Efficient unmixing algorithm using Sinkhorn distance and graph regularization constraints
- Vol. 27, Issue 11, Pages: 2603-2616(2023)
Published： 07 November 2023
DOI： 10.11834/jrs.20221126
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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
高光谱解混非负矩阵分解Sinkhorn距离熵正则图正则
Keywords
hyperspectral unmixingnonnegative matrix factorization (NMF)Sinkhorn distanceentropy regularizationgraph regularization
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.2017.2669991http://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.2010.2057434http://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.2008.929920http://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.2018.2834567http://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.2015.2468177http://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)04-1118-10http://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.2016.2616418http://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.2020.3021520http://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.2016.2519498http://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.2011.2174443http://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.2014.2320576http://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.2018.2812999http://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.20186502http://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: 10.1038/44565http://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.2019.2920687http://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.2020.2996249http://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.2016.2580702http://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.2010.2068053http://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.2012.2213825http://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/Eusipco47968.2020.9287456http://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.2016.2545341http://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.2006.888466http://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.2004.839806http://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=3.809999942.87866688sparsity-constrained nonnegative matrix factorization. IEEE Transactions on Geoscience and Remote Sensing, 49(11): 4282-4297 [DOI: 10.1109/TGRS.2011.2144605http://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.2020.3020810http://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.2020.2976799http://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:1026543900054http://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.2011.18http://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.20166264http://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.2017.2693967http://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.2006.874135http://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.2013.2242255http://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.2015.2508448http://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.2017.2724944http://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.2019.2893068http://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.2014.2365953http://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.20166179http://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.2019.2948454http://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.2018.2815044http://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/DCABES50732.2020.00046http://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.2017.8127161http://dx.doi.org/10.1109/IGARSS.2017.8127161]
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School of Geophysics and Geomatics, China University of Geosciences
Electronic Information School, Wuhan University
Institute of Aerospace Science and Technology, Wuhan University
College of Mathematics and Computer Science, Wuhan Polytechnic University
Key Laboratory of Land, Environment and Disaster Monitoring, Ministry of Natural Resources, China University of Mining and Technology
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