基于最优运输理论和TV-正则项的图像去噪模型  

IMAGE DENOISING MODEL USING OPTIMAL TRANSPORT AND TOTAL VARIATION

作　　者：黄维佳 黄忠亿[1] 杨文莉 Huang Weijia;Huang Zhongyi;Yang Wenli(Department of Mathematical Sciences,Tsinghua University,Beijing 100084,China;School of Mathematics,China University of Mining and Technology,Xuzhou 221116,China)

机构地区：[1]清华大学数学科学系,北京100084 [2]中国矿业大学数学学院,徐州221116

出　　处：《数值计算与计算机应用》2024年第4期314-335,共22页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(12025104,12001529,81930119)资助。

摘　　要：本文提出了一个基于最优运输理论中的对偶Lipschitz范数和TV-正则项的新去噪模型,说明了对偶Lipschitz范数和Meyer所提的适用于卡通纹理分解问题的G-范数的联系.该模型可以通过一个凸泛函分别关于两个变量交替最优化来求解,本文基于求解Wasserstein距离和ROF模型的方法设计了数值算法。本文证明了所提算法的收敛性,并且分析了模型最小值点的存在性和唯一性。最后,本文通过数值试验比较了所提模型与传统的ROF等图像去噪模型的去噪效果,分析了所提模型的特点,验证了算法的有效性.In this paper,we propose a new image denoising model using the dual Lipschitz norm from optimal transport(OT)and the total variation minimization.We show the relations of this model to the G-TV model proposed by Yves Meyer to decomposition an image into a cartoon component,and a component representing the texture or noise.The proposed model is solved by minimizing a convex functional alternately in two variables.We design the numerical algorithm based on the Primal-Dual Hybrid Gradient(PDHG)algorithm for the Wasserstein-1 distance and the projection algorithm for the ROF model,and we establish the convergence analysis of the proposed algorithm.The existence of a minimizer of the proposed model is proved.Numerical examples demonstrate the distinct features of the proposed model compared with the traditional models such as the ROF model,and show the effectiveness of the proposed numerical method.

关 键 词：图像去噪 最优运输 凸优化算法 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]