应用Sinkhorn距离和图正则约束的高效解混算法

杨露露; 李春芝; 陈晓华; 王丽

doi:10.11834/jrs.20221126

模型与方法 | 浏览量 : 0 下载量: 1420 CSCD: 0

R-PDF
PDF
导出
分享
收藏
专辑

应用Sinkhorn距离和图正则约束的高效解混算法
Efficient unmixing algorithm using Sinkhorn distance and graph regularization constraints
2023年27卷第11期页码：2603-2616
收稿：2021-03-11，

纸质出版：2023-11-07
DOI： 10.11834/jrs.20221126
稿件说明：

移动端阅览

杨露露，李春芝，陈晓华，王丽.2023.应用Sinkhorn距离和图正则约束的高效解混算法.遥感学报，27（11）： 2603-2616 DOI： 10.11834/jrs.20221126.

Yang L L，Li C Z，Chen X H and Wang L. 2023. Efficient unmixing algorithm using Sinkhorn distance and graph regularization constraints. National Remote Sensing Bulletin， 27（11）：2603-2616 DOI： 10.11834/jrs.20221126.

摘要

高光谱盲解混是解决混合像元问题的重要技术。其中，非负矩阵分解凭借其明确的物理意义，为无监督线性光谱解混的发展奠定了基础。由于传统非负矩阵分解采用欧氏距离度量原始矩阵与重构矩阵之间的误差，因而不能有效挖掘各维度特征间关系，影响解混精度。为充分利用高光谱图像中丰富的相关特征，本研究在地球移动距离的基础上引入熵正则约束，用Sinkhorn距离代替欧氏距离，建模不同维度特征之间的关系。同时，为刻画数据的流形结构，将图正则项作为丰度的约束条件，提出了一种基于Sinkhorn距离和图正则约束的非负矩阵解混算法。本研究采用乘性迭代规则对提出的解混模型进行求解，在模拟数据集、Urban数据集以及Jasper数据集上进行实验，实验结果验证了所提出算法的有效性。

Abstract

Hyperspectral remote sensing technology

as a new type of earth observation technology

provides rich spectral information of features and can identify and finely classify feature targets. A single pixel in hyperspectral images contains multiple features as limited by the spatial resolution. As a result

the mixed pixels become widespread. Ultimately

the accuracy of pixel-level applications is difficult to improve. Nonnegative Matrix Factorization (NMF)

with its clear physical meaning

lays the foundation for the development of unsupervised linear spectral unmixing. Thus

traditional NMF often uses Euclidean distance as a similarity measure method. On the one hand

hyperspectral data have manifold distribution. Thus

simple linear measurement between two points cannot accurately represent the distance between data. This problem makes the sample internal features weakly correlated

which results in the NMF algorithm having an inaccurate prediction of the high-dimensional spatial inaccurate prediction of the translational noise in high-dimensional space. On the other hand

the objective function constructed based on this method ignores the correlation characteristics in the image space

which inhibits the performance of the algorithm.

Method Considering the correlation between data manifolds and features

this study proposes a nonnegative matrix factorization unmixing algorithm based on Sinkhorn distance and graph regularization constraint (SDGNMF). On the basis of fully exploiting the advantages of EMD

the algorithm imposes entropy regularization constraint on EMD

improves EMD to Sinkhorn distance

and takes it as the standard of measuring error

which effectively reduces the computational complexity. In addition

EMD with entropy regularization constraint

that is

the representation of the model by Sinkhorn distance

can better model the relationship between different dimensional features and fully utilize the correlation of features. In particular

this study introduces the graph regularity constraint based on the Sinkhorn distance to further characterize the manifold structure of data. Compared with the unmixing model constructed by Euclidean distance

SDGNMF is relatively insensitive to the noise in hyperspectral data and can better extract the internal structural information of the data

which improves the unmixing accuracy.

Result An experiment was conducted on simulated and real datasets. Experimental results prove that the proposed algorithm proposed has achieved excellent subspace learning results and has good robustness. Compared with several other algorithms

SDGNMF can retain the similar structure after iteration. The correlation between the endmember features is also fully considered in SDGNMF. Thus

the similar substances distributed in adjacent regions can be separated. Therefore

SDGNMF can better display the details of local abundance and obtain a more realistic and perfect abundance map.

Conclusion In general

the proposed unmixing model can overcome noise and consider the correlation of features and data manifold structure simultaneously. Experimental results show that the proposed algorithm can effectively improve the unmixing accuracy of most hyperspectral remote sensing data

especially those with high feature correlation. However

the proposed algorithm has high computational complexity. In addition

the algorithm only considers the prior knowledge of abundance. Therefore

future work will focus on solving these problems.

关键词

Keywords

references

Akhtar N and Mian A . 2017 . RCMF: robust constrained matrix factorization for hyperspectral unmixing . IEEE Transactions on Geoscience and Remote Sensing , 55 ( 6 ): 3354 - 3366 [ DOI: 10.1109/TGRS.2017.2669991 http://dx.doi.org/10.1109/TGRS.2017.2669991 ]

Bajorski P . 2011 . Second moment linear dimensionality as an alternative to virtual dimensionality . IEEE Transactions on Geoscience and Remote Sensing , 49 ( 2 ): 672 - 678 [ DOI: 10.1109/TGRS.2010.2057434 http://dx.doi.org/10.1109/TGRS.2010.2057434 ]

Bruckstein A M , Elad M and Zibulevsky M . 2008 . On the uniqueness of nonnegative sparse solutions to underdetermined systems of equations . IEEE Transactions on Information Theory , 54 ( 11 ): 4813 - 4820 [ DOI: 10.1109/TIT.2008.929920 http://dx.doi.org/10.1109/TIT.2008.929920 ]

Cuturi M . 2013 . Sinkhorn distances: Lightspeed computation of optimal transport // Proceedings of the 26th International Conference on Neural Information Processing Systems . Lake Tahoe : Curran Associates Inc.: 2292 - 2300

Cuturi M and Avis D . 2014 . Ground metric learning . The Journal of Machine Learning Research , 15 ( 1 ): 533 - 564

Feng X R , Li H C , Li J , Du Q , Plaza A and Emery W J . 2018 . Hyperspectral unmixing using sparsity-constrained deep nonnegative matrix factorization with total variation . IEEE Transactions on Geoscience and Remote Sensing , 56 ( 10 ): 6245 - 6257 [ DOI: 10.1109/TGRS.2018.2834567 http://dx.doi.org/10.1109/TGRS.2018.2834567 ]

Févotte C and Dobigeon N . 2015 . Nonlinear hyperspectral unmixing with robust nonnegative matrix factorization . IEEE Transactions on Image Processing , 24 ( 12 ): 4810 - 4819 [ DOI: 10.1109/TIP.2015.2468177 http://dx.doi.org/10.1109/TIP.2015.2468177 ]

Frogner C , Zhang C Y , Mobahi H , Araya-Polo M and Poggio T . 2015 . Learning with a Wasserstein loss // Proceedings of the 28th International Conference on Neural Information Processing Systems . Montreal : MIT Press: 2053 - 2061 .

Gan Y Q , Liu W H , Feng X P , Yu T , Hu B L and Wen D S . 2019 . A sparse constrained graph regularized nonnegative matrix factorization algorithm for hyperspectral unmixing . Spectroscopy and Spectral Analysis , 39 ( 4 ): 1118 - 1127

甘玉泉 , 刘伟华 , 冯向朋 , 于涛 , 胡炳樑 , 汶德胜 . 2019 . 一种稀疏约束的图正则化非负矩阵光谱解混方法 . 光谱学与光谱分析 , 39 ( 4 ): 1118 - 1127 [ DOI: 10.3964/j.issn.1000-0593(2019)04-1118-10 http://dx.doi.org/10.3964/j.issn.1000-0593(2019)04-1118-10 ]

Genevay A , Chizat L , Bach F , Cuturi M and Peyré G . 2019 . Sample complexity of sinkhorn divergences // Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics . Naha : PMLR: 1574 - 1583 .

Ghamisi P , Plaza J , Chen Y S , Li J and Plaza A J . 2017 . Advanced spectral classifiers for hyperspectral images: a review . IEEE Geoscience and Remote Sensing Magazine , 5 ( 1 ): 8 - 32 [ DOI: 10.1109/MGRS.2016.2616418 http://dx.doi.org/10.1109/MGRS.2016.2616418 ]

Han H W , Wang G X , Wang M Z , Miao J Q , Guo S , Chen L , Zhang M Y and Guo K . 2020 . Hyperspectral unmixing via nonconvex sparse and low-rank constraint . IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing , 13 : 5704 - 5718 [ DOI: 10.1109/JSTARS.2020.3021520 http://dx.doi.org/10.1109/JSTARS.2020.3021520 ]

He W , Zhang H Y and Zhang L P . 2016 . Sparsity-regularized robust non-negative matrix factorization for hyperspectral unmixing . IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing , 9 ( 9 ): 4267 - 4279 [ DOI: 10.1109/JSTARS.2016.2519498 http://dx.doi.org/10.1109/JSTARS.2016.2519498 ]

Hendrix E M T , Garcia I , Plaza J , Martin G and Plaza A . 2012 . A new minimum-volume enclosing algorithm for endmember identification and abundance estimation in hyperspectral data . IEEE Transactions on Geoscience and Remote Sensing , 50 ( 7 ): 2744 - 2757 [ DOI: 10.1109/TGRS.2011.2174443 http://dx.doi.org/10.1109/TGRS.2011.2174443 ]

Heylen R , Parente M and Gader P . 2014 . A review of nonlinear hyperspectral unmixing methods . IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing , 7 ( 6 ): 1844 - 1868 . [ DOI: 10.1109/JSTARS.2014.2320576 http://dx.doi.org/10.1109/JSTARS.2014.2320576 ]

Khan M J , Khan H S , Yousaf A , Khurshid K and Abbas A . 2018 . Modern trends in hyperspectral image analysis: a review . IEEE Access , 6 : 14118 - 14129 . [ DOI: 10.1109/ACCESS.2018.2812999 http://dx.doi.org/10.1109/ACCESS.2018.2812999 ]

Lan J H , Zou J L , Hao Y S , Zeng Y L , Zhang Y Z and Dong M W . 2018 . Research progress on unmixing of hyperspectral remote sensing imagery . Journal of Remote Sensing , 22 ( 1 ): 13 - 27

蓝金辉 , 邹金霖 , 郝彦爽 , 曾溢良 , 张玉珍 , 董铭巍 . 2018 . 高光谱遥感影像混合像元分解研究进展 . 遥感学报 , 22 ( 1 ): 13 - 27 [ DOI: 10.11834/jrs.20186502 http://dx.doi.org/10.11834/jrs.20186502 ]

Lee D D and Seung H S . 1999 . Learning the parts of objects by non-negative matrix factorization . Nature , 401 ( 6755 ): 788 - 791 [ DOI: 10.1038/44565 http://dx.doi.org/10.1038/44565 ]

Lee D D and Seung H S . 2000 . Algorithms for non-negative matrix factorization // Proceedings of the 13th International Conference on Neural Information Processing Systems . Denver : MIT Press: 535 - 541

Li C Z and Chen X H . 2020 . Error approximation of hyperspectral unmixing via correntropy-induced metric . IEEE Geoscience and Remote Sensing Letters , 17 ( 2 ): 282 - 286 [ DOI: 10.1109/LGRS.2019.2920687 http://dx.doi.org/10.1109/LGRS.2019.2920687 ]

Li C Z , Gu Y G , Chen X H , Zhang Y and Ruan L J . 2021 . Hyperspectral unmixing via latent multiheterogeneous subspace . IEEE Transactions on Geoscience and Remote Sensing , 59 ( 1 ): 563 - 577 [ DOI: 10.1109/TGRS.2020.2996249 http://dx.doi.org/10.1109/TGRS.2020.2996249 ]

Li J , Bioucas-Dias J M , Plaza A and Liu L . 2016 . Robust collaborative nonnegative matrix factorization for hyperspectral unmixing . IEEE Transactions on Geoscience and Remote Sensing , 54 ( 10 ): 6076 - 6090 [ DOI: 10.1109/TGRS.2016.2580702 http://dx.doi.org/10.1109/TGRS.2016.2580702 ]

Liu X S , Xia W , Wang B and Zhang L M . 2011 . An approach based on constrained nonnegative matrix factorization to unmix hyperspectral data . IEEE Transactions on Geoscience and Remote Sensing , 49 ( 2 ): 757 - 772 [ DOI: 10.1109/TGRS.2010.2068053 http://dx.doi.org/10.1109/TGRS.2010.2068053 ]

Lu X Q , Wu H , Yuan Y , Yan P K and Li X L . 2013 . Manifold regularized sparse NMF for hyperspectral unmixing . IEEE Transactions on Geoscience and Remote Sensing , 51 ( 5 ): 2815 - 2826 [ DOI: 10.1109/TGRS.2012.2213825 http://dx.doi.org/10.1109/TGRS.2012.2213825 ]

Marrinan T and Gillis N . 2021 . Hyperspectral unmixing with rare endmembers via minimax nonnegative matrix factorization // Proceedings of the 28th European Signal Processing Conference . Amsterdam : IEEE: 1015 - 1019 [ DOI: 10.23919/Eusipco47968.2020.9287456 http://dx.doi.org/10.23919/Eusipco47968.2020.9287456 ]

Mei S H , Bi Q Q , Ji J Y , Hou J H and Du Q . 2016 . Spectral variation alleviation by low-rank matrix approximation for hyperspectral image analysis . IEEE Geoscience and Remote Sensing Letters , 13 ( 6 ): 796 - 800 [ DOI: 10.1109/LGRS.2016.2545341 http://dx.doi.org/10.1109/LGRS.2016.2545341 ]

Miao L D and Qi H R . 2007 . Endmember extraction from highly mixed data using minimum volume constrained nonnegative matrix factorization . IEEE Transactions on Geoscience and Remote Sensing , 45 ( 3 ): 765 - 777 [ DOI: 10.1109/TGRS.2006.888466 http://dx.doi.org/10.1109/TGRS.2006.888466 ]

Nascimento J M P and Dias J M B . 2005 . Does independent component analysis play a role in unmixing hyperspectral data? IEEE Transactions on Geoscience and Remote Sensing , 43 ( 1 ): 175 - 187 [ DOI: 10.1109/TGRS.2004.839806 http://dx.doi.org/10.1109/TGRS.2004.839806 ]

Qian W , Hong B , Cai D , He X F and Li X L . 2016 . Non-negative matrix factorization with sinkhorn distance // Proceedings of the 25th International Joint Conference on Artificial Intelligence . New York : AAAI Press: 1960 - 1966

Qian Y T , Jia S , Zhou J and Robles-Kelly A . 2011 . Hyperspectral unmixing via <math id="M176"><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn><mo>/</mo><mn mathvariant="normal">2</mn></mrow></msub></math> https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51142863&type= https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51142862&type= 3.80999994 2.87866688 sparsity-constrained nonnegative matrix factorization . IEEE Transactions on Geoscience and Remote Sensing , 49 ( 11 ): 4282 - 4297 [ DOI: 10.1109/TGRS.2011.2144605 http://dx.doi.org/10.1109/TGRS.2011.2144605 ]

Qin J , Lee H , Chi J T , Drumetz L , Chanussot J , Lou Y F and Bertozzi A L . 2021 . Blind hyperspectral unmixing based on graph total variation regularization . IEEE Transactions on Geoscience and Remote Sensing , 59 ( 4 ): 3338 - 3351 [ DOI: 10.1109/TGRS.2020.3020810 http://dx.doi.org/10.1109/TGRS.2020.3020810 ]

Rathnayake B , Ekanayake E M M B , Weerakoon K , Godaliyadda G M R I , Ekanayake M P B and Herath H M V R . 2020 . Graph-based blind hyperspectral unmixing via nonnegative matrix factorization . IEEE Transactions on Geoscience and Remote Sensing , 58 ( 9 ): 6391 - 6409 [ DOI: 10.1109/TGRS.2020.2976799 http://dx.doi.org/10.1109/TGRS.2020.2976799 ]

Rubner Y , Tomasi C and Guibas L J . 2000 . The earth mover’s distance as a metric for image retrieval . International Journal of Computer Vision , 40 ( 2 ): 99 - 121 [ DOI: 10.1023/A:1026543900054 http://dx.doi.org/10.1023/A:1026543900054 ]

Sandler R and Lindenbaum M . 2011 . Nonnegative matrix factorization with earth mover’s distance metric for image analysis . IEEE Transactions on Pattern Analysis and Machine Intelligence , 33 ( 8 ): 1590 - 1602 [ DOI: 10.1109/TPAMI.2011.18 http://dx.doi.org/10.1109/TPAMI.2011.18 ]

Tong Q X , Zhang B and Zhang L F . 2016 . Current progress of hyperspectral remote sensing in China . Journal of Remote Sensing , 20 ( 5 ): 689 - 707

童庆禧 , 张兵 , 张立福 . 2016 . 中国高光谱遥感的前沿进展 . 遥感学报 , 20 ( 5 ): 689 - 707 [ DOI: 10.11834/jrs.20166264 http://dx.doi.org/10.11834/jrs.20166264 ]

Tsinos C G , Rontogiannis A A and Berberidis K . 2017 . Distributed blind hyperspectral unmixing via joint sparsity and low-rank constrained non-negative matrix factorization . IEEE Transactions on Computational Imaging , 3 ( 2 ): 160 - 174 [ DOI: 10.1109/TCI.2017.2693967 http://dx.doi.org/10.1109/TCI.2017.2693967 ]

Wang J and Chang C I . 2006 . Applications of independent component analysis in endmember extraction and abundance quantification for hyperspectral imagery . IEEE Transactions on Geoscience and Remote Sensing , 44 ( 9 ): 2601 - 2616 [ DOI: 10.1109/TGRS.2006.874135 http://dx.doi.org/10.1109/TGRS.2006.874135 ]

Wang N , Du B and Zhang L P . 2013 . An endmember dissimilarity constrained non-negative matrix factorization method for hyperspectral unmixing . IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing , 6 ( 2 ): 554 - 569 [ DOI: 10.1109/JSTARS.2013.2242255 http://dx.doi.org/10.1109/JSTARS.2013.2242255 ]

Wang W H , Qian Y T and Tang Y Y . 2016 . Hypergraph-regularized sparse NMF for hyperspectral unmixing . IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing , 9 ( 2 ): 681 - 694 [ DOI: 10.1109/JSTARS.2015.2508448 http://dx.doi.org/10.1109/JSTARS.2015.2508448 ]

Wang X Y , Zhong Y F , Zhang L P and Xu Y Y . 2017 . Spatial group sparsity regularized nonnegative matrix factorization for hyperspectral unmixing . IEEE Transactions on Geoscience and Remote Sensing , 55 ( 11 ): 6287 - 6304 [ DOI: 10.1109/TGRS.2017.2724944 http://dx.doi.org/10.1109/TGRS.2017.2724944 ]

Yao J , Meng D Y , Zhao Q , Cao W F and Xu Z B . 2019 . Nonconvex-sparsity and nonlocal-smoothness-based blind hyperspectral unmixing . IEEE Transactions on Image Processing , 28 ( 6 ): 2991 - 3006 [ DOI: 10.1109/TIP.2019.2893068 http://dx.doi.org/10.1109/TIP.2019.2893068 ]

Yu Y and Sun W D . 2007 . Minimum distance constrained non-negative matrix factorization for the endmember extraction of hyperspectral images // Proceedings of SPIE 6790 , MIPPR 2007 : Remote Sensing and GIS Data Processing and Applications; and Innovative Multispectral Technology and Applications. Wuhan: SPIE Press: 679015 [DOI: 10.1117/12.748379]

Yuan Y , Fu M and Lu X Q . 2015 . Substance dependence constrained sparse NMF for hyperspectral unmixing . IEEE Transactions on Geoscience and Remote Sensing , 53 ( 6 ): 2975 - 2986 [ DOI: 10.1109/TGRS.2014.2365953 http://dx.doi.org/10.1109/TGRS.2014.2365953 ]

Zhang B . 2016 . Advancement of hyperspectral image processing and information extraction . Journal of Remote Sensing , 20 ( 5 ): 1062 - 1090

张兵 . 2016 . 高光谱图像处理与信息提取前沿 . 遥感学报 , 20 ( 5 ): 1062 - 1090 [ DOI: 10.11834/jrs.20166179 http://dx.doi.org/10.11834/jrs.20166179 ]

Zhang B , Chen Z C , Peng D L , Benediktsson J A , Liu B , Zou L , Li J and Plaza A . 2019 . Remotely sensed big data: evolution in model development for information extraction [point of view] . Proceedings of the IEEE , 107 ( 12 ): 2294 - 2301 [ DOI: 10.1109/JPROC.2019.2948454 http://dx.doi.org/10.1109/JPROC.2019.2948454 ]

Zhang X R , Zhang J Y , Li C , Cheng C , Jiao L C and Zhou H Y . 2018 . Hybrid unmixing based on adaptive region segmentation for hyperspectral imagery . IEEE Transactions on Geoscience and Remote Sensing , 56 ( 7 ): 3861 - 3875 [ DOI: 10.1109/TGRS.2018.2815044 http://dx.doi.org/10.1109/TGRS.2018.2815044 ]

Zhang Y M , Shu Z Q , Zhang J , You C Z , Weng Z H , Fan H H and Ye F Y . 2020 . Dual graph regularized NMF with sinkhorn distance // Proceedings of the 19th International Symposium on Distributed Computing and Applications for Business Engineering and Science . Xuzhou : IEEE: 146 - 149 [ DOI: 10.1109/DCABES50732.2020.00046 http://dx.doi.org/10.1109/DCABES50732.2020.00046 ]

Zhi T X , Yang B , Chen Z and Wang B . 2017 . Nonnegative matrix factorization with constraints on endmember and abundance for hyperspectral unmixing // Proceedings of 2017 IEEE International Geoscience and Remote Sensing Symposium . Fort Worth : IEEE: 1149 - 1152 [ DOI: 10.1109/IGARSS.2017.8127161 http://dx.doi.org/10.1109/IGARSS.2017.8127161 ]

文章被引用时，请邮件提醒。

提交

考虑光谱信息和超像素分割的高光谱解混网络

生成对抗网络的无监督高光谱解混

重加权稀疏和全变差约束下的深度非负矩阵分解高光谱解混

基于金字塔-光谱-注意力曼巴网络的高光谱图像解混方法研究