分数阶偏微分方程在图像处理中的应用

doi:10.11772/j.issn.1001-9081.2017.02.0546

计算机应用 ›› 2017, Vol. 37 ›› Issue (2): 546-552.DOI: 10.11772/j.issn.1001-9081.2017.02.0546

• 计算机视觉与虚拟现实 • 上一篇下一篇

分数阶偏微分方程在图像处理中的应用

周尚波¹, 王李平¹, 尹学辉²

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

收稿日期:2016-08-17 修回日期:2016-09-26 发布日期:2017-02-11 出版日期:2017-02-10
通讯作者: 周尚波,shbzhou@cqu.edu.cn
作者简介:周尚波(1963-),男,广西宁明人,教授,博士生导师,博士,主要研究方向:视频与图像处理、人工神经网络、非线性动力学;王李平(1981-),男,河南新乡人,博士研究生,主要研究方向:分数阶偏微分方程、非线性动力学、模式识别、图像重构;尹学辉(1986-),男,四川广安人,讲师,博士,主要研究方向:分数阶微积分在图像中的应用、非线性动力学。
基金资助:
重庆市基础科学与前沿技术研究（重点）项目（cstc2015jcyjBX0124）。

Applications of fractional partial differential equations in image processing

ZHOU Shangbo¹, WANG Liping¹, YIN Xuehui²

1. College of Computer Science, Chongqing University, Chongqing 400030, China;
2. School of Software Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

Received:2016-08-17 Revised:2016-09-26 Online:2017-02-11 Published:2017-02-10
Supported by:
This work is partially supported by the Major Project of Fundamental Science and Frontier Technology Research of Chongqing CSTC (cstc2015jcyjBX0124).

摘要/Abstract

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。

关键词: 分数阶偏微分方程, 图像去噪, 超分辨率图像重建

Abstract: 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.

Key words: fractional partial differential equation, image denoising, super-resolution image reconstruction

中图分类号:

TP911.73

周尚波, 王李平, 尹学辉. 分数阶偏微分方程在图像处理中的应用[J]. 计算机应用, 2017, 37(2): 546-552.

ZHOU Shangbo, WANG Liping, YIN Xuehui. Applications of fractional partial differential equations in image processing[J]. Journal of Computer Applications, 2017, 37(2): 546-552.

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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

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