变分分数阶PDE的自适应图像保边缘去噪方法  

Adaptive Image Edge Preserving Denoising Method based on Variational Fractional PDEs

作　　者：李晓明 徐国庆 杨苗苗 高雪梅 王德华[2] LI Xiaoming;XU Guoqing;YANG Miaomiao;GAO Xuemei;WANG Dehua(Xi’an Division of Surveying and Mapping,Xi’an 710054,China;School of Sciences,Xi’an Technological University,Xi’an 710021,China)

机构地区：[1]西安测绘总站,西安710054 [2]西安工业大学基础学院,西安710021

出　　处：《西安工业大学学报》2024年第4期525-531,共7页Journal of Xi’an Technological University

基　　金：教育部“春晖计划”合作研究项目(202200955);陕西省数理基础研究项目(23JSY044)。

摘　　要：为了优化图像去噪过程中的边缘保真问题,本文以ROF模型及其改进模型为基础,以分数阶变分偏微分方程方法为工具,通过构造自适应的边缘检测函数,提出了一种能更好地保护图像的边缘特征,有利于纹理细节保持和“阶梯效应”抑制的基于自适应分数阶变分PDE的图像去噪模型,并以标准图像测试了新模型的去噪效果。实验结果表明:与同类方法相比,新方法可以更加有效地提高图像的信噪比;从去噪前后的图像差可以看出,新方法在去噪的同时更好地保护了图像的边缘特征及纹理细节信息。文中提出的方法可以用于遥感成像、医学图像处理及地震图像处理等领域。The study aims to optimize the edge fidelity in the process of image denoising.On the basis of the ROF model and its improved model,this paper proposes an image denoising model based on adaptive fractional-order variational PDE by constructing an adaptive edge detection function,which can better protect image edge features of the image,maintain texture details and suppress staircase effects.The denoising effect of the new model was tested with standard images.Experimental results show that,compared with other contrastive methods,the new method can not only effectively improve the signal to noise ratio(SNR)of images but also adaptively preserve the structural information of the images.The proposed method can be applied in the fields of remote sensing imaging,medical imaging,seismic image processing.

关 键 词：图像去噪 变分正则化 分数阶PDE 保边缘 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]