基于偏微分方程与多尺度分析的图像去噪算法  

Image Denoising Algorithm Based on Partial Differential Equation and Multi-scale Analysis

作　　者：郭林[1] 孟旭东[1] GUO Lin;MENG Xudong(Department of Mathematics,Science and Technology College of NCHU,Nanchang330034,China)

机构地区：[1]南昌航空大学科技学院数学系

出　　处：《吉林大学学报（理学版）》2019年第4期882-888,共7页Journal of Jilin University:Science Edition

基　　金：江西省教育厅科学技术研究项目(批准号:GJJ171520)

摘　　要：针对传统图像去噪算法存在去噪效果和稳定性较差的问题,提出一种基于偏微分方程结合多尺度分析方法的图像去噪算法.首先利用二阶偏微分扩散方程和四阶偏微分方程对图像进行高频段和低频段的处理,对处理后的图像采用非下采样轮廓波逆变换,实现图像整体去噪;其次,采用轮廓波变换方法对整体图像进行多尺度分解得到不同子带,并利用核主成分分析算法进行整体图像降维处理,对不同子带进行分块管理,完成对整体图像的局部去噪,最终实现基于偏微分方程结合多尺度分析方法的图像去噪.实验结果表明,该算法的图像去噪效果和稳定性均较高。Aiming at the problem that the traditional image denois ing algorithm had poor denoising effect and stability,we proposed an image deno ising algorithm based on partial differential equation combined with multi-scal e analysis method. Firstly,the high frequency and low frequency bands of the im age were processed by the second order partial differential diffusion equation a nd the fourth order partial differential equation,and the processed image was denoised as a whole by usin g the inverse transform of non-down sampling profile wave. Secondly,the contour wave transform method was used to decompose the whole image into dif ferent subbands, the kernel principal component analysis algorithm was used to reduce the dimension of the whole image,and the different subbands were mana ged by blocks to complete the local denoising of the whole image. Finally,the i mage denoising based on partial differential equation and multi-scale analysis method was realized. The experimental results show that the proposed algorithm h as high image denoising effect and stability.

关 键 词：微偏分方程 多尺度分析 图像去噪 轮廓波变换 核主成分分析 图像扩散 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]