计算机科学 ›› 2021, Vol. 48 ›› Issue (8): 125-133.doi: 10.11896/jsjkx.200400143

• 计算机图形学& 多媒体 • 上一篇    下一篇

基于非凸低秩矩阵逼近和全变分正则化的高光谱图像去噪

陶星朋, 徐宏辉, 郑建炜, 陈婉君   

  1. 浙江工业大学计算机科学与技术学院 杭州310023
  • 收稿日期:2020-04-30 修回日期:2020-08-24 发布日期:2021-08-10
  • 通讯作者: 陈婉君(wanjun@zjut.edu.cn)
  • 基金资助:
    国家重点研发计划项目(2018YFE0126100);国家自然科学基金(61602413);浙江省自然科学基金(LY19F030016);浙江省实验室开放研究项目(2019KD0AD01/007);国家卫生委员会科研基金(WKJ-ZJ-2102);浙江省教育厅项目(Y201941027)

Hyperspectral Image Denoising Based on Nonconvex Low Rank Matrix Approximation and TotalVariation Regularization

TAO Xing-peng, XU Hong-hui, ZHENG Jian-wei, CHEN Wan-jun   

  1. School of Computer Science and Technology,Zhejiang University of Technology,Hangzhou 310023,China
  • Received:2020-04-30 Revised:2020-08-24 Published:2021-08-10
  • About author:TAO Xing-peng,born in 1996,postgra-duate.His main research interests include visual analysis and image proces-sing.(txpdyt@163.com)CHEN Wan-jun,born in 1982,lecturer.Her main research interests include model optimization and image proces-sing.
  • Supported by:
    National Key R&D Program of China (2018YFE0126100),National Natural Science Foundation of China (61602413),Natural Science Foundation of Zhejiang Province,China(LY19F030016),Open Research Projects of Zhejiang Lab(2019KD0AD01/007),Scientific Research Fund of the National Health Commission of China(WKJ-ZJ-2102) and Program of Department of Education of Zhejiang Province(Y201941027).

摘要: 高光谱图像在采集过程中经常受到混合噪声的干扰,严重影响了图像后续应用的性能,因此图像去噪已成为一个极其重要的预处理过程。文中采用非凸正则项代替传统的核范数重新构造逼近问题,使稀疏正则项更贴近本质秩函数的属性,进而提出了一种将非凸代理函数、全变分正则项和l2,1范数集成于统一框架的混合噪声去除算法。所提算法旨在将退化的高光谱图像以矩阵的形式分解为低秩分量和稀疏项,并利用全变分正则化保持边缘信息,提高了高光谱图像的空间分段平滑性。最后利用非凸代理函数的特殊性质,采用一种基于增广拉格朗日乘子法的迭代算法进行变量优化求解。通过多组实验进行验证,结果表明所提算法不仅能有效地去除混合噪声,而且能较好地保持图像的结构和细节,与现有的其他高光谱去噪方法相比,其在视觉效果和定量评价结果上都明显提升。

关键词: 高光谱图像, 混合噪声, 全变分, 非凸正则项, 增广拉格朗日乘子法

Abstract: Hyperspectral images (HSIs) are often interfered by hybrid noise in the acquisition process,which seriously weakens the performance of subsequent applications of HSIs.In this paper,nonconvex regularizer is used to reconstruct the approximation problem instead of the traditional nuclear norm,which guarantees a tighter approximation of the original sparsity constrained rank function.Then a hybrid noise removal model integrating nonconvex surrogate function,total variation regularization and l2,1 norms together into a unified framework is proposed.The proposed algorithm aims to decompose the degraded HSIs into low rank components and sparse terms in the matrix mode,and uses total variation regularization to maintain edge information and improve the spatial piecewise smoothness of the HSIs.Finally,using the special properties of nonconvex surrogate function,an iterative algorithm based on augmented Lagrangian multiplier method is used for optimization.Extensive experiments on several well-known datasets are conducted for model evaluation,and the results show that the proposed algorithm can not only effectively remove hybrid noise,but also can better maintain the structure and details of the images.Compared with other existing hyperspectral denoising methods,the visual effects and quantitative evaluation results of the proposed algorithm are significantly better.

Key words: Hyperspectral image, Hybrid noise, Total variation, Nonconvex regularizer, Augmented lagrangian multipliers

中图分类号: 

  • TP391.41
[1]XIE T,LI S,SUN B.Hyperspectral images denoising via nonconvex regularized low-rank and sparse matrix decomposition[J].IEEE Transactions on Image Processing,2019,29:44-56.
[2]LEE S,NEGISHI M,URAKUBO H,et al.Mu-net:Multi-scale U-net for two-photon microscopy image denoising and restoration[J].Neural Networks,2020,125:92-103.
[3]ZHANG L,WANG J,AN Z.Classification method of CO2 hyperspectral remote sensing data based on neural network[J].Computer Communications,2020,156:124-130.
[4]LI Y,XU J,XIA R,et al.A two-stage framework of target detection in high-resolution hyperspectral images[J].Signal,Image and Video Processing,2019,13(7):1339-1346.
[5]FAN H,LI J,YUAN Q,et al.Hyperspectral image denoising with bilinear low rank matrix factorization[J].Signal Proces-sing,2019,163:132-152.
[6]XING L,CHANG Q,QIAO T.The algorithms about fast non-localmeans based image denoising[J].Acta Mathematicae Applicatae Sinica,English Series,2012,28(2):247-254.
[7]BALOCH G,OZKARAMANLI H.Image denoising via correlation-based sparse representation[J].Signal,Image and Video Processing,2017,11(8):1501-1508.
[8]DABOV K,FOI A,KATKOVNIK V,et al.Image denoising by sparse 3-D transform-domain collaborative filtering[J].IEEE Transactions on Image Processing,2007,16(8):2080-2095.
[9]OTHMAN H,QIAN S E.Noise reduction of hyperspectralimagery using hybrid spatial-spectral derivative-domain wavelet shrinkage[J].IEEE Transactions on Geoscience and Remote Sensing,2006,44(2):397-408.
[10]LU C,TANG J,YAN S,et al.Nonconvex nonsmooth low rank minimization via iteratively reweighted nuclear norm[J].IEEE Transactions on Image Processing,2015,25(2):829-839.
[11]LI C,MA Y,HUANG J,et al.Hyperspectral image denoising using the robust low-rank tensor recovery[J].Journal of the Optical Society of America A,2015,32(9):1604-1612.
[12]RENARD N,BOURENNANE S,BLANC-TALON J.Denoising and dimensionality reduction using multilinear tools for hyperspectral images[J].IEEE Geoscience and Remote Sensing Letters,2008,5(2):138-142.
[13]KONG X,ZHAO Y,XUE J,et al.Hyperspectral Image Denoi-sing Using Global Weighted Tensor Norm Minimum and Nonlocal Low-Rank Approximation[J].Remote Sensing,2019,11(19):2281-2303.
[14]ZHANG H,HE W,ZHANG L,et al.Hyperspectral image restoration using low-rank matrix recovery[J].IEEE Transactions on Geoscience and Remote Sensing,2013,52(8):4729-4743.
[15]CANDÉS E J,LI X,MA Y,et al.Robust principal component analysis?[J].Journal of the ACM,2011,58(3):1-37.
[16]HE W,ZHANG H,ZHANG L,et al.Hyperspectral image denoising via noise-adjusted iterative low-rank matrix approximation[J].IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing,2015,8(6):3050-3061.
[17]HE W,ZHANG H,ZHANG L,et al.Total-variation-regularized low-rank matrix factorization for hyperspectral image restoration[J].IEEE Transactions on Geoscience and Remote Sensing,2015,54(1):178-188.
[18]WANG Y,PENG J,ZHAO Q,et al.Hyperspectral image restoration via total variation regularized low-rank tensor decomposition[J].IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing,2017,11(4):1227-1243.
[19]HE W,ZHANG H,SHEN H,et al.Hyperspectral image de-noising using local low-rank matrix recovery and global spatial-spectral total variation[J].IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing,2018,11(3):713-729.
[20]ZHENG J,QIN M,ZHOU X,et al.Efficient Implementation of Truncated Reweighting Low-Rank Matrix Approximation[J].IEEE Transactions on Industrial Informatics,2019,16(1):488-500.
[21]ZHENG J,LOU K,YANG X,et al.Weighted mixed-norm regularized regression for robust face identification[J].IEEE Transac-tions on Neural Networks and Learning Systems,2019,30(12):3788-3802.
[22]YANG Y,ZHENG J,CHEN S,et al.Hyperspectral image restoration via local low-rank matrix recovery and Moreau-enhanced total variation[J].IEEE Geoscience and Remote Sensing Letters,2019,17(6):1037-1041.
[23]XIE Y,QU Y,TAO D,et al.Hyperspectral image restorationvia iteratively regularized weighted schatten p-norm minimization[J].IEEE Transactions on Geoscience and Remote Sensing,2016,54(8):4642-4659.
[24]REHCT B,FAZEL M,PARRILO P A.Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization[J].SIAM Review,2010,52(3):471-501.
[25]CANDÉS E J,PLAN Y.Matrix completion with noise[J].Proceedings of the IEEE,2010,98(6):925-936.
[26]ZHOU Z,LI X,WRIGHT J,et al.Stable principal component pursuit[C]//2010 IEEE International Symposium on Information Theory.IEEE,2010:1518-1522.
[27]CHEN Y,GUO Y,WANG Y,et al.Denoising of hyperspectral images using nonconvex low rank matrix approximation[J].IEEE Transactions on Geoscience and Remote Sensing,2017,55(9):5366-5380.
[28]RUDIN L I,OSHER S,FATEMI E.Nonlinear total variation based noise removal algorithms[J].Physica D:Nonlinear Phenomena,1992,60(1/2/3/4):259-268.
[29]YAN J,PENG H,YU Y,et al.Compressive sensing of windspeed based on non-convex ℓp-norm sparse regularization optimization for structural health monitoring[J].Engineering Structures,2019,194:346-356.
[30]MA R,MIAO J,NIU L,et al.Transformed ℓ1 regularization for learning sparse deep neural networks[J].Neural Networks,2019,119:286-298.
[31]LIU G,LIN Z,YAN S,et al.Robust recovery of subspace structures by low-rank representation[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2012,35(1):171-184.
[32]XIE T,LI S,SUN B.Hyperspectral images denoising via non-convex regularized low-rank and sparse matrix decomposition[J].IEEE Transactions on Image Processing,2019,29:44-56.
[33]CHENG D,YANG J,WANG J,et al.Double-noise-dual-prob-lem approach to the augmented Lagrange multiplier method for robust principal component analysis[J].Soft Computing,2017,21(10):2723-2732.
[34]BECK A,TEBOULLE M.Fast gradient-based algorithms forconstrained total variation image denoising and deblurring problems[J].IEEE Transactions on Image Processing,2009,18(11):2419-2434.
[35]WANG Z,BOVIK A C,SHEIKH H R,et al.Image quality assessment:from error visibility to structural similarity[J].IEEE Transactions on Image Processing,2004,13(4):600-612.
[1] 王燕, 王丽. 面向高光谱图像分类的局部Gabor卷积神经网络[J]. 计算机科学, 2020, 47(6): 151-156.
[2] 张显,叶军. 基于非局部相似联合低秩表示的高光谱图像去噪[J]. 计算机科学, 2020, 47(1): 170-175.
[3] 张旭涛. 基于高斯-椒盐噪声的滤波算法[J]. 计算机科学, 2019, 46(6A): 263-265.
[4] 林伟俊, 赵辽英, 厉小润. 基于逐像素递归处理的高光谱实时亚像元目标检测[J]. 计算机科学, 2018, 45(6): 259-264.
[5] 李昌利, 张琳, 樊棠怀. 基于自适应主动学习与联合双边滤波的高光谱图像分类[J]. 计算机科学, 2018, 45(12): 223-228.
[6] 任守纲, 万升, 顾兴健, 王浩云, 袁培森, 徐焕良. 基于多尺度空谱鉴别特征的高光谱图像分类[J]. 计算机科学, 2018, 45(12): 243-250.
[7] 邹丽, 蔡希彪, 孙静, 孙福明. 基于双图正则的半监督NMF混合像元解混算法[J]. 计算机科学, 2018, 45(12): 251-254.
[8] 窦立云,徐丹,李杰,陈浩,刘义成. 基于双树复小波的图像修复[J]. 计算机科学, 2017, 44(Z6): 179-182.
[9] 陈代斌,杨晓梅. 基于低秩张量恢复的视频块效应处理[J]. 计算机科学, 2016, 43(9): 280-283.
[10] 刘亚男,杨晓梅,陈超楠. 基于分数阶全变分正则化的超分辨率图像重建[J]. 计算机科学, 2016, 43(5): 274-278.
[11] 王玥,周城,熊承义,舒振宇. 基于纹理自适应全变分滤波的图像分块压缩感知优化算法[J]. 计算机科学, 2016, 43(2): 307-310.
[12] 舒速,杨明. 基于分水岭分割和稀疏表示的高光谱图像分类方法[J]. 计算机科学, 2016, 43(2): 89-94.
[13] 张玉香,高旭杨,王 挺,张乐飞,杜 博. 一种基于背景自学习的高光谱图像生物信息提取方法[J]. 计算机科学, 2015, 42(4): 292-296.
[14] 许明明,张良培,杜 博,张乐飞. 基于类别可分性的高光谱图像波段选择[J]. 计算机科学, 2015, 42(4): 274-275.
[15] 胡文瑾,刘仲民,李战明. 一种改进的小波域图像修复算法[J]. 计算机科学, 2014, 41(5): 299-303.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
[1] 郭炳, 郑文萍, 韩素青. 一种基于突变基因网络的癌症驱动通路识别算法[J]. 计算机科学, 2018, 45(7): 230 -236 .
[2] 刘俊峰,李飞龙,杨杰. 基于LEO的骨干接入空间信息网络与用频策略研究[J]. 计算机科学, 2018, 45(6A): 337 -341 .
[3] 池凯凯, 魏欣晨, 林一民. 面向射频能量捕获传感网的高吞吐量负载均衡的节点接入方案[J]. 计算机科学, 2018, 45(8): 119 -124 .
[4] 任睿思, 魏玲, 祁建军. 三支类背景上的规则获取[J]. 计算机科学, 2018, 45(10): 21 -26 .
[5] 袁文兵,常亮,徐周波,古天龙. 基于果蝇优化算法的多工位装配序列规划[J]. 计算机科学, 2017, 44(4): 246 -251 .
[6] 贾晓辉,张文宁,刘安战. 分级的软件可信评估模型研究及应用[J]. 计算机科学, 2017, 44(4): 169 -172 .
[7] 侯跃恩,李伟光. 帧间连续结构稀疏表示的目标跟踪算法[J]. 计算机科学, 2017, 44(3): 307 -312 .
[8] 邹青志,黄山. 一种基于Mean Shift的快速跟踪算法[J]. 计算机科学, 2017, 44(3): 278 -282 .
[9] 许影,李强懿. 基于稀疏特性的盲二值图像去模糊[J]. 计算机科学, 2018, 45(3): 253 -257 .
[10] 刘明达,拾以娟. 基于区块链的远程证明模型[J]. 计算机科学, 2018, 45(2): 48 -52 .