基于非凸低秩约束的图像修复方法  

Image inpainting using non-convex and low-rank constraint

作　　者：孙艳敏 郭强[1,2] 张彩明 SUN Yan-min;GUO Qiang;ZHANG Cai-ming(School of Computer Science and Technology,Shandong University of Finance and Economics,Jinan Shandong 250014,China;Shandong Key Laboratory of Digital Media Technology,Jinan Shandong 250014,China;School of Software,Shandong University,Jinan Shandong 250101,China)

机构地区：[1]山东财经大学计算机科学与技术学院,山东济南250014 [2]山东省数字媒体技术重点实验室,山东济南250014 [3]山东大学软件学院,山东济南250101

出　　处：《图学学报》2021年第3期414-425,共12页Journal of Graphics

基　　金：国家自然科学基金项目(61873145,U1609218);山东省省属高校优秀青年人才联合基金(ZR2017JL029)。

摘　　要：受传输干扰或存储不当等因素的影响,现实应用中获取的某些图像通常会存在像素缺失现象,这给图像的后续分析与处理带来了一定影响。解决该问题的常用方法是对图像进行低秩修复。利用低秩特性进行修复的方法大多以秩函数建模,由于矩阵秩函数是非凸离散的,该模型的求解是一个NP难问题,所以通常利用核范数对矩阵的秩进行凸松弛。但是,基于核范数的修复方法与基于秩函数极小化的方法之间存在一定偏差,因此提出非凸低秩约束的图像修复方法。即采用log函数代替核范数对秩进行约束,能够克服核范数无法很好逼近秩最小化的问题。此外,为有效求解上述非凸模型,将目标函数转化为增广拉格朗日函数,利用交替方向乘子法求解图像修复模型。实验结果表明,该修复方法能够处理不同情况下的像素缺失问题,且修复性能明显好于现有低秩修复方法。Due to transmission interference or improper storage,there exist some missing pixels in the images obtained in the real scene,which causes obstacles to the subsequent processing and analysis of the images.The key solution for missing pixels is to recover the image with low rank prior.However,since the rank function is discrete,the model that minimizes the rank is an NP-hard problem.In order to address this issue,a commonly used method is to employ an image-inpainting algorithm based on the nuclear norm.Unlike the methods based on the nuclear norm minimization,this paper proposed an image-inpainting algorithm using non-convex low-rank constraints,which replaced the traditional nuclear norm with a log function and overcame the inability of the nuclear norm to approach the rank minimization.In addition,to optimize the non-convex model,the augmented Lagrangian multiplier method was adopted to derive an alternating minimization algorithm.Experimental results demonstrate that the proposed method can deal with different missing pixel rates,and can far outperform other low-rank inpainting methods in inpainting.

关 键 词：图像修复 核范数 交替方向乘子法 非凸低秩约束 增广拉格朗日函数 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]