基于目标分解和SVM的POL-SAR图像分类方法研究
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摘要
POL-SAR属于目前SAR领域和雷达极化领域研究的前沿课题,同时也是研究的热点和难点。在此背景下,开展关于POL-SAR的图像特征提取以及目标分类等方面的研究,对于解决如何优化POL-SAR系统整体性能,提高对POL-SAR图像的解译能力,推动我国POL-SAR系统走向应用具有重要的理论和实际意义。
本文研究的是POL-SAR图像特征提取和分类技术,研究的主要内容包括:基于目标分解的POL-SAR图像特征提取,基于灰度共生矩阵的纹理特征提取,以及基于SVM的POL-SAR图像分类。
本文首先介绍了POL-SAR系统的历史与发展现状,并针对极化图像目标分解和分类技术的国内外研究现状进行了详细的综述。同时,介绍了SVM以及它在各种不同领域中的发展应用现状,并对SVM理论进行了详细的介绍。
接下来,介绍了目标极化散射特性的表示方法,包括极化散射矩阵,协方差矩阵和相干矩阵等,给出了几种基本的极化散射机理。在此基础之上进行了基于目标分解的多种极化散射特征提取,研究了基于灰度共生矩阵的纹理特征提取,进而用ESAR L波段真实数据进行了实验,然后对实验结果做了详尽的分析和比较。
最后,着重研究了基于SVM的POL-SAR图像特征选择和分类技术。重点研究了SVM参数的选择,比较了不同的参数和分类精度的关系,提出了具体的分类算法,并用这种算法对POL-SAR图像进行分类。本文还用Cameron分类、H ?α分类和神经网络等方法进行分类,并和SVM分类结果进行了比较,从而验证SVM方法用于POL-SAR图像分类的有效性。
POL-SAR is a new kind of radar. Its imaging technique is developed from SAR. Carried forward the merit of SAR, POL-SAR can create high resolution images. Because of the wide and latent applications of POL-SAR in many areas of military, civil and scientific researches, POL-SAR is one of the most active fields in Radar and Remote Sensing nowadays.
In this dissertation,the classification of POL-SAR image is studied. Main aspects include scattering feature extraction of POL-SAR image base on target decomposition, texture feature extraction based on gray-level o-occurrence matrix and POL-SAR image classification based on SVM.
This dissertation is organized as follows, firstly, an overview of the domain of POL-SAR is provided. Then the development and achievement of POL-SAR decomposition and POL-SAR image classification is provided in detail. SVMand its application in different areas are introduced, followed by an introduction of the basic theory of SVMin chapter 2.
Next, the polarimetric scattering characteristics of the target, including polarimetric scattering matrix, covariance matrix, coherence matrix and several polarimetric scattering mechanisms, are introduced. POL-SAR image feature extraction is deep discussed combined with examples. On this basis, a set of feature extraction methods are presented, Corresponding experiments are done using ESAR L-band data. The results are also provided and detailedly analyzed.
The last step, feature selection and POL-SAR image classification based on SVM is mainly studied. Parameter selection of SVMis studied. The relationship of different parameters is compared. Then, classification arithmetic is proposed and used for POL-SAR image classification. Another classification experiments are also done. The method we proposed is validated through comparing with the results of other classification methods.
本文研究的是POL-SAR图像特征提取和分类技术,研究的主要内容包括:基于目标分解的POL-SAR图像特征提取,基于灰度共生矩阵的纹理特征提取,以及基于SVM的POL-SAR图像分类。
本文首先介绍了POL-SAR系统的历史与发展现状,并针对极化图像目标分解和分类技术的国内外研究现状进行了详细的综述。同时,介绍了SVM以及它在各种不同领域中的发展应用现状,并对SVM理论进行了详细的介绍。
接下来,介绍了目标极化散射特性的表示方法,包括极化散射矩阵,协方差矩阵和相干矩阵等,给出了几种基本的极化散射机理。在此基础之上进行了基于目标分解的多种极化散射特征提取,研究了基于灰度共生矩阵的纹理特征提取,进而用ESAR L波段真实数据进行了实验,然后对实验结果做了详尽的分析和比较。
最后,着重研究了基于SVM的POL-SAR图像特征选择和分类技术。重点研究了SVM参数的选择,比较了不同的参数和分类精度的关系,提出了具体的分类算法,并用这种算法对POL-SAR图像进行分类。本文还用Cameron分类、H ?α分类和神经网络等方法进行分类,并和SVM分类结果进行了比较,从而验证SVM方法用于POL-SAR图像分类的有效性。
POL-SAR is a new kind of radar. Its imaging technique is developed from SAR. Carried forward the merit of SAR, POL-SAR can create high resolution images. Because of the wide and latent applications of POL-SAR in many areas of military, civil and scientific researches, POL-SAR is one of the most active fields in Radar and Remote Sensing nowadays.
In this dissertation,the classification of POL-SAR image is studied. Main aspects include scattering feature extraction of POL-SAR image base on target decomposition, texture feature extraction based on gray-level o-occurrence matrix and POL-SAR image classification based on SVM.
This dissertation is organized as follows, firstly, an overview of the domain of POL-SAR is provided. Then the development and achievement of POL-SAR decomposition and POL-SAR image classification is provided in detail. SVMand its application in different areas are introduced, followed by an introduction of the basic theory of SVMin chapter 2.
Next, the polarimetric scattering characteristics of the target, including polarimetric scattering matrix, covariance matrix, coherence matrix and several polarimetric scattering mechanisms, are introduced. POL-SAR image feature extraction is deep discussed combined with examples. On this basis, a set of feature extraction methods are presented, Corresponding experiments are done using ESAR L-band data. The results are also provided and detailedly analyzed.
The last step, feature selection and POL-SAR image classification based on SVM is mainly studied. Parameter selection of SVMis studied. The relationship of different parameters is compared. Then, classification arithmetic is proposed and used for POL-SAR image classification. Another classification experiments are also done. The method we proposed is validated through comparing with the results of other classification methods.
引文
1邹斌,张腊梅,孙德明,王伟.极化干涉合成孔径雷达图像信息提取技术的进展及未来.电子与信息学报, 2006, 28(10):1979~1985.
2 J. R. Huynen. Phenomenological Theory of Radar Target. Ph.D. Dissertation, TUD, The Netherlands, 1970.
3 E. Krogager. Aspects of Polarimetric Radar Imaging. Doctoral Thesis, TUD, Lyngby, Denmark, May 1993.
4 E. Krogager, Z. H. Czyz. Properties of the Sphere, Diplane, Helix Decomposition. Proc. of JIPR’95, Nantes, France, 21~23, March 1995, 106~114.
5 S. R. Cloude. A Review of Target Decomposition Theorems in Radar Polarimetry. IEEE Trans. GRS, 1996, 34(2):498~518.
6 S. R. Cloude. Group Theory and Polarization Algebra. Optik, Dec 1986, 75(1):26~36.
7 S. R. Cloude. An Entropy Based Classification Scheme for Polarimetric SAR Data. Proc. of IGARSS’95, Firenze, Italy, 1995, 2000~2002.
8 E. Krogager, Aspects of Polarimetric Radar Imaging, Doctoral Thesis, TUD, Lyngby, Denmark, May 1993.
9 W. L. Cameron, N. N. Youssef, L. K. Leung. Simulated Polarimetric Signatures of Primitive Geometrical Shapes. IEEE Trans, GRS, May 1996, 34(3):793~803.
10 R. Touzi. Characterization of Target Symmetric Scattering using Polarimetric SARs. IEEE Trans. GRS, 2002, 40(11):2507~2516.
11 R. Touzi. Target Scattering Decomposition of One~look and Multi~look SAR Data using a New Coherent Scattering Model: The TSVM. Proc. of IGARSS’04, Alaska, USA, 2004, 2491~2494.
12 W. A. Holm, R. M. Bames. On Radar Polarization Mixed Target State Decomposition Techniques. IEEE National Radar Conf. 1988, 249~254.
13 A. Freeman, S. Durden. A Three-component Scattering Model to Describe Polarimetric SAR Data. Proc. SPZE Conf. on Radar Polarimetry, San Diego, July 1992, 213~224.
14 R. Touzi. A Unified Model for Decomposition of Coherent and Partially Coherent Target Scattering using Polarimetric SARs. Proc. of IGARSS’05,Seoul, Korea, 2005, 7: 4844~4847.
15 Y. Yamaguchi, T. Moriyama and et.al Four-Component Scattering Model for Polarimetric SAR Image Decomposition. IEEE, 2005, 1699~1705.
16 Y. Yamaguchi. A Four-Component Decomposition of POLSAR Images Based on the Coherency Matrix. IEEE Trans. GRSL, 2006, 1~5.
17 Y. Dong, B. C. Forster, C. Ticehurst. A New Decomposition of Radar Polarization Signatures. IEEE Trans. GRS, May 1998, 36(3): 933~939.
18 A. Danklmayer, M. Chandra, E. Luneburg. Principal Component Analysis in Radar Polarimetry. URSI, Kleinheubacher Berichte, Kleinheubach, Germany, 2004, Advances in Radio Science, 2005, in press, 3: 1~2.
19 A. Danklmayer. Application of Principal Component Analysis in Radar Polarimetry. Proc. of IGARSS’05, Seoul, Korea, 2005, 3: 1999~2002.
20 S. R. Cloude, E. Pottier. An Entropy Based Classification Scheme for Land Application of Polarimetric SAR. IEEE Trans. GRS, 1997, 35(1): 68~78.
21 M. Hellmann, G. Jager, E. Kratzschmar and et.al Classification of Full Polarimetric SAR-Data using Artificial Neural Networks and Fuzzy Algorithms. Proc. of IGARSS’99, Hamburg, Germany, 1999, 4: 1995~1997.
22 S. Allain, C. Lopez-Martinez, L. Ferro-Famil and et.al New Eigenvalue-based Parameters for Natural Media Characterization. Proc. of IGARSS’05, Seoul, Korea, 2005, 1: 40~43.
23 Y. Yamaguchi, M. Ishido, H. Yamada and et.al A Four-Component Decomposition of POLSAR Image. Proc. of IGARSS’05, Seoul, Korea, 2005, 6: 4073~4076.
24 T. Moriyama, S. Uratsuka, T. Umehara and et.al Polarimetric SAR Image Analysis using Model Fit for Urban Structures. IEICE Trans. COMMUN, 2005, E88-B(3): 1234~1243.
25 V. Alberga, D. Staykova, E. Krogager and et.al Comparison of Methods for Extracting and Utilizing Radar Target Characteristic Parameters. Proc. of IGARSS’05, Seoul, Korea, 2005, 3: 2019~2021.
26 M. Fujita, Y. Miho. Analysis of a Microwave Backscattering Mechanism from a Small Urban Area Imaged With SIR-C. IEEE Trans. GRS. Jan 2006, 3(1): 10~14.
27 L. J. Du, J. S. Lee. Polarimetric SAR Image Classification Based on TargetDecomposition Theorem and Complex Wishart Distribution. Proc. of IGARSS’96, Lincoln, Nebraska, USA, 1996, 1: 439~441.
28 J. S. Lee. Unsupervised Classification of Multi-frequency and Fully Polarimetric SAR Images Based on The H/A/Alpha-Wishart Classifier. Proc. of IGARSS’00, Hawaii, USA, 2000, 3: 1104~1106.
29 L. F. Famil, E. Pottier, J. S. Lee. Unsupervised Classification of Multifrequency and Fully Polarimetric SAR Images Based on the H/A/Alpha-Wishart Classifier. IEEE Trans. GRS, 2001, 39(11): 2332~2342.
30 T. Yamada, T. Hoshi. Expansion of the Unsupervised Classification of Polarimetric SAR Image Based on the Scattering Types using the Shape Feature of Polarization Signature Diagrams. Proc. of Asian Conf. Remote Sensing, Singapore, Nov 2001, 2: 1055~1060.
31 B. E. Boser, I. M. Guyon, and V. N. Vapnik, A training algorithm for optimal margin classifiers. Proc. 5th Annual ACM Workshop Comput. Learning Theory, Pittsburgh, PA, July 1992, 144~152.
32 V. N. Vapnik, The Nature of Statistical Learning Theory, Springer, New York, 1995.
33卫保国,王爱民,沈兰荪.一种新的多类模式识别支撑矢量机.模式识别与人工智能, 2002,15(2): 178~181.
34 E. Osuna, R. Freund. Training Support Vector Machines: An Application to Face Detection. Proc. of CVPR. San Juan, Puerto Rico, IEEE Computer Soc., 1997: 130~136.
35马勇,丁晓青.基于层次型SVM的人脸检测.清华大学学报(自然科学版), 2003, 43(1): 35~38.
36叶航军,白雪生,徐光祐.基于SVM的人脸姿态判定.清华大学学报(自然科学版), 2003, 43(1):67~70.
37凌旭峰,杨杰,叶晨洲.基于支撑向量机的人脸识别技术.红外与激光工程, 2001, 30(5): 318~322.
38张燕昆,杜平,刘重庆.基于主元分析与SVM的人脸识别方法.上海交通大学学报, 2002, 36(6): 884~886.
39王宏漫,欧宗瑛.采用PCA/ICA特征和SVM分类的人脸识别.计算机辅助设计与图形学学报, 2003, 15(4): 416~420.
40忻栋,杨莹春,吴朝晖.基于SVM-HMM混合模型的说话人确认.计算机辅助设计与图形学学报, 2002, 14(11): 1080~1082.
41边肇棋,张学工等,模式识别(第二版),北京:清华大学出版社, 2000.
42柳回春,马树元,吴平东. UK心理测试自动分析系统的手写体数字识别.北京理工大学学报, 2002, 22(5): 599~603.
43高学,金连文,尹俊勋等.一种基于SVM的手写汉字识别方法.电子学报, 2002, 30(5): 651~654.
44段立娟,崔国勤,高文等.多层次特定类型图像过滤方法.计算机辅助设计与图形学学报, 2002, 14(5): 1~6.
45庄越挺,刘骏伟,吴飞等.基于SVM的视频字幕自动定位与提取.计算机辅助设计与图形学学报, 2002, 14(8): 1~4.
46张磊,林福宗,张钹.基于SVM的相关反馈图像检索算法.清华大学学报(自然科学版), 2002, 42(1): 80~83.
47肖俊,吴飞,庄越挺等.基于SVM与细节层次的三维地形识别与检索.计算机辅助设计与图形学学报, 2003, 15(4).
48 S. Fukuda, H. Hirosawa. Polarimetric SAR image classification using support vector machines. IEICE Trans. Electronics, 2001 E84-C(12): 1939~1945.
49 S. Fukuda, R.Katagiri, H. Hirosawa. Unsupervised Approach for Polarimetric SAR Image Classification Using Support Vector Machines. IEEE, 2002, 2599~2601.
50 C. J. C. Burges. A Tutorial on Support Vector Machines for Pattern Recognition. Knowledge Discovery and Data Mining, 1998, 2(2): 121~167.
51 B. Schlkopf, S. Mika, C. J. C. Burges and etc. al. Input Space Versus Feature Space in Kernel-based Methods. IEEE Trans. NN, 1999, 10: 1000~1017.
52戴博伟.多极化合成孔径雷达系统与极化信息处理研究.中国科学院电子所,博士学位论文, 2000, 145~146.
53 B Furht and et al. Video and Image Processing in Multimedia Systems. Boston: Kluwer Academic Publishers, 1995, 226~270.
54 A. David, Clausi, Y. Bing. Comparing Co-occurrence Probabilityes and Markov Random Fields for Texture Analysis of SAR Sea Ice Imagery. IEEE Trans. GRS, 2004,42(1): 215~228.
55 B. E. Boser, I. M. Guyon, V. N. Vapnik. A training Algorithm for Optimal Margin Classifiers. In Haussler D, editor, Proc. of the Sth Annu. ACM Workshop Computation Learning Theory, 1992, 144~152.
56 V. N. Vapnik. Statistical Learning Theory. New York: Wiley, 1998.
57 J. Platt, Large Margin DAGs for Multiclsss Classification, in Advances in Neural Information Processing Systems, MIT Press, 2000, 547~553.
58 J. Weston, C. Watkins. Multiclass Support Vector Machines. TRCSDTR 9804, Department of Computer Science Egham, Survey TW 2003x, England, 1998.
59王翠珍.极化SAR数据分析与目标信息提取.北京:中国科学院遥感应用研究所博士论文. 1999.
2 J. R. Huynen. Phenomenological Theory of Radar Target. Ph.D. Dissertation, TUD, The Netherlands, 1970.
3 E. Krogager. Aspects of Polarimetric Radar Imaging. Doctoral Thesis, TUD, Lyngby, Denmark, May 1993.
4 E. Krogager, Z. H. Czyz. Properties of the Sphere, Diplane, Helix Decomposition. Proc. of JIPR’95, Nantes, France, 21~23, March 1995, 106~114.
5 S. R. Cloude. A Review of Target Decomposition Theorems in Radar Polarimetry. IEEE Trans. GRS, 1996, 34(2):498~518.
6 S. R. Cloude. Group Theory and Polarization Algebra. Optik, Dec 1986, 75(1):26~36.
7 S. R. Cloude. An Entropy Based Classification Scheme for Polarimetric SAR Data. Proc. of IGARSS’95, Firenze, Italy, 1995, 2000~2002.
8 E. Krogager, Aspects of Polarimetric Radar Imaging, Doctoral Thesis, TUD, Lyngby, Denmark, May 1993.
9 W. L. Cameron, N. N. Youssef, L. K. Leung. Simulated Polarimetric Signatures of Primitive Geometrical Shapes. IEEE Trans, GRS, May 1996, 34(3):793~803.
10 R. Touzi. Characterization of Target Symmetric Scattering using Polarimetric SARs. IEEE Trans. GRS, 2002, 40(11):2507~2516.
11 R. Touzi. Target Scattering Decomposition of One~look and Multi~look SAR Data using a New Coherent Scattering Model: The TSVM. Proc. of IGARSS’04, Alaska, USA, 2004, 2491~2494.
12 W. A. Holm, R. M. Bames. On Radar Polarization Mixed Target State Decomposition Techniques. IEEE National Radar Conf. 1988, 249~254.
13 A. Freeman, S. Durden. A Three-component Scattering Model to Describe Polarimetric SAR Data. Proc. SPZE Conf. on Radar Polarimetry, San Diego, July 1992, 213~224.
14 R. Touzi. A Unified Model for Decomposition of Coherent and Partially Coherent Target Scattering using Polarimetric SARs. Proc. of IGARSS’05,Seoul, Korea, 2005, 7: 4844~4847.
15 Y. Yamaguchi, T. Moriyama and et.al Four-Component Scattering Model for Polarimetric SAR Image Decomposition. IEEE, 2005, 1699~1705.
16 Y. Yamaguchi. A Four-Component Decomposition of POLSAR Images Based on the Coherency Matrix. IEEE Trans. GRSL, 2006, 1~5.
17 Y. Dong, B. C. Forster, C. Ticehurst. A New Decomposition of Radar Polarization Signatures. IEEE Trans. GRS, May 1998, 36(3): 933~939.
18 A. Danklmayer, M. Chandra, E. Luneburg. Principal Component Analysis in Radar Polarimetry. URSI, Kleinheubacher Berichte, Kleinheubach, Germany, 2004, Advances in Radio Science, 2005, in press, 3: 1~2.
19 A. Danklmayer. Application of Principal Component Analysis in Radar Polarimetry. Proc. of IGARSS’05, Seoul, Korea, 2005, 3: 1999~2002.
20 S. R. Cloude, E. Pottier. An Entropy Based Classification Scheme for Land Application of Polarimetric SAR. IEEE Trans. GRS, 1997, 35(1): 68~78.
21 M. Hellmann, G. Jager, E. Kratzschmar and et.al Classification of Full Polarimetric SAR-Data using Artificial Neural Networks and Fuzzy Algorithms. Proc. of IGARSS’99, Hamburg, Germany, 1999, 4: 1995~1997.
22 S. Allain, C. Lopez-Martinez, L. Ferro-Famil and et.al New Eigenvalue-based Parameters for Natural Media Characterization. Proc. of IGARSS’05, Seoul, Korea, 2005, 1: 40~43.
23 Y. Yamaguchi, M. Ishido, H. Yamada and et.al A Four-Component Decomposition of POLSAR Image. Proc. of IGARSS’05, Seoul, Korea, 2005, 6: 4073~4076.
24 T. Moriyama, S. Uratsuka, T. Umehara and et.al Polarimetric SAR Image Analysis using Model Fit for Urban Structures. IEICE Trans. COMMUN, 2005, E88-B(3): 1234~1243.
25 V. Alberga, D. Staykova, E. Krogager and et.al Comparison of Methods for Extracting and Utilizing Radar Target Characteristic Parameters. Proc. of IGARSS’05, Seoul, Korea, 2005, 3: 2019~2021.
26 M. Fujita, Y. Miho. Analysis of a Microwave Backscattering Mechanism from a Small Urban Area Imaged With SIR-C. IEEE Trans. GRS. Jan 2006, 3(1): 10~14.
27 L. J. Du, J. S. Lee. Polarimetric SAR Image Classification Based on TargetDecomposition Theorem and Complex Wishart Distribution. Proc. of IGARSS’96, Lincoln, Nebraska, USA, 1996, 1: 439~441.
28 J. S. Lee. Unsupervised Classification of Multi-frequency and Fully Polarimetric SAR Images Based on The H/A/Alpha-Wishart Classifier. Proc. of IGARSS’00, Hawaii, USA, 2000, 3: 1104~1106.
29 L. F. Famil, E. Pottier, J. S. Lee. Unsupervised Classification of Multifrequency and Fully Polarimetric SAR Images Based on the H/A/Alpha-Wishart Classifier. IEEE Trans. GRS, 2001, 39(11): 2332~2342.
30 T. Yamada, T. Hoshi. Expansion of the Unsupervised Classification of Polarimetric SAR Image Based on the Scattering Types using the Shape Feature of Polarization Signature Diagrams. Proc. of Asian Conf. Remote Sensing, Singapore, Nov 2001, 2: 1055~1060.
31 B. E. Boser, I. M. Guyon, and V. N. Vapnik, A training algorithm for optimal margin classifiers. Proc. 5th Annual ACM Workshop Comput. Learning Theory, Pittsburgh, PA, July 1992, 144~152.
32 V. N. Vapnik, The Nature of Statistical Learning Theory, Springer, New York, 1995.
33卫保国,王爱民,沈兰荪.一种新的多类模式识别支撑矢量机.模式识别与人工智能, 2002,15(2): 178~181.
34 E. Osuna, R. Freund. Training Support Vector Machines: An Application to Face Detection. Proc. of CVPR. San Juan, Puerto Rico, IEEE Computer Soc., 1997: 130~136.
35马勇,丁晓青.基于层次型SVM的人脸检测.清华大学学报(自然科学版), 2003, 43(1): 35~38.
36叶航军,白雪生,徐光祐.基于SVM的人脸姿态判定.清华大学学报(自然科学版), 2003, 43(1):67~70.
37凌旭峰,杨杰,叶晨洲.基于支撑向量机的人脸识别技术.红外与激光工程, 2001, 30(5): 318~322.
38张燕昆,杜平,刘重庆.基于主元分析与SVM的人脸识别方法.上海交通大学学报, 2002, 36(6): 884~886.
39王宏漫,欧宗瑛.采用PCA/ICA特征和SVM分类的人脸识别.计算机辅助设计与图形学学报, 2003, 15(4): 416~420.
40忻栋,杨莹春,吴朝晖.基于SVM-HMM混合模型的说话人确认.计算机辅助设计与图形学学报, 2002, 14(11): 1080~1082.
41边肇棋,张学工等,模式识别(第二版),北京:清华大学出版社, 2000.
42柳回春,马树元,吴平东. UK心理测试自动分析系统的手写体数字识别.北京理工大学学报, 2002, 22(5): 599~603.
43高学,金连文,尹俊勋等.一种基于SVM的手写汉字识别方法.电子学报, 2002, 30(5): 651~654.
44段立娟,崔国勤,高文等.多层次特定类型图像过滤方法.计算机辅助设计与图形学学报, 2002, 14(5): 1~6.
45庄越挺,刘骏伟,吴飞等.基于SVM的视频字幕自动定位与提取.计算机辅助设计与图形学学报, 2002, 14(8): 1~4.
46张磊,林福宗,张钹.基于SVM的相关反馈图像检索算法.清华大学学报(自然科学版), 2002, 42(1): 80~83.
47肖俊,吴飞,庄越挺等.基于SVM与细节层次的三维地形识别与检索.计算机辅助设计与图形学学报, 2003, 15(4).
48 S. Fukuda, H. Hirosawa. Polarimetric SAR image classification using support vector machines. IEICE Trans. Electronics, 2001 E84-C(12): 1939~1945.
49 S. Fukuda, R.Katagiri, H. Hirosawa. Unsupervised Approach for Polarimetric SAR Image Classification Using Support Vector Machines. IEEE, 2002, 2599~2601.
50 C. J. C. Burges. A Tutorial on Support Vector Machines for Pattern Recognition. Knowledge Discovery and Data Mining, 1998, 2(2): 121~167.
51 B. Schlkopf, S. Mika, C. J. C. Burges and etc. al. Input Space Versus Feature Space in Kernel-based Methods. IEEE Trans. NN, 1999, 10: 1000~1017.
52戴博伟.多极化合成孔径雷达系统与极化信息处理研究.中国科学院电子所,博士学位论文, 2000, 145~146.
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