极化SAR图像分类的投影寻踪方法研究
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摘要
极化合成孔径雷达(Synthetic Aperture Radar，简称SAR)以多个极化通道的方式探测地表目标的电磁极化散射特性，获取目标的多维特征以揭示目标的特性。极化SAR图像分类是遥感应用中重要的研究问题。通常，极化SAR图像根据目标物理散射特性分类或者根据统计特性分类。由于地表目标的复杂性和相干波的影响，存在分类精度问题。为此，本文提出了基于投影寻踪和混合Wishart模型的统计方法与散射特性相融合的极化SAR图像分类新方法，其主要内容是：
(1)给出投影寻踪中Cook族投影指标的小波估计，证明了该估计的渐近无偏性及均方收敛性。该估计能精确地估计投影指标，且还避免了逼近投影指标的正交多项式阶的选择和核估计带宽的选择难题，为投影寻踪的实现提供了新的工具。
(2)给出了Cook族投影指标的bootstrap估计，证明了该估计的强相合性，并以此为基础，给出基于Bootstrap样本的拟最佳投影方向和样本选取准则，为投影寻踪的快速实现提供了理论基础。
(3)提出了序列投影寻踪聚类模型及其相应的极化SAR图像无监督分类方法。该方法利用目标的极化散射特性，逐次投影数据到最佳投影方向实现分类。与现在广泛应用的基于散射特性的分类方法不同，该方法可同时利用目标的多个极化散射特性进行分类。实验结果表明，由bootstrap样本选取准则，该方法只需要较少的样本就可寻找到逆最佳投影方向，实现极化SAR图像的快速分类；与直接采用极化散射特性的方法相比，极大改进了分类效果。
(4)提出了投影寻踪子波学习网络。给出基于该网络的光学图像的无监督恢复方法，避免了光学图像恢复中求点扩展函数这一难点。给出基于该网络的极化SAR图像分类方法，和美国海军研究实验室Lee提出的Wishart方法相比，该方法避免了对极化SAR数据进行滤波预处理的这一步骤。实验结果表明，该方法在相同条件下对于复杂地形区域的分类具有较好的分类效果。
(5)提出了混合Wishart模型及其相应的多视极化SAR数据的无监督分类方法。该方法无需知道极化SAR图像中各类的先验信息就可分类图像。实验结果表明，该方法对于具有大面积匀质区域的分类结果明显优于Wishart分类方法。
(6)综合比较典型的极化SAR图像分类方法和本文提出的序列投影寻踪聚类模型、投影寻踪子波学习网络和混合Wishart模型三种分类方法。给出了本文三种分类方法的优缺点以及适用性。
The POLarimetric Synthetic Aperture Radar (POLSAR) measures the scatteringecho of a target in different polarimetric modes and obtains the object'shigh-dimensional characteristics to describe the objection. A classification ofPOLSAR image is an important research of remote senseing application. Usually,POLSAR image is classified by physical emitting features or by statisticcharacteristics. Due to the complexity of the objection of the earth's surface and theeffect of coherent echo, there is certain classification precision problem, Therefore,based on the scattering characteristics of the objection, this thesis presents newstatistical classification methods of POLSAR image, named the Sequential ProjectionPursuit Cluster-Model (SPPCM), Projection Pursuit Wavelet Learning Network(PPWLN) and Mixture Wishart Model (MWM). These methods combine thescattering characteristics of the objections of the POLSAR. The details of this thesisare as followings:
(1)A wavelet-kernel estimation of the Cook Family projection index is proposed.And its asymptotic unbiasedness and the convergence in mean squared are proved.Compare with the estimation of Cook Family projection index based on theorthogonal polynomial or the kernel function, wavelet-kernel estimation not onlyestimates precisely the projection index, but also bypasses the difficult problem of theselection of the order of orthogonal polynomial or the selection of the bandwidth ofkernel function. It provides a new tool for fulfilling projection pursuit method.
(2)Bootstrap estimation of the Cook Family projection index is proposed andstrong consistent of this estimation is proved. Based on bootstrap estimation, rules ofsample selection and quasi-optimal projection direction are defined in order to providea theory foundation for fast fulfillment of projection pursuit.
(3)The unsupervised classification method of POLSAR image, based on theSPPCM, is proposed. By using the scattering characteristics of the objection, thismethod projects data to the optimal direction to classify POLSAR image time aftertime. Unlike the current classification methods based on the scattering characteristic,this method can simultaneously makes use of multi-dimensional characteristics of theobjection to classify POLSAR image. Experimental results show that the quasi-optimal projection direction car be found with a few bootstrap samples,fulfilling the fast classification of POLSAR image. The classification results aregreatly improved.
(4)The unsupervised restoring method of optical images is proposed by usingPPWLN. PPWLN trains the network by approximating degradation factors so as tobypass the difficult task of estimating point-spread function when little is knownabout degradation factors. The supervised classification method of POLSAR image isproposed by using the PPWLN. Compare with the Wishart classifier proposed byLee, U.S. Navy Lab, this method can avoid the procedure of filter POLSAR data. Theexperiment results show that this method has the better behavior of classifying targetswith complex characteristics comparing with the Wishart classifier under sameconditions.
(5) The unsupervised classification method of POLSAR image, based on MWM,is proposed. This method directly classify POLSAR image without prior information.The experimental results show that this method is obviously superior to the Wishartclassifier on classifying targets with large homogeneous area.
(6)The typical classification methods of the POLSAR image and our methods arecompared and analyzed. The strongpoint and shortcomings of our methods and theapplicability of our methods are analyzed.
(1)给出投影寻踪中Cook族投影指标的小波估计，证明了该估计的渐近无偏性及均方收敛性。该估计能精确地估计投影指标，且还避免了逼近投影指标的正交多项式阶的选择和核估计带宽的选择难题，为投影寻踪的实现提供了新的工具。
(2)给出了Cook族投影指标的bootstrap估计，证明了该估计的强相合性，并以此为基础，给出基于Bootstrap样本的拟最佳投影方向和样本选取准则，为投影寻踪的快速实现提供了理论基础。
(3)提出了序列投影寻踪聚类模型及其相应的极化SAR图像无监督分类方法。该方法利用目标的极化散射特性，逐次投影数据到最佳投影方向实现分类。与现在广泛应用的基于散射特性的分类方法不同，该方法可同时利用目标的多个极化散射特性进行分类。实验结果表明，由bootstrap样本选取准则，该方法只需要较少的样本就可寻找到逆最佳投影方向，实现极化SAR图像的快速分类；与直接采用极化散射特性的方法相比，极大改进了分类效果。
(4)提出了投影寻踪子波学习网络。给出基于该网络的光学图像的无监督恢复方法，避免了光学图像恢复中求点扩展函数这一难点。给出基于该网络的极化SAR图像分类方法，和美国海军研究实验室Lee提出的Wishart方法相比，该方法避免了对极化SAR数据进行滤波预处理的这一步骤。实验结果表明，该方法在相同条件下对于复杂地形区域的分类具有较好的分类效果。
(5)提出了混合Wishart模型及其相应的多视极化SAR数据的无监督分类方法。该方法无需知道极化SAR图像中各类的先验信息就可分类图像。实验结果表明，该方法对于具有大面积匀质区域的分类结果明显优于Wishart分类方法。
(6)综合比较典型的极化SAR图像分类方法和本文提出的序列投影寻踪聚类模型、投影寻踪子波学习网络和混合Wishart模型三种分类方法。给出了本文三种分类方法的优缺点以及适用性。
The POLarimetric Synthetic Aperture Radar (POLSAR) measures the scatteringecho of a target in different polarimetric modes and obtains the object'shigh-dimensional characteristics to describe the objection. A classification ofPOLSAR image is an important research of remote senseing application. Usually,POLSAR image is classified by physical emitting features or by statisticcharacteristics. Due to the complexity of the objection of the earth's surface and theeffect of coherent echo, there is certain classification precision problem, Therefore,based on the scattering characteristics of the objection, this thesis presents newstatistical classification methods of POLSAR image, named the Sequential ProjectionPursuit Cluster-Model (SPPCM), Projection Pursuit Wavelet Learning Network(PPWLN) and Mixture Wishart Model (MWM). These methods combine thescattering characteristics of the objections of the POLSAR. The details of this thesisare as followings:
(1)A wavelet-kernel estimation of the Cook Family projection index is proposed.And its asymptotic unbiasedness and the convergence in mean squared are proved.Compare with the estimation of Cook Family projection index based on theorthogonal polynomial or the kernel function, wavelet-kernel estimation not onlyestimates precisely the projection index, but also bypasses the difficult problem of theselection of the order of orthogonal polynomial or the selection of the bandwidth ofkernel function. It provides a new tool for fulfilling projection pursuit method.
(2)Bootstrap estimation of the Cook Family projection index is proposed andstrong consistent of this estimation is proved. Based on bootstrap estimation, rules ofsample selection and quasi-optimal projection direction are defined in order to providea theory foundation for fast fulfillment of projection pursuit.
(3)The unsupervised classification method of POLSAR image, based on theSPPCM, is proposed. By using the scattering characteristics of the objection, thismethod projects data to the optimal direction to classify POLSAR image time aftertime. Unlike the current classification methods based on the scattering characteristic,this method can simultaneously makes use of multi-dimensional characteristics of theobjection to classify POLSAR image. Experimental results show that the quasi-optimal projection direction car be found with a few bootstrap samples,fulfilling the fast classification of POLSAR image. The classification results aregreatly improved.
(4)The unsupervised restoring method of optical images is proposed by usingPPWLN. PPWLN trains the network by approximating degradation factors so as tobypass the difficult task of estimating point-spread function when little is knownabout degradation factors. The supervised classification method of POLSAR image isproposed by using the PPWLN. Compare with the Wishart classifier proposed byLee, U.S. Navy Lab, this method can avoid the procedure of filter POLSAR data. Theexperiment results show that this method has the better behavior of classifying targetswith complex characteristics comparing with the Wishart classifier under sameconditions.
(5) The unsupervised classification method of POLSAR image, based on MWM,is proposed. This method directly classify POLSAR image without prior information.The experimental results show that this method is obviously superior to the Wishartclassifier on classifying targets with large homogeneous area.
(6)The typical classification methods of the POLSAR image and our methods arecompared and analyzed. The strongpoint and shortcomings of our methods and theapplicability of our methods are analyzed.
引文
[1] Henri Maitre编．合成孔径雷达图像处理．电子工业出版社．北京，2005．2．
[2] 董庆，郭华东编．合成孔径雷达海洋遥感．科学出版社．北京，2005．
[3] 庄钊文，肖顺平，王雪松著．雷达极化信息处理及其应用．国防工业出版社，北京．1999．
[4] W. M. Boemer. Recent advances in polarimetric-interferometric SAR theory & technology and its application. 212-229
[5] J. R. Huynen. Phenomenological theory of radar targets [D]. Ph. D. Dissertation, Drukkeriz Bronder-Offsets, N. V.Rotterdam, 1970.
[6] S. R. Cloude. Target decompositions in radar scattering. Electron. Letters, 1985, 21(1): 22-24
[7] E. Krogager. New decomposition of the radar target scattering matrix [J]. Electronics Letters, 1990, 26(18): 1525-1527
[8] S. R. Cloude and E. Pottier. The concept of polarization entropy in optical scattering. Opt. Eng., ISSN 0091-3286, 34(6): 1599-1610
[9] J. Yang, Y. N. Peng, and S. M. Lin. Similarity between two scattering matrices [J]. Electron. Lett., 2001, 37 (3): 193-194.
[10] Goodman, N. R. Statistical analysis based on a certain multivariate complex Gaussian distribution (An Introduction). Annals of Mathematical Statistics, 34, 152-177
[11] J. W. Goodman. Statistical optics. Wiley, New York, 1985.
[12] J. S. Lee, et al. Intensity and phase statistics of multi-look polarimetric and interferometric SAR imagery. IEEE Trans. Geos. Remote Sensing, 1994, 32(5): 1017-1028
[13] E. Rignot, R. Chellappa, and P. Dubois. Unsupervised segmentation of polarimetric SAR data using the covariance matrix. IEEE Trans. Geosci. Remote Sensing, 1992, 30: 697-705
[14] L. J. Du, J. S. Lee, K. Hoppel, and S. A. Mango. Segmentation of SAR image using the wavelet transforms. Int. J. Image. Syst. Technol., 1992, 4: 319-329
[15]Y.Hara, R.GAtkins, et al. Application of neural networks to radar image classification. IEEE Trans. Geosci. Remote Sensing, 1994, 32:100-110
[16] J.R.Huynen. Target decomposition theorem for real target polarimetric data analysis. International Conference on Radar, Paris, 1989
[17]W.L. Cameron, L.K. Leung. Feature motivated polarization scattering matrix decomposition. International Conference On Radar, 1990.
[18]J.J.Van Zyl.Unsupervised classification of scattering behavior using radar polarimetry data. IEEE Trans. Geos. Remote Sensing, 1989,27: 36-44
[19] Y.Yamaguchi, T.Moriyama, et al. Four-component scattering model for polarimetric SAR image decomposition. IEEE Trans. Geos. Remote Sensing, 2005,43(8): 1699-1706
[20] Y.Yamaguchi, Y.Yajima, and H.Yamada. A four-component decomposition of POLSAR images based on the coherency matrix. IEEE Geos. Remote Sensing Lett. , 2006, 3(3): 292-296
[21] E.Rignot and R.Chellappa. Segmentation of polarimetric synthetic aperture radar data. IEEE Trans. Image Proc, 1992,1(3): 281-300
[22] S.R.Cloude. Uniqueness of target decomposition theorems in radar polarimetry. Direct and Inverse Methods in Radar Polarimetry. Part 1, NATO-ARW, W.M.Boerner et al., Eds. New York: Kluwer Academic, 1992, 267-296
[23] S.R.Cloude and E.Pottier. A review of target decomposition theorems in radar polarimetry. IEEE Trans. Geos. Remote Sensing, 1996,34(2): 498-518
[24] Cloude, S.R. et al. An entropy based classification scheme for land applications of polarimetric SAR. IEEE Trans. Geos. Remote Sensing, 1997,35(1): 68-78
[25] J.Y.Xu, J.Yang, Y.N.Peng, and C.Wang.Using similarity parameters for supervised polarimetric SAR image classification. IEICE Trans. Commun, 2002, VOL.E85-B (12): 2934-2942
[26] 徐俊毅,杨健,彭应宁．双波段极化雷达遥感图像分类的新方法．中国科学E辑,2005,35(10)：1083-1095
[27] M. Ouarzeddine, B.Souissi, and A.B.Aissa. Target detection and characterization using H/alpha decomposition and polarimetric signatures. IEEE conference, 2006: 395-340
[28] E. Pottier and J.S. Lee. Application of the H/A/α polarimetric decomposition theorem for unsupervised classification of fully polarimetric SAR data based on the Wishart distribution [C]. European Space Agency, (Special Publication) ESA SP, 2000: 335-340
[29] J. Praks and M. Hallikainen. An alternative for entropy-alpha classification for polarimetric SAR image. 2000
[30] S. E. Park and W. M. Moon. Classification of the polarimetric SAR using fuzzy boundaries in entropy and alpha plane. IEEE conference, 2005: 5517-5519
[31] Y. Q. Jin and F. Chen. Polarimetric scattering indexes and information entropy of the SAR imagery for surface monitoring. IEEE Trans. Geos. Remote Sensing, 2002, 40(11): 2502-2506
[32] 金亚秋，陈扉．SAR图像中极化散射指数和信息熵及其地表识别应用．自然科学进展，2003，13(2)：174-178
[33] S. Fukuda. Relating polarimetric SAR image texture to the scattering entropy. IEEE conference, 2004: 2475-2478
[34] 陈体刚，李彦佐．全极化SAR图像中相干矩阵特征值及其应用．信息与电子工程，2005，3(3)：161-166
[35] C. L. Martinez, E. Pottier, and S. R. Cloude. Statistical assessment of eigenvector-based target decomposition theorems in radar polarimetry. IEEE Trans. Geos. Remote Sensing, 2005, 43(9): 2058-2074
[36] J. S. Lee, M. R. Grunes, et al. Unsupervised classification using polarimetric decomposition and the complex Wishart classifier. IEEE Trans. Geos. Remote Sensing, 1999, 37(5): 2249-2258
[37] H. A. Yueh, A. A. Swarta, J. A. Kong, et al. Bayes classification of terrain cover using normalized polarimetric data. J.Geophys. Res., B, 1988, 93: 15261-15267
[38] 王之禹，朱敏慧，白有天．基于最优状态的多波段全极化SAR数据ML分类方法[J]．电子与信息学报，2001，(5)：507-511
[39] L. Du and J. S. Lee. Fuzzy classification of earth terrain covers using complex polarimetric SAR data [J]. International of Journal of Remote Sensing, 1996, 17(4): 809-826.
[40] C. T. Chen, K. S, Chen, and J. S. Lee. The use of fully polarimetric information for the fuzzy neural classification of SAR images. IEEE Trans Geos. Remote Sensing, 2003, 41 (9): 2089-2100
[41] K. S. Chen et al. Classification of multifrequency polarimetric SAR image using a dynamic learning neural network [J]. IEEE Trans. Geosci. Remote Sensing, 1996, 34: 814-820.
[42] Y. C.Tzeng and K. S. Chen. A fuzzy neural network to SAR image classification. IEEE Trans. Geos. Remo. Sens., 1998, 36(1): 301-307
[43] J. J. Van Zyl, et al. Bayesian classification of polarimetric SAR images using adaptive a priori probabilities [J]. International of Journal of Remote Sensing, 1992, 13(5): 835-840.
[44] J. S. Lee and M. R. Grunes. Classification of multi-look polarimetric SAR imagery based on complex Wishart distribution. Int. J. Remote Sensing, 1994, 15(11): 2299-2311
[45] J. S. Lee, M. Grunes, and G. deGrandi. Polarimetric SAR speckle filtering and its implication for classification. IEEE Trans. Geos. Remote Sensing, 1999, 37(5): 2363-2373
[46] Kconradsen et al. A test statistic in the complex Wishart distribution and its application to change detection in polarimetric SAR data. IEEE Trans. Geos. Remote Sensing, 2003, 41 (1): 4-19
[47] J. S. Lee, et al. Unsupervised terrain classification preserving polarimetric scattering characteristics. IEEE Trans. Geos. Remote Sensing, 2004, 42(4): 722-731
[48] P. R. Kersten et al. Unsupervised classification of polarimetric synthetic aperture radar images using fuzzy clustering and EM clustering. IEEE Trans. Geos. Remote Sensing, 2005, 43(3): 519—527
[49] J. M. Beaulieu and R. Touzi. Segmentation of textured polarimetric SAR scenes by likelihood approximation. IEEE Trans. Geos. Remote Sensing, 2004, 42(10): 2063-2072
[50] 杨震，杨汝良，刘秀清．SAR图像的极化干涉非监督Wishart分类方法和实验研究．电子与信息学报，2004，26(5)：752-759
[51] L. M. Novak and M. C. Burl. Optimal speckle reduction in polarimetric SAR imagery. IEEE Trans. Aerosp. Electron. Syst., 1990, 26: 293-305
[52] L. M. Novak, M. C. Burl, and W. W. Irving. Optimal polarimetric processing for enhanced target detection. IEEE AES, 1993, 29:234-243
[53] J.S.Lee, M.R.Grunes, and S.A.Mango. Speckle reduction in multipolarization multifrequehcy SAR imagery. IEEE Trans. GRS., 1991,29(4): 535-544
[54] J.S.Lee et al. Speckle filtering of synthetic aperture radar images: a review [J]. Remote Sensing Review, 1994, 8(30): 313-340
[55] J.S.Lee, M.R.Grunes, et al. Scattering-model-based speckle filtering of polarimetric SAR data. IEEE Trans. Geos. Remote Sensing, 2006,44(1): 176-187
[56] J.W.Goodman.Some fundamental properties of speckle. J.Opt.Soc.Amer., 1976,66(11):1145-1150,.
[57] GQ.Liu, S.J.Huang, A.Torre, and F.Rubertone. The multilook polarimetric whitening filter (MPWF) for intensity speckle reduction in polarimetric SAR images. IEEE Trans. GRS, 1998,36:1016-1020
[58] J.B.Kruskal. Toward a practical method which helps uncover the structure of a set of multivariate observations by finding the linear transformation which optimizes a new 'index of condesation'. Statistical Computation (R. C. Milton and J. A. Nelder, editors). New York, Academic Press, 1969
[59] J.B.Kruskal. Linear transformations of multivariate data to reveal clustering. In Multidimensional Scaling: Theory and application in the behavioural sciences, part I: theory. Seminar Press, New York and London, 1972
[60] J.H. Friedman and J.W.Tukey. A projection pursuit algorithm for exploratory data analysis. IEEE Trans. Comput., 1974, Vol.23: 881-889
[61] J.H Friedman and W.Stuetzle. A projection pursuit regression. J. Amer. Statist. Assoc, 1981,76:817-823
[62] M.C.Jones. The projection pursuit algorithm for exploratory data analysis. PhD Thesis, University of Bath, 1983
[63] J.H. Friedman, W. Stuetzle and A. Schroeder. Projection pursuit density estimation. J. Amer. Statist. Assoc, 1984, 79:599-608
[64] P. H. Hurber. Projection pursuit. Ann. Statist., 1985,13(2): 435-475
[65] Z.Chen and GLi. Robust principal components and dispersion matrix via projection pursuit. Research Report PJH-8 Dept. of Statistics, Harvard Univ., 1981
[66] GLi and Z.Chen. Projection pursuit approach to robust dispersion matrices and principal components. Primary theory and Monte-Carlo. J. Amer. Stat. Assoc, 1985, 80 (391): 759-766
[67] D. Donoho. Minimum entropy deconvolution. D.Findley editor, Applied time series analysis II, 1981
[68] D. Donoho. Breakdown properties of multivaritate location estimation. Ph.D. Qualifying Paper, Dept. of Statistics, Harvard Univ., 1982
[69] J.H Friedman and J.W.Tukey. Exploratory projection pursuit. J.Amer. Statist. Assoc, 1982, 82(397): 249-266
[70] M.C.Jones and R. Sibson. What is projection pursuit? (With discussion). J. Roy. Statist. Ser. A, 1987, 150:29-30
[71] P. Hall. On polynomial-based projection indices for exploratory projection pursuit. Ann. Statist., 1989, 17(2): 589-605
[72] G P.Nason. Design and choice of projection indices. Ph.D thesis, University of Bath, 1992
[73] D. Cook, A. Buja, and J. Cabrera. Projection pursuit indices based on expansions with orthonormal functions. Journal of Computational and Graphical Statistics, 1993,2(3): 225-250
[74] GP.Nason. Robust projection indecs. Technical Report 05, Department of Mathematics, University of Bristol, 2000
[75] E.K.Lee, D.Cook, et al. Projection pursuit for exploratory supervised classification. Journal of Computational and Graphical Statistics, 2005, 14(4): 831-846
[76] Andreas Krause and Volkmar Liebscher. Projection pursuit using the dip statistic. 2005
[77] GP.Nason and R.Sibson. Using projection pursuit in multispectral image analysis. In Elaine M.Keramidas editor, Proceedings of the 23rd Symposium on the Interface, VA 22039-7460,1991: 579-582
[78] Leng-Neng Hwang, et al. Regression modeling in back-propagation and projection pursuit learning. IEEE Transactions on Neural Networks, 1994, 5(3): 342-353
[79] C. M. Bachmann, et al. Dynamically reconfigurable projection pursuit ensemble for cloud detection in AVIRIS Imagery. Geoscience and Remote Sensing Symposium on Quantitative Remote Sensing for Science and Applications, 1995, part 1: 256-259
[80] M.M.Van Hulle. Nonparametric regression analysis achieved with topographic maps developed in combination with projection pursuit leaning. IEEE Trans.Signal Processing, 1997,4(5): 117-120
[81] S.R.Safavian,H.R.Rabiee, and M.Fardanesh. Projection pursuit image compression with variable block size segmentation. IEEE Sig. Proc. Lett., 1997,4(5): 117-120
[82] S. S. Chiang et al. Unsupervised target detection in hyperspectral images using projection pursuit. IEEE Trans. Geoscience and Remote Sensing, 2001, 39(7):
[83] D.B Triza, C.M.Bachmann, et.al. Projection pursuit classification of multiband polarimetric SAR land image. IEEE Trans. Geosci. Remote sensing, 2001, 39:2380-2386
[84] Shah, C.A., Arora, M.K., Robila, S.A., and Varshney, P.K.: ICA mixture model based unsupervised classification of hyperspectral imagery. Proc. 31st Applied Imagery Pattern Recognition Workshop, 2002:
[85] Corchado, E., Koetsier, J., Macdonald, D., and Fyfe, C: Classification and ICA using maximum likelihood hebbian learning. International conference of IEEE, 2002:327-336
[86] S.GMallat. Multiresolution approximations and wavelet orthonormal bases of L2 (R). Trans. Amer. Math. Soc, 1989, 315:69-87
[87] S.GMallat. A theory for multiresolution signal decomposition: The wavelet representation. IEEE Trans. Patt. Anal. Mach. Intell, 1989, 11(7): 674-693
[88] B.Efron. Bootstrap methods: another look at the jackknife [J]. Ann. Statistics, 1979,7(1):1-26.
[89] Brani Vidakovic. Statistics Modeling by Wavelets [M]. John Wiley and Sons, New York. 1999.
[90] W. Hardle, G. Kerkyacharian, D. Pickard, A. Tsybakov. Wavelets, Approximation and Statistical Applications. Lecture Notes in Statistics 129, Springer, 1998.
[91] P.Hall. The bootstrap and edgeworth expansion. Springer-Verlag, New York, 1992.
[92] M.Zribi. Non-parametric and unsupervised Bayesian classification with bootstrap sampling. Image and Vision computing, 2004, 22:1-8
[93] J. Shao and D.Tu. The jackknife and bootstrap. Springer-Verlag, New York. 1995.
[94] A. C. Davison, D. V. Hinkley. Bootstrap and their application. Cambridge University Press, Cambridge. 1997.
[95] A. Sakov and P. J. Bickel. An edgeworth expansion for the m out of n bootstrapped median. Statistics & Probability Letters, 2000, 49:217-223
[96] A. Sakov. Using the m out of n bootstrap in hypothesis testing. Ph. D. Thesis, University of California, Berkeley. 1998.
[97] A. Lopes et ai. Structure Detection and Statistical Adaptive Speckle Filtering in SAR images [J]. Int. J. Remote Sensing, 1993, 4(9): 1735～1758
[98] J. Romberg et al. Bayesian tree-structured image modeling using waelet-domain hidden markov models [J]. IEEE Transactions on Image Processing, 2001, 10(7): 1056-1067.
[99] 郭小卫，田铮，林伟．基于Markov四义树模型的无监督图像分割．计算机科学，2005，32(2)：219-223
[100] 郭小卫，田铮，林伟，熊毅．多尺度Markov模型的可适应图像分割方法．电子学报，2005，33(7)：1279-1283
[101] Y. Ito and S. Omatu. Gategory classification method using a self-organizing neural network [J]. Int. J. Remote Sensing., 1997, 18(4): 829-845.
[102] Y. Hara, R. G. Atkins, S. H. Yueh, et al. Application of neural networks to radar image classification. IEEE Trans. Geosci. Remote Sensing, 1994, 32: 100-110
[103] X. B. Wen and Z. Tian. Mixture multiscale autoregressive modeling of SAR imagery for segmentation [J]. Electronics Letters of IEE, 2003, 39: 1272-1274.
[104] Tian, Z., Wen, X. B, and Lin, W. Multiscale segmentation of SAR imagery with bootstrap sampling. 7th International conference on signal processing proceedings, 2004, 713-716
[105] 宋立新，崔景泉．一类特殊PP回归模型的估计．吉林大学自然科学学报，1995，4：5-13．
[106] M. Maechler, D. Martin, J. Schimert, et al. Projection pursuit learning networks for regression. IEEE international conference 1990: 350-358
[107] Q. Zhang and A. Benveniste. Wavelet Networks [J]. IEEE Trans Neural Networks, 1992, 3:889-898
[108] 焦李成，侯彪，刘芳．基函数网络逼近：进展与展望．工程数学学报，2002，19(1)：21-36
[109] 彭祖赠，孙韫玉编．模糊(Fuzzy)数学及其应用．武汉大学出版社，武汉．2002．
[110] 张尧庭，方开泰著．多元统计分析．科学出版社，北京，1982．
[111] 刘会山．Wishart分布引论．科学出版社，北京，2005．
[112] 茆诗松，王静龙，濮晓龙．高等数理统计．高等教育出版社，施普林格出版社，北京，1998．
[113] G. Soromenho. Comparing approaches for testing the number of components in a finite mixture model. Computational statistics, 1993, 9, 65-78
[114] G. Celeux and G. Soromenho. An entropy-criterion for assessing the number of clusters in a mixture model. Classification Journal, 1996, 13: 195-211
[115] M. Ishiguro, Y. Sakamoto, and G. Kitagawa. Bootstrapping log-likelihood and EIC, an extension of AIC. Annals of the institute of Statistical mathematics, 1997, 49: 411-434
[116] C. Biernacki, G. Celeux, and G. Govaert. An improvement of the NEC criterion for assessing the number of clusters in a mixture model. Pattern Recognition Letters, 1999, 20:267-272
[117] G. Mclachlan and D. Peel. Finite mixture models. John Wiley & Sons, New York, 2000.
[2] 董庆，郭华东编．合成孔径雷达海洋遥感．科学出版社．北京，2005．
[3] 庄钊文，肖顺平，王雪松著．雷达极化信息处理及其应用．国防工业出版社，北京．1999．
[4] W. M. Boemer. Recent advances in polarimetric-interferometric SAR theory & technology and its application. 212-229
[5] J. R. Huynen. Phenomenological theory of radar targets [D]. Ph. D. Dissertation, Drukkeriz Bronder-Offsets, N. V.Rotterdam, 1970.
[6] S. R. Cloude. Target decompositions in radar scattering. Electron. Letters, 1985, 21(1): 22-24
[7] E. Krogager. New decomposition of the radar target scattering matrix [J]. Electronics Letters, 1990, 26(18): 1525-1527
[8] S. R. Cloude and E. Pottier. The concept of polarization entropy in optical scattering. Opt. Eng., ISSN 0091-3286, 34(6): 1599-1610
[9] J. Yang, Y. N. Peng, and S. M. Lin. Similarity between two scattering matrices [J]. Electron. Lett., 2001, 37 (3): 193-194.
[10] Goodman, N. R. Statistical analysis based on a certain multivariate complex Gaussian distribution (An Introduction). Annals of Mathematical Statistics, 34, 152-177
[11] J. W. Goodman. Statistical optics. Wiley, New York, 1985.
[12] J. S. Lee, et al. Intensity and phase statistics of multi-look polarimetric and interferometric SAR imagery. IEEE Trans. Geos. Remote Sensing, 1994, 32(5): 1017-1028
[13] E. Rignot, R. Chellappa, and P. Dubois. Unsupervised segmentation of polarimetric SAR data using the covariance matrix. IEEE Trans. Geosci. Remote Sensing, 1992, 30: 697-705
[14] L. J. Du, J. S. Lee, K. Hoppel, and S. A. Mango. Segmentation of SAR image using the wavelet transforms. Int. J. Image. Syst. Technol., 1992, 4: 319-329
[15]Y.Hara, R.GAtkins, et al. Application of neural networks to radar image classification. IEEE Trans. Geosci. Remote Sensing, 1994, 32:100-110
[16] J.R.Huynen. Target decomposition theorem for real target polarimetric data analysis. International Conference on Radar, Paris, 1989
[17]W.L. Cameron, L.K. Leung. Feature motivated polarization scattering matrix decomposition. International Conference On Radar, 1990.
[18]J.J.Van Zyl.Unsupervised classification of scattering behavior using radar polarimetry data. IEEE Trans. Geos. Remote Sensing, 1989,27: 36-44
[19] Y.Yamaguchi, T.Moriyama, et al. Four-component scattering model for polarimetric SAR image decomposition. IEEE Trans. Geos. Remote Sensing, 2005,43(8): 1699-1706
[20] Y.Yamaguchi, Y.Yajima, and H.Yamada. A four-component decomposition of POLSAR images based on the coherency matrix. IEEE Geos. Remote Sensing Lett. , 2006, 3(3): 292-296
[21] E.Rignot and R.Chellappa. Segmentation of polarimetric synthetic aperture radar data. IEEE Trans. Image Proc, 1992,1(3): 281-300
[22] S.R.Cloude. Uniqueness of target decomposition theorems in radar polarimetry. Direct and Inverse Methods in Radar Polarimetry. Part 1, NATO-ARW, W.M.Boerner et al., Eds. New York: Kluwer Academic, 1992, 267-296
[23] S.R.Cloude and E.Pottier. A review of target decomposition theorems in radar polarimetry. IEEE Trans. Geos. Remote Sensing, 1996,34(2): 498-518
[24] Cloude, S.R. et al. An entropy based classification scheme for land applications of polarimetric SAR. IEEE Trans. Geos. Remote Sensing, 1997,35(1): 68-78
[25] J.Y.Xu, J.Yang, Y.N.Peng, and C.Wang.Using similarity parameters for supervised polarimetric SAR image classification. IEICE Trans. Commun, 2002, VOL.E85-B (12): 2934-2942
[26] 徐俊毅,杨健,彭应宁．双波段极化雷达遥感图像分类的新方法．中国科学E辑,2005,35(10)：1083-1095
[27] M. Ouarzeddine, B.Souissi, and A.B.Aissa. Target detection and characterization using H/alpha decomposition and polarimetric signatures. IEEE conference, 2006: 395-340
[28] E. Pottier and J.S. Lee. Application of the H/A/α polarimetric decomposition theorem for unsupervised classification of fully polarimetric SAR data based on the Wishart distribution [C]. European Space Agency, (Special Publication) ESA SP, 2000: 335-340
[29] J. Praks and M. Hallikainen. An alternative for entropy-alpha classification for polarimetric SAR image. 2000
[30] S. E. Park and W. M. Moon. Classification of the polarimetric SAR using fuzzy boundaries in entropy and alpha plane. IEEE conference, 2005: 5517-5519
[31] Y. Q. Jin and F. Chen. Polarimetric scattering indexes and information entropy of the SAR imagery for surface monitoring. IEEE Trans. Geos. Remote Sensing, 2002, 40(11): 2502-2506
[32] 金亚秋，陈扉．SAR图像中极化散射指数和信息熵及其地表识别应用．自然科学进展，2003，13(2)：174-178
[33] S. Fukuda. Relating polarimetric SAR image texture to the scattering entropy. IEEE conference, 2004: 2475-2478
[34] 陈体刚，李彦佐．全极化SAR图像中相干矩阵特征值及其应用．信息与电子工程，2005，3(3)：161-166
[35] C. L. Martinez, E. Pottier, and S. R. Cloude. Statistical assessment of eigenvector-based target decomposition theorems in radar polarimetry. IEEE Trans. Geos. Remote Sensing, 2005, 43(9): 2058-2074
[36] J. S. Lee, M. R. Grunes, et al. Unsupervised classification using polarimetric decomposition and the complex Wishart classifier. IEEE Trans. Geos. Remote Sensing, 1999, 37(5): 2249-2258
[37] H. A. Yueh, A. A. Swarta, J. A. Kong, et al. Bayes classification of terrain cover using normalized polarimetric data. J.Geophys. Res., B, 1988, 93: 15261-15267
[38] 王之禹，朱敏慧，白有天．基于最优状态的多波段全极化SAR数据ML分类方法[J]．电子与信息学报，2001，(5)：507-511
[39] L. Du and J. S. Lee. Fuzzy classification of earth terrain covers using complex polarimetric SAR data [J]. International of Journal of Remote Sensing, 1996, 17(4): 809-826.
[40] C. T. Chen, K. S, Chen, and J. S. Lee. The use of fully polarimetric information for the fuzzy neural classification of SAR images. IEEE Trans Geos. Remote Sensing, 2003, 41 (9): 2089-2100
[41] K. S. Chen et al. Classification of multifrequency polarimetric SAR image using a dynamic learning neural network [J]. IEEE Trans. Geosci. Remote Sensing, 1996, 34: 814-820.
[42] Y. C.Tzeng and K. S. Chen. A fuzzy neural network to SAR image classification. IEEE Trans. Geos. Remo. Sens., 1998, 36(1): 301-307
[43] J. J. Van Zyl, et al. Bayesian classification of polarimetric SAR images using adaptive a priori probabilities [J]. International of Journal of Remote Sensing, 1992, 13(5): 835-840.
[44] J. S. Lee and M. R. Grunes. Classification of multi-look polarimetric SAR imagery based on complex Wishart distribution. Int. J. Remote Sensing, 1994, 15(11): 2299-2311
[45] J. S. Lee, M. Grunes, and G. deGrandi. Polarimetric SAR speckle filtering and its implication for classification. IEEE Trans. Geos. Remote Sensing, 1999, 37(5): 2363-2373
[46] Kconradsen et al. A test statistic in the complex Wishart distribution and its application to change detection in polarimetric SAR data. IEEE Trans. Geos. Remote Sensing, 2003, 41 (1): 4-19
[47] J. S. Lee, et al. Unsupervised terrain classification preserving polarimetric scattering characteristics. IEEE Trans. Geos. Remote Sensing, 2004, 42(4): 722-731
[48] P. R. Kersten et al. Unsupervised classification of polarimetric synthetic aperture radar images using fuzzy clustering and EM clustering. IEEE Trans. Geos. Remote Sensing, 2005, 43(3): 519—527
[49] J. M. Beaulieu and R. Touzi. Segmentation of textured polarimetric SAR scenes by likelihood approximation. IEEE Trans. Geos. Remote Sensing, 2004, 42(10): 2063-2072
[50] 杨震，杨汝良，刘秀清．SAR图像的极化干涉非监督Wishart分类方法和实验研究．电子与信息学报，2004，26(5)：752-759
[51] L. M. Novak and M. C. Burl. Optimal speckle reduction in polarimetric SAR imagery. IEEE Trans. Aerosp. Electron. Syst., 1990, 26: 293-305
[52] L. M. Novak, M. C. Burl, and W. W. Irving. Optimal polarimetric processing for enhanced target detection. IEEE AES, 1993, 29:234-243
[53] J.S.Lee, M.R.Grunes, and S.A.Mango. Speckle reduction in multipolarization multifrequehcy SAR imagery. IEEE Trans. GRS., 1991,29(4): 535-544
[54] J.S.Lee et al. Speckle filtering of synthetic aperture radar images: a review [J]. Remote Sensing Review, 1994, 8(30): 313-340
[55] J.S.Lee, M.R.Grunes, et al. Scattering-model-based speckle filtering of polarimetric SAR data. IEEE Trans. Geos. Remote Sensing, 2006,44(1): 176-187
[56] J.W.Goodman.Some fundamental properties of speckle. J.Opt.Soc.Amer., 1976,66(11):1145-1150,.
[57] GQ.Liu, S.J.Huang, A.Torre, and F.Rubertone. The multilook polarimetric whitening filter (MPWF) for intensity speckle reduction in polarimetric SAR images. IEEE Trans. GRS, 1998,36:1016-1020
[58] J.B.Kruskal. Toward a practical method which helps uncover the structure of a set of multivariate observations by finding the linear transformation which optimizes a new 'index of condesation'. Statistical Computation (R. C. Milton and J. A. Nelder, editors). New York, Academic Press, 1969
[59] J.B.Kruskal. Linear transformations of multivariate data to reveal clustering. In Multidimensional Scaling: Theory and application in the behavioural sciences, part I: theory. Seminar Press, New York and London, 1972
[60] J.H. Friedman and J.W.Tukey. A projection pursuit algorithm for exploratory data analysis. IEEE Trans. Comput., 1974, Vol.23: 881-889
[61] J.H Friedman and W.Stuetzle. A projection pursuit regression. J. Amer. Statist. Assoc, 1981,76:817-823
[62] M.C.Jones. The projection pursuit algorithm for exploratory data analysis. PhD Thesis, University of Bath, 1983
[63] J.H. Friedman, W. Stuetzle and A. Schroeder. Projection pursuit density estimation. J. Amer. Statist. Assoc, 1984, 79:599-608
[64] P. H. Hurber. Projection pursuit. Ann. Statist., 1985,13(2): 435-475
[65] Z.Chen and GLi. Robust principal components and dispersion matrix via projection pursuit. Research Report PJH-8 Dept. of Statistics, Harvard Univ., 1981
[66] GLi and Z.Chen. Projection pursuit approach to robust dispersion matrices and principal components. Primary theory and Monte-Carlo. J. Amer. Stat. Assoc, 1985, 80 (391): 759-766
[67] D. Donoho. Minimum entropy deconvolution. D.Findley editor, Applied time series analysis II, 1981
[68] D. Donoho. Breakdown properties of multivaritate location estimation. Ph.D. Qualifying Paper, Dept. of Statistics, Harvard Univ., 1982
[69] J.H Friedman and J.W.Tukey. Exploratory projection pursuit. J.Amer. Statist. Assoc, 1982, 82(397): 249-266
[70] M.C.Jones and R. Sibson. What is projection pursuit? (With discussion). J. Roy. Statist. Ser. A, 1987, 150:29-30
[71] P. Hall. On polynomial-based projection indices for exploratory projection pursuit. Ann. Statist., 1989, 17(2): 589-605
[72] G P.Nason. Design and choice of projection indices. Ph.D thesis, University of Bath, 1992
[73] D. Cook, A. Buja, and J. Cabrera. Projection pursuit indices based on expansions with orthonormal functions. Journal of Computational and Graphical Statistics, 1993,2(3): 225-250
[74] GP.Nason. Robust projection indecs. Technical Report 05, Department of Mathematics, University of Bristol, 2000
[75] E.K.Lee, D.Cook, et al. Projection pursuit for exploratory supervised classification. Journal of Computational and Graphical Statistics, 2005, 14(4): 831-846
[76] Andreas Krause and Volkmar Liebscher. Projection pursuit using the dip statistic. 2005
[77] GP.Nason and R.Sibson. Using projection pursuit in multispectral image analysis. In Elaine M.Keramidas editor, Proceedings of the 23rd Symposium on the Interface, VA 22039-7460,1991: 579-582
[78] Leng-Neng Hwang, et al. Regression modeling in back-propagation and projection pursuit learning. IEEE Transactions on Neural Networks, 1994, 5(3): 342-353
[79] C. M. Bachmann, et al. Dynamically reconfigurable projection pursuit ensemble for cloud detection in AVIRIS Imagery. Geoscience and Remote Sensing Symposium on Quantitative Remote Sensing for Science and Applications, 1995, part 1: 256-259
[80] M.M.Van Hulle. Nonparametric regression analysis achieved with topographic maps developed in combination with projection pursuit leaning. IEEE Trans.Signal Processing, 1997,4(5): 117-120
[81] S.R.Safavian,H.R.Rabiee, and M.Fardanesh. Projection pursuit image compression with variable block size segmentation. IEEE Sig. Proc. Lett., 1997,4(5): 117-120
[82] S. S. Chiang et al. Unsupervised target detection in hyperspectral images using projection pursuit. IEEE Trans. Geoscience and Remote Sensing, 2001, 39(7):
[83] D.B Triza, C.M.Bachmann, et.al. Projection pursuit classification of multiband polarimetric SAR land image. IEEE Trans. Geosci. Remote sensing, 2001, 39:2380-2386
[84] Shah, C.A., Arora, M.K., Robila, S.A., and Varshney, P.K.: ICA mixture model based unsupervised classification of hyperspectral imagery. Proc. 31st Applied Imagery Pattern Recognition Workshop, 2002:
[85] Corchado, E., Koetsier, J., Macdonald, D., and Fyfe, C: Classification and ICA using maximum likelihood hebbian learning. International conference of IEEE, 2002:327-336
[86] S.GMallat. Multiresolution approximations and wavelet orthonormal bases of L2 (R). Trans. Amer. Math. Soc, 1989, 315:69-87
[87] S.GMallat. A theory for multiresolution signal decomposition: The wavelet representation. IEEE Trans. Patt. Anal. Mach. Intell, 1989, 11(7): 674-693
[88] B.Efron. Bootstrap methods: another look at the jackknife [J]. Ann. Statistics, 1979,7(1):1-26.
[89] Brani Vidakovic. Statistics Modeling by Wavelets [M]. John Wiley and Sons, New York. 1999.
[90] W. Hardle, G. Kerkyacharian, D. Pickard, A. Tsybakov. Wavelets, Approximation and Statistical Applications. Lecture Notes in Statistics 129, Springer, 1998.
[91] P.Hall. The bootstrap and edgeworth expansion. Springer-Verlag, New York, 1992.
[92] M.Zribi. Non-parametric and unsupervised Bayesian classification with bootstrap sampling. Image and Vision computing, 2004, 22:1-8
[93] J. Shao and D.Tu. The jackknife and bootstrap. Springer-Verlag, New York. 1995.
[94] A. C. Davison, D. V. Hinkley. Bootstrap and their application. Cambridge University Press, Cambridge. 1997.
[95] A. Sakov and P. J. Bickel. An edgeworth expansion for the m out of n bootstrapped median. Statistics & Probability Letters, 2000, 49:217-223
[96] A. Sakov. Using the m out of n bootstrap in hypothesis testing. Ph. D. Thesis, University of California, Berkeley. 1998.
[97] A. Lopes et ai. Structure Detection and Statistical Adaptive Speckle Filtering in SAR images [J]. Int. J. Remote Sensing, 1993, 4(9): 1735～1758
[98] J. Romberg et al. Bayesian tree-structured image modeling using waelet-domain hidden markov models [J]. IEEE Transactions on Image Processing, 2001, 10(7): 1056-1067.
[99] 郭小卫，田铮，林伟．基于Markov四义树模型的无监督图像分割．计算机科学，2005，32(2)：219-223
[100] 郭小卫，田铮，林伟，熊毅．多尺度Markov模型的可适应图像分割方法．电子学报，2005，33(7)：1279-1283
[101] Y. Ito and S. Omatu. Gategory classification method using a self-organizing neural network [J]. Int. J. Remote Sensing., 1997, 18(4): 829-845.
[102] Y. Hara, R. G. Atkins, S. H. Yueh, et al. Application of neural networks to radar image classification. IEEE Trans. Geosci. Remote Sensing, 1994, 32: 100-110
[103] X. B. Wen and Z. Tian. Mixture multiscale autoregressive modeling of SAR imagery for segmentation [J]. Electronics Letters of IEE, 2003, 39: 1272-1274.
[104] Tian, Z., Wen, X. B, and Lin, W. Multiscale segmentation of SAR imagery with bootstrap sampling. 7th International conference on signal processing proceedings, 2004, 713-716
[105] 宋立新，崔景泉．一类特殊PP回归模型的估计．吉林大学自然科学学报，1995，4：5-13．
[106] M. Maechler, D. Martin, J. Schimert, et al. Projection pursuit learning networks for regression. IEEE international conference 1990: 350-358
[107] Q. Zhang and A. Benveniste. Wavelet Networks [J]. IEEE Trans Neural Networks, 1992, 3:889-898
[108] 焦李成，侯彪，刘芳．基函数网络逼近：进展与展望．工程数学学报，2002，19(1)：21-36
[109] 彭祖赠，孙韫玉编．模糊(Fuzzy)数学及其应用．武汉大学出版社，武汉．2002．
[110] 张尧庭，方开泰著．多元统计分析．科学出版社，北京，1982．
[111] 刘会山．Wishart分布引论．科学出版社，北京，2005．
[112] 茆诗松，王静龙，濮晓龙．高等数理统计．高等教育出版社，施普林格出版社，北京，1998．
[113] G. Soromenho. Comparing approaches for testing the number of components in a finite mixture model. Computational statistics, 1993, 9, 65-78
[114] G. Celeux and G. Soromenho. An entropy-criterion for assessing the number of clusters in a mixture model. Classification Journal, 1996, 13: 195-211
[115] M. Ishiguro, Y. Sakamoto, and G. Kitagawa. Bootstrapping log-likelihood and EIC, an extension of AIC. Annals of the institute of Statistical mathematics, 1997, 49: 411-434
[116] C. Biernacki, G. Celeux, and G. Govaert. An improvement of the NEC criterion for assessing the number of clusters in a mixture model. Pattern Recognition Letters, 1999, 20:267-272
[117] G. Mclachlan and D. Peel. Finite mixture models. John Wiley & Sons, New York, 2000.