基于流形学习像素分布流的高光谱图像数据分割方法
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摘要
高光谱遥感又称为高光谱分辨率遥感,是当前遥感技术的前沿领域,它利用很多很窄的电磁波波段从感兴趣的物体获得有关数据,它包含了丰富的空间、辐射和光谱三重信息。
在处理这种具有更多光谱波段的图像数据时,一个不可避免的问题出现了,那就是数百甚至上千个波段对传统的图像处理方法在维数上提出了新的要求,如何应用高光谱图像数据丰富的空间和光谱信息来进行更为精确的分类、目标识别以及高光谱图像的分割问题已经成为各种高光谱图像数据处理方法的所面对的共同问题。
针对一般意义下应用流形学习算法解决高光谱数据很难给出分类的标识信息,本文提出了一种引入2维空间信息向量的基于流形学习算法的高光谱图像分类方法。我们将空间信息与光谱反射系数信息加权结合后,通过调节两种特征的权重关系得到了由图上空间信息到光谱反射系数信息稳定的变化规律,由此确定用以分类的边界点,并对高光谱数据进行较高正确率的分类标识。
本文工作主要通过引入描述像素位置关系的空间特征而构建的联合高斯距离测度改进了拉普拉斯特征映射算法,构建了像素分布流用于处理高光谱图像数据。主要包括以下三个方面:
(1)在像素的光谱特征基础上引入图像的空间特征,将这两种不同近邻选取特征通过自定义的高斯距离相乘结合起来,包括如何加权结合两种输入空间的数据,以及参数的选取。像素分布流的提出以及构建方法。并且通过简化参数来解释像素分布流的实际物理意义,为之后的应用做了理论准备。
(2)应用像素分布流到实际的高光谱图像数据上,根据数据的实际特点对于映射结果提出了必须进行的两种后处理方法:包括非线性几何校正,这种校正可以把映射的结果人为的通过先验的空间特征知识固定,得到较为稳定的映射结果;以及边界收缩效应的校正,这种校正是针对算法本身引入空间特征所导致的映射结果边界相比内部不合理的收缩的现象,得到了边界与内部结果接近一致的结果。最后用单阈值选取边界点的方法给出小区域高光谱图像数据的分割结果。
(3)对于大规模的高光谱图像映射结果,上述的边界收缩效应会更加严重,导致单阈值无法选取有效边界点的结果。本文提出了一种通过多个阈值同时选取边界点综合处理的方法解决了这一问题。
Hyperspectral remote sensing is the current frontier remote sensing technology, which uses a lot of narrow band of electromagnetic waves from objects of interest to obtain the relevant data, which contains abundance information of spatial, radiation and spectral.
In dealing with the image data with more spectral bands, an inevitable question arises, hundreds or even thousands of bands presented in the dimensions of the new requirements on the traditional image processing methods. It has become a common problem of analysis of hyperspectral image that is how to use the abundance spatial and spectral information of hyperspectral image data to carry out a more precise classification, recognition and the segmentation of hyperspectral image.
Manifold learning methods results effectively apply to nonlinear dimensionality problem. Recently, there are a lot of related researches carried on hyperspectral image processing using manifold learning. For the problem that normally using manifold learning algorithms applied to hyperspectral data which can hardly given label information, a method based on manifold learning algorithm which the spatial context within a 2-dimensional array is introduced for classification of hyperspectral image is proposed in this paper. We weighted combination of the spatial information and the information of spectral reflection coefficient, a regular variation of stability from the spatial information to the information of spectral reflection coefficient, through adjusting the weights of the two characteristics, is acquired. Using this variation the pixels of the boundaries for classification is found, and labeled the hyperspectral data with high accuracy.
This paper mainly introduced the spatial characteristics which describes the relation of position of two pixels on the image. Propose the joint Gassian distance measurement to improved Laplacian Eigenmap algorithm, constructed the Pixel Distribution-Flow and apply to the Hyperspectral image data. The main innovative points are as follows:
(1) Introduce the spatial characteristics to the spectral characteristics of each pixel, we combined these two kind of characteristics which used for the selection of neighbors via multiplied Gaussian distances, including how to combine the data of two input spaces, and the selection of parameters. The construction of Pixel Distribution Flow is proposed in this paper. The actual physical meaning of Pixel Distribution Flow is explained through the simplifying the parameters.
(2) Apply Laplacian Eigenmap Pixel Distribution-Flow on Hyperspectral image data. According to the actual characteristics of the data set and the intrinsic problem of the result of the mapping, we proposed two kind necessary adjustments. Including nonlinear geometry adjustment which can obtain stable mapping result via fix the original mapping through the prior knowledge of the spatial characteristics. And the adjustment for aggregation of the marginal part of the image. This adjustment is for the algorithm introduced the spatial characteristics lead to the unreasonable aggregation of marginal part of the image compare to the internal part of the image. Then we select the boundary points via hard-threshold and obtain the result of segmentation of hyperspectral data with high accuracy.
(3) For large scale problem applying Laplacian Eigenmap Pixel Distribution-Flow, the aggregation of the marginal part of the image will be more serious, and this will lead the hard-threshold do not work anymore, in this paper we proposed mulit-thresholds method which use several useful thresholds to select the boundary points simultaneously to solve this problem.
在处理这种具有更多光谱波段的图像数据时,一个不可避免的问题出现了,那就是数百甚至上千个波段对传统的图像处理方法在维数上提出了新的要求,如何应用高光谱图像数据丰富的空间和光谱信息来进行更为精确的分类、目标识别以及高光谱图像的分割问题已经成为各种高光谱图像数据处理方法的所面对的共同问题。
针对一般意义下应用流形学习算法解决高光谱数据很难给出分类的标识信息,本文提出了一种引入2维空间信息向量的基于流形学习算法的高光谱图像分类方法。我们将空间信息与光谱反射系数信息加权结合后,通过调节两种特征的权重关系得到了由图上空间信息到光谱反射系数信息稳定的变化规律,由此确定用以分类的边界点,并对高光谱数据进行较高正确率的分类标识。
本文工作主要通过引入描述像素位置关系的空间特征而构建的联合高斯距离测度改进了拉普拉斯特征映射算法,构建了像素分布流用于处理高光谱图像数据。主要包括以下三个方面:
(1)在像素的光谱特征基础上引入图像的空间特征,将这两种不同近邻选取特征通过自定义的高斯距离相乘结合起来,包括如何加权结合两种输入空间的数据,以及参数的选取。像素分布流的提出以及构建方法。并且通过简化参数来解释像素分布流的实际物理意义,为之后的应用做了理论准备。
(2)应用像素分布流到实际的高光谱图像数据上,根据数据的实际特点对于映射结果提出了必须进行的两种后处理方法:包括非线性几何校正,这种校正可以把映射的结果人为的通过先验的空间特征知识固定,得到较为稳定的映射结果;以及边界收缩效应的校正,这种校正是针对算法本身引入空间特征所导致的映射结果边界相比内部不合理的收缩的现象,得到了边界与内部结果接近一致的结果。最后用单阈值选取边界点的方法给出小区域高光谱图像数据的分割结果。
(3)对于大规模的高光谱图像映射结果,上述的边界收缩效应会更加严重,导致单阈值无法选取有效边界点的结果。本文提出了一种通过多个阈值同时选取边界点综合处理的方法解决了这一问题。
Hyperspectral remote sensing is the current frontier remote sensing technology, which uses a lot of narrow band of electromagnetic waves from objects of interest to obtain the relevant data, which contains abundance information of spatial, radiation and spectral.
In dealing with the image data with more spectral bands, an inevitable question arises, hundreds or even thousands of bands presented in the dimensions of the new requirements on the traditional image processing methods. It has become a common problem of analysis of hyperspectral image that is how to use the abundance spatial and spectral information of hyperspectral image data to carry out a more precise classification, recognition and the segmentation of hyperspectral image.
Manifold learning methods results effectively apply to nonlinear dimensionality problem. Recently, there are a lot of related researches carried on hyperspectral image processing using manifold learning. For the problem that normally using manifold learning algorithms applied to hyperspectral data which can hardly given label information, a method based on manifold learning algorithm which the spatial context within a 2-dimensional array is introduced for classification of hyperspectral image is proposed in this paper. We weighted combination of the spatial information and the information of spectral reflection coefficient, a regular variation of stability from the spatial information to the information of spectral reflection coefficient, through adjusting the weights of the two characteristics, is acquired. Using this variation the pixels of the boundaries for classification is found, and labeled the hyperspectral data with high accuracy.
This paper mainly introduced the spatial characteristics which describes the relation of position of two pixels on the image. Propose the joint Gassian distance measurement to improved Laplacian Eigenmap algorithm, constructed the Pixel Distribution-Flow and apply to the Hyperspectral image data. The main innovative points are as follows:
(1) Introduce the spatial characteristics to the spectral characteristics of each pixel, we combined these two kind of characteristics which used for the selection of neighbors via multiplied Gaussian distances, including how to combine the data of two input spaces, and the selection of parameters. The construction of Pixel Distribution Flow is proposed in this paper. The actual physical meaning of Pixel Distribution Flow is explained through the simplifying the parameters.
(2) Apply Laplacian Eigenmap Pixel Distribution-Flow on Hyperspectral image data. According to the actual characteristics of the data set and the intrinsic problem of the result of the mapping, we proposed two kind necessary adjustments. Including nonlinear geometry adjustment which can obtain stable mapping result via fix the original mapping through the prior knowledge of the spatial characteristics. And the adjustment for aggregation of the marginal part of the image. This adjustment is for the algorithm introduced the spatial characteristics lead to the unreasonable aggregation of marginal part of the image compare to the internal part of the image. Then we select the boundary points via hard-threshold and obtain the result of segmentation of hyperspectral data with high accuracy.
(3) For large scale problem applying Laplacian Eigenmap Pixel Distribution-Flow, the aggregation of the marginal part of the image will be more serious, and this will lead the hard-threshold do not work anymore, in this paper we proposed mulit-thresholds method which use several useful thresholds to select the boundary points simultaneously to solve this problem.
引文
[1] T. M. Lillesand, R. W. Kiefer, and J. W. Chipman, Remote Sensing and Image Interpretation, 5th ed. John Wiley & Sons, Inc., 2004.
[2] J. P. Kerekes and J. E. Baum,“Spectral imaging system analytical model for subpixel object detection,”IEEE Transactions on Geoscience and Remote Sensing, 2002, vol.40, no.5, pp. 1088–1101.
[3] J. Bioucas-Dias and J. Nascimento,“Hyperspectral subspace identification,”IEEE Transactions on Geoscience and Remote Sensing, 2008, vol. 46, no. 8.
[4] C. Chang and S. Wang,“Constrained band selection for hyperspectral imagery,”IEEE Trans. Geosci. Remote Sensing, 2006, June, vol. 44, no. 6, pp. 1575–1585,.
[5] S. D. Backer, P. Kempeneers, W. Debruyn, and P. Scheunders,“A band selection technique for spectral classification,”IEEE Geoscience Remote Sensing Letters. 2005, vol. 2, no. 3, pp. 319–323.
[6] R. Huang and M. He,“Band selection based on feature weighting for classification of hyperspectral data,”IEEE Geoscience Remote Sensing Letters, 2005, vol. 2, no. 2, pp. 156–159.
[7] S. S. Shen and E. M. Bassett,“Information-theory-based band selection and utility evaluation for reflective spectral systems,”in Proc.of the SPIE Conference on Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery VIII, 2002, vol. 4725, pp. 18–29.
[8] S. Haykin, Neural Networks: A Comprehensive Foundation. Englewood Cliffs, NJ: Prentice- Hall, 1999.
[9] B.E.Boser,I.M.Guyon,and V.N.Vapnik,“A training algorithm for optimal margin classifiers,”in 5th Annu.ACM Workshop on COLT,D. Haussler, Ed., Pittsburgh, PA, 1992, pp. 144–152.
[10] B. Sch?lkopf and A. Smola, Learning With Kernels—Support VectorMachines, Regularization, Optimization and Beyond. Cambridge,MA: MIT Press, 2001.
[11] J. A. Gualtieri and R. F. Cromp,“Support vector machines for hyperspectralremote sensing classification,”in Proc. SPIE 27th AIPR Workshop,Feb. 1998, pp. 221–232.
[12] J. A. Gualtieri, S. R. Chettri, R. F. Cromp, and L. F. Johnson,“Support vector machine classifiers as applied to AVIRIS data,”presented at the 1999 Airborne Geoscience Workshop, Feb. 1999.
[13] G. Camps-Valls, L. Gómez-Chova, J. Calpe, E. Soria, J. D. Martín, L.Alonso, and J. Moreno,“Robust support vector method for hyperspectraldata classification andknowledge discovery,”IEEE Transactions on Geoscience and Remote Sensing, 2004, Jul, vol. 42, no. 7, pp. 1530–1542.
[14] N. Cristianini and J. Shawe-Taylor, An Introduction to Support VectorMachines. Cambridge, U.K.: Cambridge Univ. Press, 2000.
[15] M. Murat Dundar and A. Landgrebe,“A cost-effective semisupervisedclassifier approach with kernels,”IEEE Transactions on Geoscience and Remote Sensing, 2004, Jan. vol. 42, no. 1, pp. 264–270.
[16] C. Rodarmel and J. Shan,“Principal component analysis for hyperspectralimage classification,”Surv. Land Inf. Sci., Jun. 2002 vol. 62, no. 2, pp. 115–122,.
[17] J. B. Kruskal and M. Wish, Multidimensional Scaling. Beverly Hills,CA: Sage, 1977.
[18] Anish Mohan, Guillermo Sapiro, and Edward Bosch,“Spatially Coherent Nonlinear DimensionalityReduction and Segmentation of Hyperspectral Images,”IEEE Geoscience Remote Sensing Letters, 2007 April, VOL. 4, NO. 2, pp. 206-210.
[19] C. M. Bachmann, T. L. Ainsworth, and R. A. Fusina,“Exploiting manifold geometry in hyperspectral imagery,”IEEE Transactions on Geoscience and Remote Sensing, 2005, March, vol. 43, no. 3, pp. 441–454.
[20] Y. Chen, M. M. Crawford, and J. Ghosh,“Applying nonlinear manifold learning to hyperspectral data for land cover classification,”in Proc.IGARSS, Soeul, Korea, 2005, pp. 4311–4314
[21] D. H. Kim and L. H. Finkel,“Hyperspectral image processing using locally linear embedding,”in Proc. 1st Int. IEEE EMBS Conf. Neural Eng., 2003, pp. 316–319.
[22] Tian Han,Goodenough, D.G.“Nonlinear Feature Extraction of Hyperspectral Data Based on Locally Linear Embedding (LLE)”Geoscience and Remote Sensing Symposium, 2005. IGARSS '05. Proceedings. 2005 IEEE International, 2005 July, Vol.2, pp.1237- 1240, 25-29.
[23] S. T. Roweis and L. K. Saul,“Nonlinear dimensionality reduction by local linear embedding,”2000, Science, vol. 290, no. 5500, pp. 2323–2326.
[24] J. B. Tenenbaum, V. de Silva, and J. C. Langford,“A global geometric framework for nonlinear dimensionality reduction,”2000, Science, vol. 290, no. 5500, pp. 2319–2323.
[25] Mikhail Belkin and Partha Niyogi,“Laplacian eigenmaps for dimensionality reduction and data representation,”2003 June, Neural Computation, vol. 15, no. 6, pp. 1373–1396.
[26] P. Demartines and J. H′erault,“Curvilinear component analysis : A self-organizing neural network for nonlinear mapping of data sets,”IEEE Transactions on Neural Networks, 1997, vol. 8, no. 1, pp. 148–154.
[27] M. Lennon, G. Mercier, M. Mouchot, and L. Hubert-Moy,“Curvilinear component analysis for nonlinear dimensionality reduction ofhyperspectral images,”in Proc. of the SPIE Symp. on Remote Sensing Conference on Image and Signal Processing for Remote Sensing VII, 2001 , vol. 4541, pp. 157–169.
[28] J. Wang and C.-I. Chang,“Independent component analysis-based dimensionality reduction with applications in hyperspectral image analysis,”IEEE Transactions on Geoscience and Remote Sensing, vol. 44, no. 6, pp. 1586–1600, 2006.
[29] M. Lennon, M. Mouchot, G. Mercier, and L. Hubert-Moy,“Independent component analysis as a tool for the dimensionality reduction and the representation of hyperspectral images,”in Proc. of the IEEE Int. Geosci. and Remote Sensing Symp., 2001.
[30] A. Ifarraguerri and C.-I. Chang,“Unsupervised hyperspectral image analysis with projection pursuit,”IEEE Transactions on Geoscience and Remote Sensing, 2000, vol. 38, no. 6, pp. 127–143.
[31] C. Bachmann and T. Donato,“An information theoretic comparison of projection pursuit and principal component features for classification of landsat tm imagery of central colorado,”Int. J. Rem. Sens., 2000, vol. 21, no. 15, pp. 2927–2935(9).
[32] H. Othman and S.-E. Qian,“Noise reduction of hyperspectral imagery using hybrid spatial-spectral derivative-domain wavelet shrinkage,”IEEE Transactions on Geoscience and Remote Sensing, 2006, vol. 44, no. 2, pp. 397–408.
[33] S. Kaewpijit, J. L. Moigne, and T. El-Ghazawi,“Automatic reduction of hyperspectral imagery using wavelet spectral analysis,”IEEE Transactions on Geoscience and Remote Sensing, 2003, vol. 41, no. 4, pp. 863– 871.
[34] B. Sch?lkopf and A. Smola, Learning With Kernels. Cambridge, MA:MIT Press, 2001.
[35] Yuliya Tarabalka, Jón Atli Benediktsson and Jocelyn Chanussot,“Spectral-Spatial Classification of Hyperspectral Imagery Based on Partitional Clustering Techniques”, IEEE Transactions on Geoscience and Remote Sensing, 2009 August, Vol. 47, No. 8.
[36] Mathieu Fauvel, Jón Atli Benediktsson, Jocelyn Chanussot and Johannes R. Sveinsson,“Spectral and Spatial Classification of Hyperspectral Data Using SVMs and Morphological Profiles”, IEEE Transactions on Geoscience andRemote Sensing , 2008 November, Vol. 46, No. 11,.
[37] L. Saul and S. Roweis.“Think globally, fit locally: unsupervised learning of low dimensional manifolds,”Journal of Machine Learning Research,2003,Vol 4:119–155,.
[38] Mikhail Belkin, Partha Niyogi, and Vikas Sindhwani,“Manifold regularization: A geometric framework for learning from labeled and unlabeled examples,”Journal of Machine Learning Research, 2006, vol. 7, pp. 2399–2434.
[39] Y. Bengio, J.-F. Paiement, P. Vincent, O. Delalleau, N. Le Roux, and M. Ouimet,“Out-of-sample extensions for LLE, Isomap, MDS, eigenmaps, and spectral clustering,”in Advances in Neural Information Processing Systems, vol. 16. Cambridge, MA: MIT Press, 2004.
[40] Tian Han, Goodenough, D.G.“Nonlinear Feature Extraction of Hyperspectral Data Based on Locally Linear Embedding (LLE)”Geoscience and Remote Sensing Symposium, 2005. IGARSS '05. Proceedings. 2005 IEEE International.,2005 July ,Vol.2, pp.1237- 1240, 25-29.
[2] J. P. Kerekes and J. E. Baum,“Spectral imaging system analytical model for subpixel object detection,”IEEE Transactions on Geoscience and Remote Sensing, 2002, vol.40, no.5, pp. 1088–1101.
[3] J. Bioucas-Dias and J. Nascimento,“Hyperspectral subspace identification,”IEEE Transactions on Geoscience and Remote Sensing, 2008, vol. 46, no. 8.
[4] C. Chang and S. Wang,“Constrained band selection for hyperspectral imagery,”IEEE Trans. Geosci. Remote Sensing, 2006, June, vol. 44, no. 6, pp. 1575–1585,.
[5] S. D. Backer, P. Kempeneers, W. Debruyn, and P. Scheunders,“A band selection technique for spectral classification,”IEEE Geoscience Remote Sensing Letters. 2005, vol. 2, no. 3, pp. 319–323.
[6] R. Huang and M. He,“Band selection based on feature weighting for classification of hyperspectral data,”IEEE Geoscience Remote Sensing Letters, 2005, vol. 2, no. 2, pp. 156–159.
[7] S. S. Shen and E. M. Bassett,“Information-theory-based band selection and utility evaluation for reflective spectral systems,”in Proc.of the SPIE Conference on Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery VIII, 2002, vol. 4725, pp. 18–29.
[8] S. Haykin, Neural Networks: A Comprehensive Foundation. Englewood Cliffs, NJ: Prentice- Hall, 1999.
[9] B.E.Boser,I.M.Guyon,and V.N.Vapnik,“A training algorithm for optimal margin classifiers,”in 5th Annu.ACM Workshop on COLT,D. Haussler, Ed., Pittsburgh, PA, 1992, pp. 144–152.
[10] B. Sch?lkopf and A. Smola, Learning With Kernels—Support VectorMachines, Regularization, Optimization and Beyond. Cambridge,MA: MIT Press, 2001.
[11] J. A. Gualtieri and R. F. Cromp,“Support vector machines for hyperspectralremote sensing classification,”in Proc. SPIE 27th AIPR Workshop,Feb. 1998, pp. 221–232.
[12] J. A. Gualtieri, S. R. Chettri, R. F. Cromp, and L. F. Johnson,“Support vector machine classifiers as applied to AVIRIS data,”presented at the 1999 Airborne Geoscience Workshop, Feb. 1999.
[13] G. Camps-Valls, L. Gómez-Chova, J. Calpe, E. Soria, J. D. Martín, L.Alonso, and J. Moreno,“Robust support vector method for hyperspectraldata classification andknowledge discovery,”IEEE Transactions on Geoscience and Remote Sensing, 2004, Jul, vol. 42, no. 7, pp. 1530–1542.
[14] N. Cristianini and J. Shawe-Taylor, An Introduction to Support VectorMachines. Cambridge, U.K.: Cambridge Univ. Press, 2000.
[15] M. Murat Dundar and A. Landgrebe,“A cost-effective semisupervisedclassifier approach with kernels,”IEEE Transactions on Geoscience and Remote Sensing, 2004, Jan. vol. 42, no. 1, pp. 264–270.
[16] C. Rodarmel and J. Shan,“Principal component analysis for hyperspectralimage classification,”Surv. Land Inf. Sci., Jun. 2002 vol. 62, no. 2, pp. 115–122,.
[17] J. B. Kruskal and M. Wish, Multidimensional Scaling. Beverly Hills,CA: Sage, 1977.
[18] Anish Mohan, Guillermo Sapiro, and Edward Bosch,“Spatially Coherent Nonlinear DimensionalityReduction and Segmentation of Hyperspectral Images,”IEEE Geoscience Remote Sensing Letters, 2007 April, VOL. 4, NO. 2, pp. 206-210.
[19] C. M. Bachmann, T. L. Ainsworth, and R. A. Fusina,“Exploiting manifold geometry in hyperspectral imagery,”IEEE Transactions on Geoscience and Remote Sensing, 2005, March, vol. 43, no. 3, pp. 441–454.
[20] Y. Chen, M. M. Crawford, and J. Ghosh,“Applying nonlinear manifold learning to hyperspectral data for land cover classification,”in Proc.IGARSS, Soeul, Korea, 2005, pp. 4311–4314
[21] D. H. Kim and L. H. Finkel,“Hyperspectral image processing using locally linear embedding,”in Proc. 1st Int. IEEE EMBS Conf. Neural Eng., 2003, pp. 316–319.
[22] Tian Han,Goodenough, D.G.“Nonlinear Feature Extraction of Hyperspectral Data Based on Locally Linear Embedding (LLE)”Geoscience and Remote Sensing Symposium, 2005. IGARSS '05. Proceedings. 2005 IEEE International, 2005 July, Vol.2, pp.1237- 1240, 25-29.
[23] S. T. Roweis and L. K. Saul,“Nonlinear dimensionality reduction by local linear embedding,”2000, Science, vol. 290, no. 5500, pp. 2323–2326.
[24] J. B. Tenenbaum, V. de Silva, and J. C. Langford,“A global geometric framework for nonlinear dimensionality reduction,”2000, Science, vol. 290, no. 5500, pp. 2319–2323.
[25] Mikhail Belkin and Partha Niyogi,“Laplacian eigenmaps for dimensionality reduction and data representation,”2003 June, Neural Computation, vol. 15, no. 6, pp. 1373–1396.
[26] P. Demartines and J. H′erault,“Curvilinear component analysis : A self-organizing neural network for nonlinear mapping of data sets,”IEEE Transactions on Neural Networks, 1997, vol. 8, no. 1, pp. 148–154.
[27] M. Lennon, G. Mercier, M. Mouchot, and L. Hubert-Moy,“Curvilinear component analysis for nonlinear dimensionality reduction ofhyperspectral images,”in Proc. of the SPIE Symp. on Remote Sensing Conference on Image and Signal Processing for Remote Sensing VII, 2001 , vol. 4541, pp. 157–169.
[28] J. Wang and C.-I. Chang,“Independent component analysis-based dimensionality reduction with applications in hyperspectral image analysis,”IEEE Transactions on Geoscience and Remote Sensing, vol. 44, no. 6, pp. 1586–1600, 2006.
[29] M. Lennon, M. Mouchot, G. Mercier, and L. Hubert-Moy,“Independent component analysis as a tool for the dimensionality reduction and the representation of hyperspectral images,”in Proc. of the IEEE Int. Geosci. and Remote Sensing Symp., 2001.
[30] A. Ifarraguerri and C.-I. Chang,“Unsupervised hyperspectral image analysis with projection pursuit,”IEEE Transactions on Geoscience and Remote Sensing, 2000, vol. 38, no. 6, pp. 127–143.
[31] C. Bachmann and T. Donato,“An information theoretic comparison of projection pursuit and principal component features for classification of landsat tm imagery of central colorado,”Int. J. Rem. Sens., 2000, vol. 21, no. 15, pp. 2927–2935(9).
[32] H. Othman and S.-E. Qian,“Noise reduction of hyperspectral imagery using hybrid spatial-spectral derivative-domain wavelet shrinkage,”IEEE Transactions on Geoscience and Remote Sensing, 2006, vol. 44, no. 2, pp. 397–408.
[33] S. Kaewpijit, J. L. Moigne, and T. El-Ghazawi,“Automatic reduction of hyperspectral imagery using wavelet spectral analysis,”IEEE Transactions on Geoscience and Remote Sensing, 2003, vol. 41, no. 4, pp. 863– 871.
[34] B. Sch?lkopf and A. Smola, Learning With Kernels. Cambridge, MA:MIT Press, 2001.
[35] Yuliya Tarabalka, Jón Atli Benediktsson and Jocelyn Chanussot,“Spectral-Spatial Classification of Hyperspectral Imagery Based on Partitional Clustering Techniques”, IEEE Transactions on Geoscience and Remote Sensing, 2009 August, Vol. 47, No. 8.
[36] Mathieu Fauvel, Jón Atli Benediktsson, Jocelyn Chanussot and Johannes R. Sveinsson,“Spectral and Spatial Classification of Hyperspectral Data Using SVMs and Morphological Profiles”, IEEE Transactions on Geoscience andRemote Sensing , 2008 November, Vol. 46, No. 11,.
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