化的思想,以拓扑导数为指标,提取边缘点,并在边缘点处选取最优的各向异性扩散系数.利用对时间的分数阶扩散方程对图像扩散.本文确定扩散系数的方法具有全局性的特征.数值实验证明,算法能有效地去除图像中的噪声,并能很好地保留图像的边缘等细节信息.因此将分数阶扩散方法与拓扑优化思想相结合能获得很好的图像去噪效果.Edges of image will blur when the classical denoising method is used to remove noise. In order to solve this problem, a denoising method based on topological optimization and fractional diffusion is proposed. Topological derivative is taken as an indicator to pick up the edge points, on which the most optimal anisotropic diffusion coefficients are chosen. Then the original image is processed using the fractional diffusion equation. The method for choosing diffusion coefficients has the global property. Numerical experiments show that the new method can effectively remove noise and preserve such details as edges. So by combining the fractional diffusion method and topological optimization, a better denoising effect can be obtained.

关 键 词：图像去噪 热方程 波方程 分数阶扩散 拓扑导数 信噪比 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]