融入结构信息的稀疏低秩丰度估计算法研究

丰度估计(AE)是从高光谱图像中识别地物的关键预处理技术.鉴于线性混合模型的可解释性以及数学上的可操作性,带约束的线性回归技术在丰度矩阵估计中备受关注.目前,这类方法存在的缺陷是其拟合过程中仅仅考虑到估计数据与真实数据之间的拟合误差,忽略了估计数据的结构与真实数据的结构之间的相似性信息.因此,提出了融合结构信息的线性回归模型,并应用于稀疏低秩丰度矩阵估计领域.首先,通过增加结构信息改进传统的带约束的线性回归模型,并经数学理论证明了增加结构信息的模型较传统模型更加有效；其次,应用该方法改进稀疏低秩丰度估计的数学模型；最后,采用交替乘子法(ADMM)技术求解新模型.实验结果表明,融入结构信息的稀疏低秩丰度估计算法能够有效地提高仿真数据和实际高光谱数据的丰度估计的估计精度,改善其抗噪性能.

Abstract

Abundance estimation (AE) plays an essential role in the hyperspectral image processing and analysis. Owing to the simplicity and mathematical tractability, various methods based on the constrained linear regression are usually developed to estimate abundance matrix. The obvious limitation of these approaches is that the fitness between the estimated data and ground-truth data does not include the structural information, e.g. row difference and column difference. In this paper, a novel linear regression algorithm is proposed by jointly adding the multi-structured information to the traditional linear regression model. And it is employed to modify sparse and low-rank abundance estimation model to improve estimated accuracy and robustness. Firstly, a new linear regression model is established by taking into account the structural information. Then, mathematical proof of the new linear regression method is presented. Afterwards, it is applied to modify the sparse low-rank abundance estimation model. Finally, Alternating Direction Method of Multipliers(ADMM) technique is adopted to solve the new model. The experimental results demonstrate that the proposed algorithms can capture structural information and improve the estimated performance on the simulated dataset and the real hyperspectral remote sensing images.

参考文献

[1] Keshava N, Mustard J F. Spectral unmixing[J]. IEEE Signal Processing Magazine, 2002, 19(1):44-57.

[2] Smith M O, Johnson P E, Adams J B. Quantitative determination of mineral types and abundances from reflectance spectra using principal components analysis[C]. Lunar and Planetary Science Conference Proceedings,1985:C797-C804.

[3] Adams J B, Smith M O, Johnson P E. Spectral mixture modeling: a new analysis of rock and soil types at the Viking Lander I site [J]. Journal of Geophysical Research Atmospheres, 1986, 91(B8): 8098-8112.

[4] Gillespie A R, Smith M O, Adams J B, et al, Interpretation of residual images: Spectral mixture analysis of AVIRIS images[C]. Proceedings of the 2nd AVIRIS Workshop,1990:243-270.

[5] Vane G, Green R O, Chrien T G, et al. The airborne/infrared imaging spectrometer (AVIRIS)[J], Remote Sensing of Environment, 1993, 44:127-143.

[6] Swayze G, Clark R, Sutley S, et al. Ground-truthing AVIRIS mineral mapping at Cuprite, Nevada[C]// Summaries of the Third Jpl Airborne Geosciences Workshop. 1992.

[7] Green R O, Eastwood M L, Sarture C M, et al. Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS)[J]. Remote Sensing of Environment, 1998, 65(3):227-248.

[8] Shaw G, Manolakis D. Signal processing for hyperspectral image exploitation[J]. IEEE Signal Processing Magazine, 2002, 19(1):12-16.

[9] Landgrebe D. Hyperspectral image data analysis[J]. IEEE Signal Processing Magazine, 2002, 19(1):17-28.

[10] Manolakis D, Shaw G. Detection algorithms for hyperspectral imaging applications[J]. IEEE Signal Processing Magazine, 2002, 19(1):29-43.

[11] Stein D W J, Beaven S G, Hoff L E, et al. Anomaly detection from hyperspectral imagery[J]. IEEE Signal Processing Magazine, 2002, 19(1):58-69.

[12] Lu G, Qin X, Wang D, et al. Estimation of tissue optical parameters with hyperspectral imaging and spectral unmixing[M]. 2015.

[13] Matsuki T, Yokoya N, Iwasaki A. Hyperspectral tree species classification of Japanese complex mixed forest with the aid of lidar data[J]. IEEE Journal of Selected Topics in Applied Earth Observations & Remote Sensing, 2015, 8(5):2177-2187.

[14] Brook A, Dor E B. Quantitative detection of settled dust over green canopy using sparse unmixing of airborne hyperspectral data[J]. IEEE Journal of Selected Topics in Applied Earth Observations & Remote Sensing, 2016, 9(2):884-897.

[15] Alam M S, Sidike P. Trends in oil spill detection via hyperspectral imaging[C]// IEEE International Conference on Electrical & Computer Engineering, 2013:858-862.

[16] Lin H, Zhang X. Retrieving the hydrous minerals on Mars by sparse unmixing and the Hapke model using MRO/CRISM data[J]. Icarus, 2017, 288:160-171.

[17] Baskurt D O, Omruuzun F, Cetin Y Y. Hyperspectral unmixing based analysis of forested areas[C]// IEEE Signal Processing and Communications Applications Conference. 2015:2329-2332.

[18] Das B S, Sarathjith M C, Santra P, et al. Hyperspectral remote sensing: opportunities, status and challenges for rapid soil assessment in India[J]. Current Science, 2015, 108(5):860-868.

[19] Ji C C, Jia Y H, Li X S, et al. Estimation of vegetation coverage of Nitraria tangutorum by linear / non-linear spectral mixing model[J]. Journal of Remote Sensing, 2016.20(6): 1402-1412.

[20] Zhang B, Shen Q, Junsheng L I, et al. Retrieval of three kinds of representative water quality parameters of Lake Taihu from hyperspectral remote sensing data[J]. Journal of Lake Sciences, 2009, 21(2)：182-192.

[21] Rosin P L. Robust pixel unmixing[J]. IEEE Transactions on Geoscience & Remote Sensing, 2001, 39(9):1978-1983.

[22] 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 & Remote Sensing, 2012, 5(2):354-379.

[23] 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.

[24] Feng R, Zhong Y, Zhang L. Adaptive spatial regularization sparse unmixing strategy based on joint MAP for hyperspectral remote sensing imagery[J]. IEEE Journal of Selected Topics in Applied Earth Observations & Remote Sensing, 2016, 9(12):5791-5805.

[25] Iordache M D, Bioucas-Dias J, Plaza A. Unmixing sparse hyperspectral mixtures[C]// IEEE International Geoscience and Remote Sensing ,2009:IV-85 - IV-88.

[26] Candès E J, Romberg J, Tao T. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information[J]. IEEE Transactions on Information Theory, 2006, 52(2):489-509.

[27] Iordache M D, Bioucas-Dias J M, Plaza A. Sparse unmixing of hyperspectral data[J]. IEEE Transactions on Geoscience & Remote Sensing, 2011, 49(6):2014-2039.

[28] Chen F, Zhang Y. Sparse hyperspectral unmixing based on constrained p-2 optimization[J]. IEEE Geoscience & Remote Sensing Letters, 2013, 10(5):1142-1146.

[29] Tang W, Shi Z, Duren Z. Sparse hyperspectral unmixing using an approximate 0 norm[J]. Optik -International Journal for Light and Electron Optics, 2014, 125(1):31-38.

[30] Sun L, Jeon B, Zheng Y, et al. Hyperspectral unmixing based on 2-1 sparsity and total variation[C]// IEEE International Conference on Image Processing. IEEE, 2016:4349-4353.

[31] He W, Zhang H, Zhang L. Hyperspectral unmixing using total variation regularized reweighted sparse non-negative matrix factorization[C]// Geoscience and Remote Sensing Symposium. IEEE, 2016:7034-7037.

[32] 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.

[33] Rontogiannis A, Themelis K, Sykioti O, et al. A fast variational Bayes algorithm for sparse semi-supervised unmixing of OMEGA/Mars Express data[C]// IEEE Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing, 2013.

[34] Zhao Y, Yang J. Hyperspectral image denoising via sparsity and low rank[C]// Geoscience and Remote Sensing Symposium. IEEE, 2014:1091-1094.

[35] Iordache M D, Bioucas-Dias J M, Plaza A. Collaborative sparse regression for hyperspectral unmixing[J]. IEEE Transactions on Geoscience & Remote Sensing, 2014, 52(1):341-354.

[36] Qu Q, Nasrabadi N M, Tran T D. Abundance estimation for bilinear mixture models via joint sparse and low-rank representation[J]. IEEE Transactions on Geoscience & Remote Sensing, 2014, 52(7):4404-4423.

[37] Giampouras P V, Themelis K E, Rontogiannis A A, et al. Simultaneously sparse and low-rank abundance matrix estimation for hyperspectral image unmixing[J]. IEEE Transactions on Geoscience & Remote Sensing, 2016, 54(8):4775-4789.

[38] Richard E, Savalle P A, Vayatis N. Estimation of simultaneously sparse and low rank matrices[J]. Computer Science, 2012.

[39] Oymak S, Jalali A, Fazel M, et al. Simultaneously structured models with application to sparse and low-rank matrices[J]. IEEE Transactions on Information Theory, 2012, 61(5):2886-2908.

[40] Golbabaee M, Vandergheynst P. Compressed sensing of simultaneous low-rank and joint-sparse matrices[J]. Mathematics, 2012, 1-32.

[41] Richard E, Obozinski G, Vert J P. Tight convex relaxations for sparse matrix factorization[J]. Advances in Neural Information Processing Systems, 2014, 4:3284-3292.

[42] Chen L S, Huang J H Z. Sparse reduced-rank regression for simultaneous dimension reduction and variable selection[J]. Journal of the American Statistical Association, 2012, 107(500):1533-1545.

[43] Bach F R. Consistency of trace norm minimization[J]. Journal of Machine Learning Research, 2008, 9(2):2008.

[44] Bioucas-Dias J M, Figueiredo M A T. Alternating direction algorithms for constrained sparse regression: Application to hyperspectral unmixing[C]// The Workshop on Hyperspectral Image & Signal Processing: Evolution in Remote Sensing. IEEE, 2012:1-4.

[45] Negahban S, Wainwright M J. Estimation of (near) low-rank matrices with noise and high-dimensional scaling[J]. Annals of Statistics, 2011, 39(2):1069-1097.

[46] 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.

[47] https://en.wikipedia.org/wiki/Structure. "structure, n.". Oxford English Dictionary (Online ed.). Retrieved 1 October 2015.

[48] Yuan J, Zhang Y J. Application of sparse denoising auto encoder network with gradient difference information for abnormal action detection [J]. Journal of Automatica Sinica, 2017, 43(4):604-610.

[49] Boyd S, Vandenberghe L. Convex optimization[M]. Cambridge University Press, 2004.

[50] Zhang X D, Matrix analysis and applications[M]. Beijing: Tsinghua university press, 2004:44.

[51] Lu C S. Solution of the matrix equation AX+XB = C[J]. Electronics Letters, 1986, 37(4):351-355.

[52] Iordache M D, Bioucas-Dias J M, Plaza A. Total variation spatial regularization for sparse hyperspectral unmixing[J]. IEEE Transactions on Geoscience & Remote Sensing, 2012, 50(11):4484-4502.

[53] Clark R N, Swayze G A, Wise R, et al. U.S Geological Survey Library. splib06b[EB/OL].2007,http://speclab. cr.usgs.gov/spectral.lib06b.

[54] Zhu F, Wang Y, Fan B, et al. Effective spectral unmixing via robust representation and learning-based sparsity[EB/OL]. 2014,http://arxiv.org/abs/1409.0685.

袁静, 章毓晋, 杨德贺. 融入结构信息的稀疏低秩丰度估计算法研究[J]. 红外与毫米波学报, 2018, 37(2): 144. YUAN Jing, ZHANG Yu-Jin, YANG De-He. Sparse and low-rank abundance estimation with structural information[J]. Journal of Infrared and Millimeter Waves, 2018, 37(2): 144.

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