分数阶偏微分方程在图像处理中的应用  

Applications of fractional partial differential equations in image processing

作　　者：周尚波[1] 王李平[1] 尹学辉 ZHOU Shangbo WANG Liping YIN Xuehui(College of Computer Science, Chongqing University, Chongqing 400030, China School of Software Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China)

机构地区：[1]重庆大学计算机学院,重庆400030 [2]重庆邮电大学软件工程学院,重庆400065

出　　处：《计算机应用》2017年第2期546-552,共7页journal of Computer Applications

基　　金：重庆市基础科学与前沿技术研究(重点)项目(cstc2015jcyj BX0124)~~

摘　　要：分数阶偏微分方程在图像处理中的应用已受到了广泛的关注,尤其在图像去噪和图像超分辨率(SR)重建方面,目前的研究成果已显示了分数阶应用的优势与效果。对分数阶微积分在图像处理中的作用进行了分析;介绍并讨论了分数阶偏微分方程在图像去噪和图像超分辨率重建中的相关理论与模型;通过仿真实验表明,基于分数阶偏微分方程的方法在去噪和减少阶梯效应等方面比整数阶偏微分方程更具有优势;最后指出了未来的相关研究问题。It has been widely concerned to apply fractional partial differential equations in image processing, especially in the image denoising and image Super Resolution （SR） reconstruction. The current research results have shown the advantages and effects of fractional order applications. The theory and model of fractional partial differential equations in image denoising and image super-resolution reconstruction were introduced and discussed. The simulation results show that the methods based on fractional partial differential equations has more advantages than the methods based on integer order partial differential equations in terms of denoising and reducing the staircase effect. Finally, the related research problems were pointed out.

关 键 词：分数阶偏微分方程 图像去噪 超分辨率图像重建 

分 类 号：TP911.73[自动化与计算机技术]