加权Schatten范数低秩表示的高光谱图像恢复
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摘要
高光谱图像在获取过程中常受到多种噪声的干扰,如高斯噪声、脉冲噪声、条纹噪声等,为确保后续应用的顺利进行,提出了一种基于加权Schatten范数低秩表示的高光谱图像恢复方法。该方法引入低秩表示模型恢复高光谱数据,采用加权Schatten范数代替核函数,更精确地逼近秩函数;并选用初步无噪图像作为低秩表示的字典,进一步提高了模型对图像的恢复能力。另外,引入拉普拉斯正则项刻画数据内部的几何结构,能保持图像的细节。模拟和实际高光谱数据的实验结果表明,较多种相关的方法在视觉效果和量化指标值都有很大地改进。与经典的基于低秩先验的恢复方法相比,本文算法的平均峰值信噪比提高2.74dB,平均结构相似性数值指标提高0.03,而平均光谱角降低1.40。新模型不仅能充分利用高光谱图像光谱维的低秩先验,而且保持了数据内部的几何结构,有利于恢复出高质量的清晰图像。
Hyperspectral Image(HSI)always suffers from various noises such as Gaussian noise,impulse,stripe noise,etc.To ensure the performance of subsequent applications,a new method for HSI restoration was proposed based on weighted Schatten norm Low-Rank Representation(LRR).The proposed method introduced the LRR model into the HSI restoration.It can accurately approximate rank using the weighted Schatten norm instead of the nuclear norm.Furthermore,the initial noiseless image was utilized as the dictionary for LRR to improve the restoration ability.Then,the Laplacian regularizer was used to describe the intrinsic geometric information of the data and to protect details of the HSI.Experimental results on synthetic and real HSI data demonstrated that the proposed method achieves better visual quality and quantitative indices than several existing related methods.Compared with the classical restoration method based on low-rank priori,the mean peak signal-to-noise ratio and structural similarity indices of this algorithm increased by 2.74 dB and 0.03 respectively,and the mean spectral angle was reduced by 1.40.The new method not only takes advantage of the low-rank prior information in the spatial domain,but also keeps the intrinsic geometric structures in data,which helps restore quality clean images.
Hyperspectral Image(HSI)always suffers from various noises such as Gaussian noise,impulse,stripe noise,etc.To ensure the performance of subsequent applications,a new method for HSI restoration was proposed based on weighted Schatten norm Low-Rank Representation(LRR).The proposed method introduced the LRR model into the HSI restoration.It can accurately approximate rank using the weighted Schatten norm instead of the nuclear norm.Furthermore,the initial noiseless image was utilized as the dictionary for LRR to improve the restoration ability.Then,the Laplacian regularizer was used to describe the intrinsic geometric information of the data and to protect details of the HSI.Experimental results on synthetic and real HSI data demonstrated that the proposed method achieves better visual quality and quantitative indices than several existing related methods.Compared with the classical restoration method based on low-rank priori,the mean peak signal-to-noise ratio and structural similarity indices of this algorithm increased by 2.74 dB and 0.03 respectively,and the mean spectral angle was reduced by 1.40.The new method not only takes advantage of the low-rank prior information in the spatial domain,but also keeps the intrinsic geometric structures in data,which helps restore quality clean images.
引文
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[18]XU Y,WU Z,LI J,et al..Anomaly detection in hyperspectral images based on low-rank and sparse representation[J].IEEE Transactions on Geoscience&Remote Sensing,2016,54(4):1990-2000.
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[21]CAI J F,CAND,S,E J,et al..A singular value thresholding algorithm for matrix completion[J].Siam Journal on Optimization,2008,20(4):1956-1982.
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[23]XIE Y,GU S,LIU Y,et al..Weighted Schatten p-norm minimization for image denoising and background subtraction[J].IEEE Transactions on Image Processing,2015,25(10):4842-4857.
[24]ZUO W,MENG D,ZHANG L,et al..A generalized iterated shrinkage algorithm for non-convex sparse coding[C].IEEE International Conference on Computer Vision.IEEE,2013:217-224.
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[26]JOSM B-D,JOSM P N.Hyperspectral subspace identification[J].IEEE Transactions on Geoscience&Remote Sensing,2008,46(8):2435-2445.
[2]黄鸿,陈美利,段宇乐,等.空-谱协同流形重构的高光谱影响分类[J].光学精密工程,2018,26(7):1827-1836.HUANG H,CHEN M L,DUAN Y L,et al..Hyper-spectral image classification using spatialspectral manifold reconstruction[J].Opt.Precision Eng.,2018,26(7):1827-1836.(in Chinese)
[3]TOCHON G,CHANUSSOT J,MURA M D,et al..Object tracking by hierarchical decomposition of hyperspectral video sequences:application to chemical gas plume tracking[J].IEEE Transactions on Geoscience&Remote Sensing,2017,55(8):4567-4585.
[4]何芳,王榕,于强,等.加权空谱局部保持投影的高光谱图像特征提取[J].光学精密工程,2017,25(1):263-273.HE F,WANG R,YU Q,et al..Feature extraction of hyperspectral images of weighted spatial and spectral locality preserving projection(WSSLPP)[J].Opt.Precision Eng.,2017,25(1):263-273.(in Chinese)
[5]张良培,李家艺.高光谱图像稀疏信息处理综述与展望[J].遥感学报,2016,20(5):1091-1101.ZHANG L P,LI J Y.Development and prospect of sparse representation-based hyperspectral image processing and analysis[J].Journal of Remote Sensing,2016,20(5):1091-1101.(in Chinese)
[6]ZHANG H,HE W,ZHANG L,et al..Hyperspectral image restoration using low-rank matrix recovery[J].IEEE Transactions on Geoscience and Remote Sensing,2014,52(8):4729-4743.
[7]CAI J,DONG B,OSHER S,et al..Image restoration:total variation,wavelet frames,and beyond[J].Journal of the American Mathematical Society,2012,25(4):1033-1089.
[8]ELAD M,AHARON M.Image denoising via sparse and redundant representations over learned dictionaries[J].IEEE Transactions on Image Processing,2006,15(12):3736-3745.
[9]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.
[10]MAGGIONI M,KATKOVNIK V,EGIAZARIAN K,et al..Nonlocal transform-domain filter for volumetric data denoising and reconstruction[J].IEEE Transactions on Image Processing,2012,22(1):119-133.
[11]WANG Y,PENG J,ZHAO Q,et al..Hyperspectral image restoration via total variation regularized lowrank tensor decomposition[J].IEEE Journal of Selected Topics in Applied Earth Observations&Remote Sensing,2018,11(4):1227-1243.
[12]CHANG C I,DU Q.Interference and noise-adjusted principal components analysis[J].IEEETransactions on Geoscience and Remote Sensing,1999,37(5):2387-2396.
[13]CANDS E J,LI X,MA Y,et al..Robust principal component analysis?JACM 58(3):11[J].Journal of the Acm.,2011,58(3):1-37.
[14]XIE Y,QU Y,TAO D,et al..Hyperspectral image restoration via iteratively regularized weighted Schatten p-norm minimization[J].IEEE Transactions on Geoscience and Remote Sensing,2016,54(8):4642-4659.
[15]LIU G C,LIN Z C,YAN S C,et al..Robust recovery of subspace structures by low-rank representation[J].IEEE Trans.on Pattern Analysis and Machine Intelligence,2013,35(1):171-184.
[16]蔡荣荣,王斌.一种基于低秩表示的高光谱图像恢复方法[J].复旦学报(自然科学版),2017,56(3):346-358.CAI R R,WANG B.Hyperspectral imagery restoration based on low-rank representation[J].Journal of Fudan University(Natural Science),2017,56(3):346-358.(in Chinese)
[17]SUMARSONO A,DU Q.Low-rank subspace representation for supervised and unsupervised classification of hyperspectral imagery[J].IEEE Journal of Selected Topics in Applied Earth Observations&Remote Sensing,2016,9(9):4188-4195.
[18]XU Y,WU Z,LI J,et al..Anomaly detection in hyperspectral images based on low-rank and sparse representation[J].IEEE Transactions on Geoscience&Remote Sensing,2016,54(4):1990-2000.
[19]GU S,ZHANG L,ZUO W,et al..Weighted nuclear norm minimization with application to image denoising[C].Computer Vision and Pattern Recognition.IEEE,2014:2862-2869.
[20]YIN M,GAO J B,LIN Z C.Laplacian regularized low-rank representation and its applications[J].IEEE Trans.on Pattern Anal.Mach.Intell.,2016,38(3):504-517.
[21]CAI J F,CAND,S,E J,et al..A singular value thresholding algorithm for matrix completion[J].Siam Journal on Optimization,2008,20(4):1956-1982.
[22]BOYD S,PARIKH N,CHU E,et al..Distributed optimization and statistical learning via the alternating direction method of multipliers[J].Foundations&Trends in Machine Learning,2010,3(1):1-122.
[23]XIE Y,GU S,LIU Y,et al..Weighted Schatten p-norm minimization for image denoising and background subtraction[J].IEEE Transactions on Image Processing,2015,25(10):4842-4857.
[24]ZUO W,MENG D,ZHANG L,et al..A generalized iterated shrinkage algorithm for non-convex sparse coding[C].IEEE International Conference on Computer Vision.IEEE,2013:217-224.
[25]LIN Z,LIU R,SU Z.Linearized alternating direction method with adaptive penalty for low-rank representation[J].Advances in Neural Information Processing Systems,2011:612-620.
[26]JOSM B-D,JOSM P N.Hyperspectral subspace identification[J].IEEE Transactions on Geoscience&Remote Sensing,2008,46(8):2435-2445.