分数阶微积分在图像处理中的研究综述*

综述了关于分数阶微积分理论在数字图像底层处理中的应用研究,具体包括:分数阶微积分和分数阶偏微分方程的基本理论及分数阶傅里叶变换的基本性质;分数阶微分滤波器的构造及在图像增强中的应用研究;分数阶积分滤波器的构造及在图像去噪中的应用研究;分数阶偏微分方程在图像去噪中的应用研究。最后,总结了分数阶微积分理论在图像处理中已取得的研究成果,并结合已有的基于分数阶微积分理论的图像底层处理模型,展望了分数阶微积分理论在图像处理中的应用前景。

Summary of research on image processing using fractional calculus

The main contents of this paper were about fractional calculus application in digital image low-level processing. Specifically included the following: fractional calculus and fractional-order partial differential equations and the basic properties of fractional Fourier transform; the structure of the fractional differential filter and its application to image enhancement; the structure of the fractional integration filter and its application to image denoising; the image denoising model based on fractional partial differential equations. Finally, summarized fractional calculus had been made research results and related problems in image processing. Associated with the image processing models, forecasted the applications prospect about fractional calculus applied to image processing.