基于交叠组合稀疏高阶全变分的图像复原  

High order total variation with overlapping group sparsity for image restoration

作　　者：范梦佳 周先春[1,2] Fan Mengjia;Zhou Xianchun(School of Electronic&Information Engineering,Nanjing University of Information Science&Technology,Nanjing 210044,Chin;Jiangsu Collaborative Innovation Center of Atmospheric Environment&Equipment Technology,Nanjing University of Information Science&Technology,Nanjing 210044,China)

机构地区：[1]南京信息工程大学电子与信息工程学院,南京210044 [2]南京信息工程大学江苏省大气环境与装备技术协同创新中心,南京210044

出　　处：《计算机应用研究》2020年第10期3159-3163,3174,共6页Application Research of Computers

基　　金：国家自然科学基金资助项目(11202106,61302188);江苏省“信息与通信工程”优势学科建设项目;江苏高校品牌专业建设工程资助项目。

摘　　要：针对传统全变分进行扩展,提出了一种高阶全变分结合交叠组合稀疏的新算法,将像素级别梯度信息推广为高阶交叠组合稀疏梯度信息,更好地抑制了因全变分产生的阶梯效应并保存了图像边缘等细节信息。为了解决提出的图像复原新算法的优化问题,采用交替方向乘子算法(ADMM)来交替求解优化问题。将新算法与其他几种相关算法相比,并用峰值信噪比(PSNR)和结构相似性(SSIM)两个评价指标来评价图像复原后的质量,从而论证了新算法的优越性。To extend the traditional total variation,this paper proposed a new algorithm of high-order total variation combined with overlapping group sparsity.This algorithm promoted pixel-level gradient information to high-order overlapping combined sparse gradient information,which could better suppress the staircase effect caused by total variation and preserve the details of image edges.In order to solve the optimization problem of the proposed image restoration,this algorithm used the alternating direction method of multipliers(ADMM)to solve the optimization problem alternately.Compared with several other related algorithms,the new algorithm used the two factors of peak signal-to-noise ratio(PSNR)and structural similarity(SSIM)to evaluate the quality of the image after restoration.The results demonstrate the superiority of the new algorithm.

关 键 词：高阶导数 交叠组合稀疏 交替方向乘子法 全变分 图像复原 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]