Applications of fractional partial differential equations in image processing

doi:10.11772/j.issn.1001-9081.2017.02.0546

Abstract

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

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

CLC Number:

TP911.73

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.

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.

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