对时间的分数阶扩散方程在图像恢复中的应用  

Application of time fractional diffusion equation to image restoration

作　　者：张文娟[1,2] 王艳红[1] 

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

出　　处：《陕西理工学院学报（自然科学版）》2009年第2期45-48,共4页Journal of Shananxi University of Technology:Natural Science Edition

摘　　要：提出了一种包含对时间的分数阶导数的非线性扩散方程,它是对Perona-Malik的非线性扩散方程和Cuesta提出的方程的推广,介于非线性抛物方程和非线性双曲方程之间,从而能有效地控制扩散过程,使得在去除图像噪声的同时能够尽可能地保留图像的边缘等细节信息。数值试验结果显示,该方程比Perona-Malik的非线性扩散方程有更好的去噪效果。In this paper a nonlinear diffusion equation containing time fractional derivative is proposed.It is a generalization of the nonlinear diffusion equation proposed by Perona-Malik and the method presented by Cuesta,and interpolates between the nonlinear parabolic equation and the nonlinear hyperbolic equation,thus can effectively control the diffusion process so that noises can be removed and details of the image such as edges can be preserved as much as possible simultaneously.Experiment results show this equation has better denoising result than the nonlinear diffusion equation proposed by Perona-Malik.

关 键 词：分数阶导数(积分) 非线性分数阶扩散方程 图象恢复 去噪 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]