稀疏差异先验信息支持的高光谱图像稀疏解混算法

doi:10.11947/j.AGCS.2020.20190205

摘要/Abstract

摘要： 基于光谱库的高光谱稀疏解混技术近年来得到了人们的关注，该技术利用光谱库中光谱样本作为端元，将解混问题转化为稀疏表示问题。然而，由于测量环境的差异，待解混图像的实际端元往往与光谱库中相应光谱信号存在差异。本文提出了一种光谱差异稀疏约束的联合稀疏回归解混算法。首先，假设光谱差异具有稀疏特性，建立了光谱库校正模型，使得在解混过程中可对光谱库进行自适应地调整；然后，将光谱库校正模型与联合稀疏回归解混模型结合，建立了考虑光谱差异的稀疏解混模型；最后，基于交替方向乘子法得到了迭代优化解决方案。分别利用仿真和真实高光谱数据进行了试验验证，结果表明，在光谱库不匹配的情形下，本文方法能够有效提高稀疏解混算法的解混性能。

关键词: 高光谱图像, 解混, 稀疏回归, 光谱差异, 光谱库校正

Abstract: Spectral library-based hyperspectral sparse unmixing technology has received attention in recent years, which uses spectral samples in the spectral library as endmembers and transforms the unmixing problem into a sparse representation problem. However, due to differences in the measurement environment, the actual endmembers of the hyperspectral image to be unmixed tend to differ from the corresponding spectral signatures in the spectral library. In this paper, an unmixing algorithm named spectral difference sparse constrained collaborative sparse regression is proposed. Firstly, we assume that the spectral differences have sparse property, and a spectral library correction model is established, which can make the spectral library be adaptively adjusted during the unmixing process; Then, the spectral library correction model is combined with the collaborative sparse regression unmixing model to establish a sparse unmixing model considering spectral differences; Finally, an iterative optimization solution based on the alternating direction method of multipliers is given. Synthetic and real hyperspectral data are used to verify the performance of different algorithms. The results show that the proposed algorithm is more effective than the compared algorithms in the presence of spectral library mismatches.

Key words: hyperspectral image, unmixing, sparse regression, spectral difference, spectral library c orrection

中图分类号:

P237

张作宇, 廖守亿, 孙大为, 张合新, 王仕成. 稀疏差异先验信息支持的高光谱图像稀疏解混算法[J]. 测绘学报, 2020, 49(8): 1032-1041.

ZHANG Zuoyu, LIAO Shouyi, SUN Dawei, ZHANG Hexin, WANG Shicheng. Sparse hyperspectral unmixing algorithm supported by sparse difference prior information[J]. Acta Geodaetica et Cartographica Sinica, 2020, 49(8): 1032-1041.

参考文献

[1] 童庆禧, 张兵, 郑兰芬. 高光谱遥感:原理、技术与应用[M]. 北京:高等教育出版社, 2006. TONG Qingxi, ZHANG Bing, ZHENG Lanfen. Hyperspectral remote sensing[M]. Beijing:Higher Education Press, 2006.
[2] GHAMISI P, YOKOYA N, LI Jun, et al. Advances in hyperspectral image and signal processing:a comprehensive overview of the state of the art[J]. IEEE Geoscience and Remote Sensing Magazine, 2017, 5(4):37-78.
[3] 谷雨, 徐英, 郭宝峰. 融合空谱特征和集成超限学习机的高光谱图像分类[J]. 测绘学报, 2018, 47(9):1238-1249. DOI:10.11947/j.AGCS.2018.20170476. GU Yu, XU Ying, GUO Baofeng. Hyperspectral image classification by combination of spatial-spectral features and ensemble extreme learning machines[J]. Acta Geodaetica et Cartographica Sinica, 2018, 47(9):1238-1249. DOI:10.11947/j.AGCS.2018.20170476.
[4] 黄鸿, 郑新磊. 高光谱影像空-谱协同嵌入的地物分类算法[J]. 测绘学报, 2016, 45(8):964-972. DOI:10.11947/j.AGCS.2016.20150654. HUANG Hong, ZHENG Xinlei. Hyperspectral image land cover classification algorithm based on spatial-spectral coordination embedding[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(8):964-972. DOI:10.11947/j.AGCS.2016.20150654.
[5] 袁静, 章毓晋, 高方平. 线性高光谱解混模型综述[J]. 红外与毫米波学报, 2018, 37(5):553-571. YUAN Jing, ZHANG Yujin, GAO Fangping. An overview on linear hyperspectral unmixing[J]. Journal of Infrared and Millimeter Waves, 2018, 37(5):553-571.
[6] BIOUCAS-DIAS J M, PLAZA A, DOBIGEON N, et al. Hyperspectral unmixing overview:geometrical, statistical, and sparse regression-based approaches[J]. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2012, 5(2):354-379.
[7] MA W K, BIOUCAS-DIAS J M, CHAN T H, et al. A signal processing perspective on hyperspectral unmixing:insights from remote sensing[J]. IEEE Signal Processing Magazine, 2014, 31(1):67-81.
[8] NASCIMENTO J M P, DIAS J M B. Vertex component analysis:a fast algorithm to unmix hyperspectral data[J]. IEEE Transactions on Geoscience and Remote Sensing, 2005, 43(4):898-910.
[9] LI Jun, AGATHOS A, ZAHARIE D, et al. Minimum volume simplex analysis:a fast algorithm for linear hyperspectral unmixing[J]. IEEE Transactions on Geoscience and Remote Sensing, 2015, 53(9):5067-5082.
[10] 袁博. 空间与谱间相关性分析的NMF高光谱解混[J]. 遥感学报, 2018, 22(2):256-276. YUAN Bo. NMF hyperspectral unmixing algorithm combined with spatial and spectral correlation analysis[J]. Journal of Remote Sensing, 2018, 22(2):256-276.
[11] MIAO Lidan, QI Hairong. Endmember extraction from highly mixed data using minimum volume constrained nonnegative matrix factorization[J]. IEEE Transactions on Geoscience and Remote Sensing, 2007, 45(3):765-777.
[12] QIAN Yuntao, JIA Sen, ZHOU Jun, et al. Hyperspectral unmixing via l_1/2 sparsity-constrained nonnegative matrix factorization[J]. IEEE Transactions on Geoscience and Remote Sensing, 2011, 49(11):4282-4297.
[13] WANG Nan, DU Bo, ZHANG Liangpei, et al. An abundance characteristic-based independent component analysis for hyperspectral unmixing[J]. IEEE Transactions on Geoscience and Remote Sensing, 2015, 53(1):416-428.
[14] THEMELIS K E, RONTOGIANNIS A A, KOUTROUMBAS K D. A novel hierarchical bayesian approach for sparse semisupervised hyperspectral unmixing[J]. IEEE Transactions on Signal Processing, 2012, 60(2):585-599.
[15] CLARK R N, SWAYZE G A, WISE R, et al. USGS digital spectral library splib06a[R].[S.l.]:U.S. Geological Survey, 2007.
[16] 许宁, 尤红建, 耿修瑞, 等. 基于光谱相似度量的高光谱图像多任务联合稀疏光谱解混方法[J]. 电子与信息学报, 2016, 38(11):2701-2708. XU Ning, YOU Hongjian, GENG Xiurui, et al. Multi-task jointly sparse spectral unmixing method based on spectral similarity measure of hyperspectral imagery[J]. Journal of Electronics & Information Technology, 2016, 38(11):2701-2708.
[17] 王毓乾. 基于空间-光谱分析的高光谱遥感影像稀疏解混研究[J]. 测绘学报, 2017, 46(8):1072. DOI:10.11947/j.AGCS.2017.20170167. WANG Yuqian. Hyperspectral imagery sparse unmixing based on spatial and spectral analysis[J]. Acta Geodaetica et Cartographica Sinica, 2017, 46(8):1072. DOI:10.11947/j.AGCS.2017.20170167.
[18] BIOUCAS-DIAS J M, FIGUEIREDO M A T. Alternating direction algorithms for constrained sparse regression:Application to hyperspectral unmixing[C]//Proceedings of the 2nd Workshop on Hyperspectral Image and Signal Processing:Evolution in Remote Sensing. Reykjavik:IEEE, 2010.
[19] IORDACHE M D, BIOUCAS-DIAS J M, PLAZA A. Total variation spatial regularization for sparse hyperspectral unmixing[J]. IEEE Transactions on Geoscience and Remote Sensing, 2012, 50(11):4484-4502.
[20] IORDACHE M D, BIOUCAS-DIAS J M, PLAZA A. Collaborative sparse regression for hyperspectral unmixing[J]. IEEE Transactions on Geoscience and Remote Sensing, 2014, 52(1):341-354.
[21] FU Xiao, MA W K, BIOUCAS-DIAS J M, et al. Semiblind hyperspectral unmixing in the presence of spectral library mismatches[J]. IEEE Transactions on Geoscience and Remote Sensing, 2016, 54(9):5171-5184.
[22] WANG Dan, SHI Zhenwei, CUI Xinrui. Robust sparse unmixing for hyperspectral imagery[J]. IEEE Transactions on Geoscience and Remote Sensing, 2018, 56(3):1348-1359.
[23] AFONSO M V, BIOUCAS-DIAS J M, FIGUEIREDO M A T. An augmented lagrangian approach to the constrained optimization formulation of imaging inverse problems[J]. IEEE Transactions on Image Processing, 2011, 20(3):681-695.
[24] WRIGHT S J, NOWAK R D, FIGUEIREDO M A T. Sparse reconstruction by separable approximation[J]. IEEE Transactions on Signal Processing, 2009, 57(7):2479-2493.
[25] CHEN S S, DONOHO D L, SAUNDERS M A. Atomic decomposition by basis pursuit[J]. SIAM Review, 2001, 43(1):129-159.
[26] CLARK R N, SWAYZE G A, LIVO K E, et al. Imaging spectroscopy:earth and planetary remote sensing with the USGS Tetracorder and expert systems[J]. Journal of Geophysical Research:Planets, 2003, 108(E12):5131.
[27] LIN Wenjie, LI Yu, ZHAO Quanhua. High-resolution remote sensing image segmentation using minimum spanning tree tessellation and RHMRF-FCM algorithm[J]. Journal of Geodesy and Geoinformation Science, 2020, 3(1):52-63.