基于重叠群稀疏分数阶全变分正则化模型的图像去噪算法  

Image Denoising Algorithm Based on Overlapping Group Sparse Fractional Order Total Variation Regularization Model

作　　者：吴亮 唐利明 WU Liang;TANG Liming(School of Mathematics and Statistics,Hubei Minzu University,Enshi 445000,China)

机构地区：[1]湖北民族大学数学与统计学院,湖北恩施445000

出　　处：《湖北民族大学学报（自然科学版）》2023年第1期40-50,共11页Journal of Hubei Minzu University:Natural Science Edition

基　　金：国家自然科学基金项目(62061016,61561019);湖北民族大学研究生创新项目(MYK2022028)。

摘　　要：为了兼顾图像边缘和纹理信息的恢复,提出了重叠群稀疏分数阶全变分正则化图像去噪(overlapping group sparse fractional order total variation regularization,OGS-FOTV)模型。该模型利用图像分数阶变分域的重叠群稀疏度量作为正则项,用经典的L2范数作为保真项。利用交替方向乘子法(alternating direction method of multipliers,ADMM)将模型分解成若干个子问题分别求解。其中,重叠群稀疏分数阶正则化子的结构十分复杂,因此利用均值不等式构造出该子问题的1个替代函数后,再使用优化-最小化(majorize-minimize,MM)算法对其求解。实验结果表明,OGS-FOTV模型能较好地恢复图像的纹理和边缘信息,且和一些先进的变分模型相比,OGS-FOTV模型在峰值信噪比(peak signal noise ratio,PSNR)和结构相似度(structural similarity index measure,SSIM)上具有最佳的性能。In order to recover both image edge and texture information,we propose an image denoising model based on overlapping group sparse fractional order total variation regularization(OGS-FOTV).In this model,an overlapping group sparse measure of the fractional variational domain is used as the regularization term,and the classical L~2 norm is used as the fidelity term.The alternating direction method of multipliers(ADMM)algorithm is used to decompose the model into several sub-problems.Among them,the structure of the overlapping group sparse fractional order regularizer is very complex,so an alternative function of the sub-problem is constructed by using the mean inequality,and then the majorize-minimize(MM)algorithm is used to solve it.The experimental results show that OGS-FOTV can recover the texture and edge information of the image well.Compared with several state-of-the-art variational models,OGS-FOTV has the best performance in terms of peak signal noise ratio(PSNR)and structural similarity index measure(SSIM)indexes.

关 键 词：图像去噪 正则化 分数阶变分 重叠群稀疏 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]