Review of nonlinear unmixing for hyperspectral remote sensing imagery

YANG Bin; WANG Bin

doi:10.11972/j.issn.1001-9014.2017.02.009

[1] Goetz A F H, Vane G, Solomon J E, et al. Imaging spectrometry for earth remote-sensing [J]. Science, 1985, 228(4704): 1147-1153.

[3] Tong Q, Xue Y, Zhang L. Progress in hyperspectral remote sensing science and technology in china over the past three decades [J]. IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens., 2014, 7(1): 70-91.

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

[5] Bioucas-Dias J M, Plaza A, Dobigeon N, et al. Hyperspectral unmixing overview: Geometrical, statistical, and sparse regression-based approaches [J]. IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens., 2012, 5(2): 354-379.

[6] Boardman J W, Kruse F A, Green R O. Mapping target signatures via partial unmixing of AVIRIS data [J]. in Proc. Summ. 5th Annu. JPL Airborne Geosci. Workshop, R. O. Green, Ed, 1995, 1: 23-26.

[7] Winter M E. N-FINDR: An algorithm for fast autonomous spectral endmember determination in hyperspectral data [J].in Proc. SPIE Conf. Imaging Spectrometry V, 1999, 3753: 266-275.

[8] Nascimento J M P, Dias J M B. Vertex component analysis: A fast algorithm to unmix hyperspectral data [J]. IEEE Trans. Geosci. Remote Sens., 2005, 43(4):898-910.

[9] Tao X, Wang B, Zhang L. Orthogonal bases approach for the decomposition of mixed pixels in hyperspectral imagery [J]. IEEE Geosci. Remote Sens. Lett., 2009, 6(2): 219-223.

[10] Heinz D C, Chang C. Fully constrained least squares linear spectral mixture analysis method for material quantification in hyperspectral imagery [J]. IEEE Trans. Geosci. Remote Sens., 2001, 39(3):529-545.

[11] Pu H, Xia W, Wang B, et al. A fully constrained linear spectral unmixing algorithm based on distance geometry [J]. IEEE Trans. Geosci. Remote Sens., 2014, 52(2):1157-1176.

[12] Xia W, Liu X, Wang B, et al. Independent component analysis for blind unmixing of hyperspectral imagery with additional constraints [J]. IEEE Trans. Geosci. Remote Sens., 2011, 49(6):2165-2171.

[13] Lee D D, Seung H S. Learning the parts of objects by nonnegative matrix factorization [J]. Nature, 1999, 401(6755):788-791.

[14] Miao L, Qi H. Endmember extraction from highly mixed data using minimum volume constrained nonnegative matrix factorization [J]. IEEE Trans. Geosci. Remote Sens., 2007, 45(3):765-777.

[15] Yu Y, Guo S, Sun W. Minimum distance constrained nonnegative matrix factorization for the endmember extraction of hyperspectral images [J]. in Proc. SPIE MIPPR 2007: Remote Sensing and GIS Data Processing and Applications, and Innovative Multispectral Technology and Applications, 2007, 6790:151-159.

[16] Wang N, Du B, Zhang L. An endmember dissimilarity constrained non-negative matrix factorization method for hyperspectral unmixing [J]. IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens., 2013, 6(2):554-569.

[17] Schachtner R, P ppel G, Tomé A M, et al. Minimum determinant constraint for non-negative matrix factorization [J]. Lecture Notes in Computer Science, 2009, 5441:106-133.

[18] Jia S, Qian Y. Constrained nonnegative matrix factorization for hyperspectral unmixing [J]. IEEE Trans. Geosci. Remote Sens., 2009, 47(1):161-173.

[19] Liu X, Xia W, Wang B, et al. An approach based on constrained nonnegative matrix factorization to unmix hyperspectral data [J]. IEEE Trans. Geosci. Remote Sens., 2011, 42(9): 757-772.

[20] Hapke B W. Bidirectional reflectance spectroscopy. I. Theory [J]. J. Geophys. Res., 1981, 86:3039-3054.

[21] Dobigeon N, Tourneret J, Richard C, et al. Nonlinear unmixing of hyperspectral images: models and algorithms [J]. IEEE Signal Process. Mag., 2014, 31(1):82-94.

[22] Heylen R, Parente M, Gader P. A review of nonlinear hyperspectral unmixing methods [J]. IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens., 2014,7(6):1844-1868.

[23] Close R, Gader P, Wilson J, et al. Using physics-based macroscopic and microscopic mixture models for hyperspectral pixel unmixing [J]. in Proc. Soc. Photo-Opt. Instrum. Eng. (SPIE), Algorithms Technol. Multispectral Hyperspectral Ultraspectral Imagery XVIII, 2012, 8390: 1-13.

[24] Mustard J F, Pieters C M. Quantitative abundance estimates from bidirectional reflectance measurements [J]. J. Geophys. Res. Solid Earth, 1987, 92:617-626.

[25] Rahman M T, Alam M S. Nonlinear unmixing of hyperspectral data using BDRF and maximum likelihood algorithm [J]. in Proc. Soc. Photo-Opt. Instrum. Eng. (SPIE), Automatic Target Recognition. XVII, 2007, 6566: 1-10.

[27] Close R, Gader P, Zare A, et al. Endmember extraction using the physics-based multi-mixture pixel model [J]. in Proc. Soc. Photo-Opt. Instrum. Eng. (SPIE), Imag. Spectrom. XVII, 2012, 8515: 1-14.

[28] Close R, Gader P, Wilson J. Hyperspectral unmixing using macroscopic and microscopic mixture models [J]. J. Appl. Remote Sens., 2014, 8(1): 1-16.

[29] Heylen R, Gader P. Nonlinear spectral unmixing with a linear mixture of intimate mixtures model [J]. IEEE Geosci. Remote Sens. Lett., 2014, 11(7):1195-1199.

[30] Borel C C, Gerstl S A. Nonlinear spectral unmixing models for vegetative and soil surfaces [J]. Remote Sens. Environ., 1994, 47:403-416.

[31] Ray T W, Murray B C. Nonlinear spectral mixing in desert vegetation [J]. Remote Sens. Environ., 1996, 55(1): 59-64.

[32] Nascimento J M P, Bioucas-Dias J M. Nonlinear mixture model for hyperspectral unmixing [J]. in Proc. Soc. Photo-Opt. Instrum. Eng.(SPIE), Image Signal Process. Remote Sens. XV, 2009, 7477: 1-8.

[33] Altmann Y, Dobigeon N, Tourneret J. Bilinear models for nonlinear unmixing of hyperspectral images[C]. Lisbon: 2011.

[34] Fan W, Hu B, Miller J, et al. Comparative study between a new nonlinear model and common linear model for analysing laboratory simulated forest hyperspectral data [J]. Int. J. Remote Sens., 2009, 30(11): 2951-2962.

[35] Halimi A, Altmann Y, Dobigeon N, et al. Nonlinear unmixing of hyperspectral images using a generalized bilinear model [J]. IEEE Trans. Geosci. Remote Sens., 2011, 49(11): 4153-4162.

[36] Halimi A, Altmann Y, Dobigeon N, et al. Unmixing hyperspectral images using the generalized bilinear model [C]. Vancouver: 2011.

[37] Altmann Y, Halimi A, Dobigeon N, et al. A post nonlinear mixing model for hyperspectral images unmixing [C]. Vancouver: 2011.

[38] Altmann Y, Halimi A, Dobigeon N, et al. Supervised nonlinear spectral unmixing using a post-nonlinear mixing model for hyperspectral imagery [J]. IEEE Trans. Image Process., 2012, 21(6):3017-3025.

[41] Meganem I, Déliot P, Briottet X, et al. Linear quadratic mixing model for reflectances in urban environments [J]. IEEE Trans. Geosci. Remote Sens., 2014, 52(1):544-558.

[42] Somers B, Cools K, Delalieux S, et al. Nonlinear hyperspectral image analysis for tree cover estimates in orchards [J]. Remote Sens. Environ., 2009, 113:1183-1193.

[43] Tits L, Delabastita W, Somers B, et al. First results of quantifying nonlinear mixing effects in heterogeneous forests: A modeling approach [C]. Munich: 2012.

[44] Somers B, Tits L, Coppin P. Quantifying nonlinear spectral mixing in vegetated areas: Computer simulation model validation and first results [J]. IEEE J. Sel. Topics Appl. Earth Observ., 2014, 7(6):1956-1965.

[45] Dobigeon N, Tits L, Somers B, et al. A comparison of nonlinear mixing models for vegetated areas using simulated and real hyperspectral data [J]. IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens., 2014, 7(6): 1869-1878.

[46] Dobigeon N, Tits L, Somers B, et al. Nonlinear unmixing of vegetated areas: a model comparison based on simulated and real hyperspectral data [C]. in Proc. IEEE Int. Workshop Hyperspectral Image Signal Process., 2014:1-4.

[47] Tits L, Delabastita W, Somers B, et al. Validating nonlinear mixing models: benchmark datasets from vegetated areas [C]. in Proc. IEEE Workshop Hyperspectral Image Signal Process. Evol. Remote Sens. (WHISPERS), 2014:1-6.

[48] Heylen R, Scheunders P. A multilinear mixing model for nonlinear spectral unmixing [J]. IEEE Trans. Geosci. Remote Sens., 2015, 54(1):240-251.

[49] Marinoni A, Gamba P. A novel approach for efficient p-linear hyperspectral unmixing [J]. IEEE J. Sel. Signal Process, 2015, 9(6):1156-1168.

[50] Marinoni A, Plaza J, Plaza A, et al. Nonlinear hyperspectral unmixing using nonlinearity order estimation and polytope decomposition [J]. IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens., 2015, 8(6):2644-2654.

[51] Pu H, Chen Z, Wang B, et al. Constrained least squares algorithms for nonlinear unmixing of hyperspectral imagery [J]. IEEE Trans. Geosci. Remote Sens., 2015, 53(3):1287-1303.

[52] Heylen R, Scheunders P, Rangarajan A, et al. Nonlinear unmixing by using different metrics in a linear unmixing chain [J]. IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens., 2014, 8(6): 2655-2664.

[53] Heylen R, Scheunders P. Calculation of geodesic distances in non-linear mixing models: Application to the generalized bilinear model[J]. IEEE Geosci. Remote Sens. Lett., 2012, 9(4):644-648.

[54] Chen X, Chen J, Jia X, et al. A quantitative analysis of virtual endmembers’ increased impact on the collinearity effect in spectral unmixing [J]. IEEE Trans. Geosci. Remote Sens., 2011, 49(8):2945-2956.

[55] Raksuntorn N, Du Q. Nonlinear spectral mixture analysis for hyperspectral imagery in an unknown environment [J]. IEEE Geosci. Remote Sens. Lett., 2010, 7(4):836-840.

[56] Raksuntorn N, Du Q, Younan N, et al. Orthogonal matching pursuit for nonlinear unmixing of hyperspectral imagery [C]. Xi'an: 2014.

[57] Cui J, Li X, Zhao L. Nonlinear spectral mixture analysis by determining per-pixel endmember sets [J]. IEEE Geosci. Remote Sens. Lett., 2014, 11(8):1404-1408.

[58] Chen J, Richard C, Honeine P. Nonlinear estimation of material abundances in hyperspectral images with l1-norm spatial regularization [J]. IEEE Trans. Geosci. Remote Sens., 2013, 52(5):2654-2665.

[59] Chen J, Richard C, Hero A O. Nonlinear unmixing of hyperspectral images using a semiparametric model and spatial regularization[C]. Florence: 2014.

[60] Qu Q, Nasrabadi N M, Tran T D. Abundance estimation for bilinear mixture models via joint sparse and low-rank representation [J]. IEEE Trans. Geosci. Remote Sens., 2014, 52(7):4404-4423.

[61] Altmann Y, Dobigeon N, McLaughlin S, et al. Unsupervised nonlinear unmixing of hyperspectral images using Gaussian processes [C]. Kyoto: 2012.

[62] Altmann Y, Dobigeon N, McLaughlin S, et al. Nonlinear spectral unmixing of hyperspectral images using gaussian processes [J]. IEEE Trans. Signal Process, 2013, 61(10):2442-2453.

[63] Altmann Y, Dobigeon N, Tourneret J. Bayesian unsupervised unmixing of hyperspectral images using a post-nonlinear model [C]. Marrakech: 2013.

[64] Altmann Y, Dobigeon N, Tourneret J. Unsupervised post-nonlinear unmixing of hyperspectral images using a hamiltonian monte carlo algorithm [J]. IEEE Trans. Image Process., 2014, 23(6):2663-2675.

[65] Eches O, Guillaume M. A bilinear-bilinear nonnegative matrix factorization method for hyperspectral unmixing [J]. IEEE Geosci. Remote Sens. Lett., 2014, 11(4):778-782.

[66] Yokoya N, Chanussot J, Iwasaki A. Nonlinear unmixing of hyperspectral data using semi-nonnegative matrix factorization [J]. IEEE Trans. Geosci. Remote Sens., 2014, 52(2):1430-1437.

[67] Taylor J S, Cristianini N. Kernel methods for pattern analysis [M]. England: Cambridge University Press, 2004.

[68] Guilfoyle K J, Althouse M L, Chang C. A quantitative and comparative analysis of linear and nonlinear spectral mixture models using radial basis function neural networks [J]. IEEE Trans. Geosci. Remote Sens., 2001, 39(10):2314-2318.

[69] Plaza J, Martínez P, Péerez R, et al. Nonlinear neural network mixture models for fractional abundance estimation in AVIRIS hyperspectral images [C]. in Proc. AVIRIS Workshop, Pasadena, CA, 2004.

[70] Plaza J, Plaza A, Perez R, et al. On the use of small training sets for neural network-based characterization of mixed pixels in remotely sensed hyperspectral images [J]. Pattern Recogn., 2009, 42(11): 3032-3045.

[71] Altmann Y, Dobigeon N, Tourneret J, et al. Nonlinear unmixing of hyperspectral images using radial basis functions and orthogonal least squares [C]. Vancouver: 2011.

[72] Ayerdi B, Grana M. Hyperspectral image nonlinear unmixing and reconstruction by ELM regression ensemble [J]. Neurocomputing, 2015, 14(2):143-167.

[73] Ayerdi B, Grana M. Hyperspectral image nonlinear unmixing by ensemble ELM regression [J]. in Proc. Adaptation, Learning and Optimization, 2015, 4:289-297.

[74] Liao W, Pizurica A, Philips W, et al. A fast iterative kernel PCA feature extraction for hyperspectral images [C]. Hong Kong:2010.

[75] Zhang L, Wu B, Huang B, et al. Nonlinear estimation of subpixel proportion via kernel least square regression [J]. Int. J. Remote Sens., 2007, 28(18):4157-4172.

[76] Broadwater J, Chellappa R, Banerjee A, et al. Kernel fully constrained least squares abundance estimates [C]. Barcelona: 2007.

[77] Broadwater J, Banerjee A. A comparison of kernel functions for intimate mixture models [C]. Grenoble: 2009.

[78] Broadwater J, Banerjee A. A generalized kernel for areal and intimate mixtures [C]. Reykjavik: 2010.

[79] Broadwater J, Banerjee A. Mapping intimate mixtures using an adaptive kernel-based technique [C]. Lisbon: 2011.

[80] Rand R S. Automated endmember determination and adaptive spectral mixture analysis using kernel methods [J]. Imaging Spectrometry, 2013, 8870:1-17.

[81] Rand R S. Using kernel-based and single-scattering albedo approaches for generalized spectral mixture analysis of hyperspectral imagery [J]. Imaging Spectrometry, 2014, 9222:1-18.

[82] Rand R S, Resmini R G, Allen D W. Characterizing intimate mixtures of materials in hyperspectral imagery with albedo-based and kernel-based approaches [J]. Imaging Spectrometry, 2015, 9611:1-20.

[83] Plaza J, Plaza A, Martinez P, et al. Nonlinear mixture models for analyzing laboratory simulated-forest hyperspectral data [J]. Image and Signal Processing for Remote Sensing, 2004, 5238:480-487.

[86] Chen J, Richard C, Honeine P. Nonlinear unmixing of hyperspectral data with partially linear least-squares support vector regression [C]. Vancouver: 2013.

[87] Wu B, Zhang L, Li P, et al. Nonlinear estimation of hyperspectral mixture pixel proportion based on kernel orthogonal subspace projection [J]. Advances in Neural Networks, 2006, 3971:1070-1075.

[88] Zhao L, Zheng J, Li X, et al. Kernel simplex growing algorithm for hyperspectral endmember extraction [J]. Journal of Applied Remote Sensing, 2014, 8(1):1-15.

[89] Zhao L, Li F, Cui J. An endmember extraction algorithm for hyperspectral imagery based on kernel orthogonal subspace projection [C]. Sichuan: 2012.

[90] Liu K, Wong E, Du E Y, et al. Kernel-based linear spectral mixture analysis [J]. IEEE Geosci. Remote Sens. Lett., 2012, 9(1):129-133.

[91] Zhao L, Fan M, Li X, et al. Fast implementation of linear and nonlinear simplex growing algorithm for hyperspectral endmember extraction [J]. Optik -International Journal for Light and Electron Optics, 2015, 126:1-20.

[92] Chen J, Richard C, Honeine P. A novel kernel-based nonlinear unmixing scheme of hyperspectral images [C]. Pacific Grove: 2011.

[93] Chen J, Richard C, Honeine P. Nonlinear unmixing of hyperspectral data based on a linear mixture/nonlinear-fuctuation model [J]. IEEE Trans. Signal Process, 2013, 61(2):480-492.

[94] Chen J, Richard C, Honeine P. Nonlinear unmixing of hyperspectral images with multi-kernel learning [C]. Shanghai: 2012.

[95] Liu K, Lin Y, Chen C. Linear spectral mixture analysis via multiple-kernel learning for hyperspectral image classification [J]. IEEE Trans. Geosci. Remote Sens., 2015, 53(4):2254-2269.

[96] Gu Y, Wang S, Jia X. Spectral unmixing in multiple-kernel hilbert space for hyperspectral imagery [J]. IEEE Trans. Geosci. Remote Sens., 2013, 51(7):3968-3980.

[98] Dobigeon N, Fevotte C. Robust nonnegative matrix factorization for nonlinear unmixing of hyperspectral images [C]. 5rd Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing, 2013.

[99] Harmeling S, Ziehe A, Kawanabe M, et al. Kernel feature spaces and nonlinear blind source separation [J]. Advances in neural information processing systems, 2002:1-8.

[100] Duong V, Hsieh W, Bao P T, et al. An overview of kernel based nonnegative matrix factorization [C]. Xi’an: 2014.

[101] Zhang D, Zhou Z, Chen S. Non-negative matrix factorization on kernels. 2004.

[102] Wu X, Li X, Zhao L. A kernel spatial complexity-based nonlinear unmixing method of hyperspectral imagery [J]. in Proc. Life Syst. Model. Intell. Comput., 2010, 6330: 451-458.

[103] Fang B, Li Y, Zhang P, et al. Kernel sparse NMF for hyperspectral unmixing [C]. Xi’an: 2014.

[105] Li X, Cui J, Zhao J. Blind nonlinear hyperspectral unmixing based on constrained kernel nonnegative matrix factorization [J]. Signal, Image and Video Processing, 2012, 8(8):1555-1567.

[107] An A, Yun J, Choi S. Multiple kernel nonnegative matrix factorization [C]. Prague: 2011.

[108] Gu Y, Wang Q, Wang H, et al. Multiple kernel learning via low-rank nonnegative matrix factorization for classification of hyperspectral imagery [J]. IEEE J. Sel. Topics Appl. Earth Observ., 2015, 8(6): 2739-2751.

[109] Cui J, Li X, Zhao L. Nonlinear hyperspectral unmixing based on constrained multiple kernel NMF [J]. Satellite Data Compression, Communications, and Processing, 2014, 9124:1-6.

[110] Tenenbaum J B, DeSilva V, Langford J C. A global geometric framework for nonlinear dimensionality reduction [J]. Science, 2000, 290(22): 2319-2323.

[111] Roweis S T, Saul L K. Nonlinear dimensionality reduction by locally linear embedding [J]. Science, 2000, 290(22):2323-2326.

[112] Heylen R, Burazerovic′ D, Scheunders P. Nonlinear spectral unmixing by geodesic simplex volume maximization [J]. IEEE J. Sel. Topics Signal Process., 2011, 5(3):534-542.

[113] Heylen R, Scheunders P. Non-linear fully-constrained spectral unmixing [C]. Vancouver: 2011.

[114] Heylen R, Scheunders P. A distance geometric framework for nonlinear hyperspectral unmixing [J]. IEEE J. Sel. Topics Signal Process., 2014, 7(6):1879-1888.

[115] Chi J, Crawford M M. Selection of landmark points on nonlinear manifolds for spectral unmixing using local homogeneity [J]. IEEE Geosci. Remote Sens. Lett., 2013, 10(4): 711-715.

[116] Chi J, Crawford M M. Active landmark sampling for manifold learning based spectral unmixing [J]. IEEE Geosci. Remote Sens. Lett., 2014, 11(11):1881-1885.

[118] Lu X, Wu H, Yuan Y, et al. Manifold regularized sparse NMF for hyperspectral unmixing [J]. IEEE Trans. Geosci. Remote Sens., 2013, 51(5):2815-2825.

[119] Altmann Y, Dobigeon N, Tourneret J. Detecting nonlinear mixtures in hyperspectral images [C]. Shanghai: 2012.

[120] Altmann Y, Dobigeon N, Tourneret J. Nonlinearity detection in hyperspectral images using a polynomial post-nonlinear mixing model [J]. IEEE Trans. Image Process., 2013, 22(4):1267-1276.

[121] Altmann Y, Dobigeon N, Tourneret J, et al. A robust test for nonlinear mixture detection in hyperspectral images [C]. Vancouver: 2013.

[122] Altmann Y, Dobigeon N, McLaughlin S, et al. Residual component analysis of hyperspectral images: application to joint nonlinear unmixing and nonlinearity detection [J]. IEEE Trans. Image Process, 2014, 23(5): 2148-2158.