一种基于分数阶积分的数字图像去噪算法

针对现有图像去噪算法丢失图像纹理信息的问题,将基于Riemann-Liouville定义的分数阶积分应用于数字图像的噪声去除,提出8个方向上的图像任意阶积分掩模,给出运用该掩模进行图像去噪的数值运算方法及相应的算法实现电路模型.仿真实验结果在定性和定量的方面表明本文的算法对灰度图像和彩色图像同样适用,具有能够一次性完成积分,去噪精度高,同时能最大限度保持图像的纹理细节信息的特点.该算法特别适用于高精度的图像实时去噪.

A Digital Image Denoising Method Based on Fractional Calculus

In order to solve the problem of losing texture information in the existing image denoising algorithms, fractional calculus based on the definition of Riemann-Liouville is applied to image denoising. The structures and numerical calculation methods of the fractional integral masks on eight directions are given. Then, the corresponding circuit model is proposed. The qualitative analysis and quantitative analysis of the simulation experiments have proved that the method of this paper could be applied to both grayscale images and color images. And through the method, the fractional integral operation could be completed one off, the noises could be removed in high precision and the texture information of the images could be held on. The method could be used to image denoising in real time.