基于非负矩阵分解的高光谱遥感图像混合像元分解研究
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摘要
由于遥感拍摄仪器空间分辨率的限制,高光谱遥感图像中的一个像元对应的地面区域通常覆盖了多种地物,其像元的光谱实际上是几种纯净地物光谱的混合,这种像元被称为混合像元。将混合像元分解为典型的地物(即端元)和它们的混合比例(即丰度),可以获取亚像元级的信息,提高地物识别的精度,实现定量遥感。因此,混合像元分解对于基于高光谱遥感图像的高精度地物分类以及地面目标的检测有着重要的意义。目前在该领域中,国际上不断有新思路新方法涌现。如何用无监督的方法在高光谱遥感数据中将混合像元更快更精确的进行盲分解,已经成为当今遥感领域里的一个研究热点。作为一种先进的统计学方法,非负矩阵分解方法能够保证结果的非负性,因而在近年来得到了广泛研究。然而它还存在局部极小很多和运算量大的缺点,本论文针对非负矩阵分解在高光谱遥感图像混合像元分解中的应用作了大量研究,主要工作与创新包括以下几部分：
1.提出一种基于有约束非负矩阵分解的混合像元分解方法。传统非负矩阵分解算法的目标函数具有大量的局部极小,在进行高光谱图像的光谱解混时,受初始值的影响很大。本研究通过在目标函数中引入丰度分离性和平滑性的约束条件来解决这一问题。同时该算法能够满足混合像元分解问题所要求的丰度值非负以及和为一的约束。模拟和实际数据实验结果表明,所提出的算法能够很好地克服局部极小的问题,从而得到更优的解。同时该算法表现出了较强的抗噪声能力,并且能够适用于无纯像元数据的混合像元分解。
2.针对非负矩阵分解运算速度较慢的问题,本文提出一种使用多核并行处理来提高其效率的方法。本方法对有约束非负矩阵分解方法的步骤进行分解,根据高光谱图像的特点选择合适的并行处理方案。实验结果表明,使用并行处理后,多核CPu的效能被充分利用,混合像元分解的速度得到了大幅度的提高。
3.由于高光谱图像波段之间的相关性极高,而非负矩阵分解是一种统计学方法,当直接使用原始的数据时,势必会带来大量的冗余信息。基于这一问题,本文提出一种适用于非负矩阵分解的,基于最大信息量的高光谱图像波段选择方法。它以保留的波段中所包含的信息量最大为目标,通过迭代方法逐个移除波段。实验结果表明,该方法能在大幅降低高光谱图像维度,从而提高运算效率的同时,仍然得到精确的分解结果。
4.通常对混合像元分解方法的实验研究只局限于数量较为有限的免费数据,它们大多是由美国研制的成像仪拍摄,并且年代较为久远。本文在保留这些数据的同时,也对由国产成像仪拍摄于近几年的高光谱图像进行了实验,以验证混合像元分解方法在实际应用中的有效性。
Due to the resolution limitation of the sensors and the variability of the ground surface, the observation of one pixel in a hyperspectral remote sensing image may contain several disparate substances, causing it to be a "mixed pixel". In order to utilize the hyperspectral data, these mixed pixels have to be decomposed into a set of constituent spectra, called endmember signatures, and their corresponding proportions, called abundances. Mixed pixels exist in almost all hyperspectral images, thus how to unmix these pixels has become an important problem of hyperspectral imagery, for whose application in the identification and detection of ground targets. In recent years, new ideas and approaches for hyperspectral unmixing are springing up. Using unsupervised method to decompose mixed-pixels more efficiently and accurately has become a hotspot in the research area of remote sensing. As an advanced statistical approach, Nonnegative Matrix Factorization (NMF) has been frequently researched recently for hyperspectral unmixing, because it can ensure the nonnegativity of results. However, it has some disadvantages, such as large amount of local minima and high computational complexity. Focusing on the application of nonnegative matrix factorization in hyperspectral unmixing, this thesis has made a lot of research, and the main works and innovations are as follows:
1. A constrained NMF approach has been proposed. Because of the local minima in the objective function, the traditional NMF algorithm is sensitive to the initial value when being applied to hyperspectral unmixing. In order to solve the problem, a new approach based on constrained NMF is proposed for decomposition of mixed pixels by introducing constraints of abundance separation and smoothness into the objective function of NMF. The algorithm can also satisfy the abundance nonnegative and sum-to-one constraints, which are necessary for hyperspectral unmixing. Experimental results on simulated and real hyperspectral data demonstrate that the proposed approach can overcome the shortcoming of local minima, and obtain better results. Meanwhile, the algorithm performs well for noisy data, and can also be used for the unmixing of hyperspectral data in which pure pixels do not exist.
2. On account of the low computational speed of NMF, a multi-core parallel processing method is proposed to increase its efficiency. The method decomposes the constrained NMF algorithm to several blocks, and choose appropriate parallel strategy according to the features of hyperspectral imagery. Experimental results show that, the multi-core CPU is utilized sufficiently after the execution of parallel processing, and the computational speed of unmixing has got an obvious improvement.
3. The correlation between neighboring bands of hyperspectral imagery is very high, while NMF is a statistical approach, thus a large amount of redundant information will be processed if the original data is used directly. In order to solve this problem, a maximum-information-based band selection approach for NMF is proposed. It aims at preserving the maximum amount of information, and removes bands one by one iteratively. Experimental results show that, the proposed approach can obviously reduce the number of dimensions of hyperspectral imagery and increase the processing efficiency, and obtain accurate results at the same time.
4. Some general free datasets are usually used for the experimental research of hyperspectral unmixing. These datasets are mostly captured over a decade ago by U.S.-made devices. In this thesis, datasets lately obtained by China-made devices are also used for experiments, in order to evaluate the performance of algorithms for practical application.
1.提出一种基于有约束非负矩阵分解的混合像元分解方法。传统非负矩阵分解算法的目标函数具有大量的局部极小,在进行高光谱图像的光谱解混时,受初始值的影响很大。本研究通过在目标函数中引入丰度分离性和平滑性的约束条件来解决这一问题。同时该算法能够满足混合像元分解问题所要求的丰度值非负以及和为一的约束。模拟和实际数据实验结果表明,所提出的算法能够很好地克服局部极小的问题,从而得到更优的解。同时该算法表现出了较强的抗噪声能力,并且能够适用于无纯像元数据的混合像元分解。
2.针对非负矩阵分解运算速度较慢的问题,本文提出一种使用多核并行处理来提高其效率的方法。本方法对有约束非负矩阵分解方法的步骤进行分解,根据高光谱图像的特点选择合适的并行处理方案。实验结果表明,使用并行处理后,多核CPu的效能被充分利用,混合像元分解的速度得到了大幅度的提高。
3.由于高光谱图像波段之间的相关性极高,而非负矩阵分解是一种统计学方法,当直接使用原始的数据时,势必会带来大量的冗余信息。基于这一问题,本文提出一种适用于非负矩阵分解的,基于最大信息量的高光谱图像波段选择方法。它以保留的波段中所包含的信息量最大为目标,通过迭代方法逐个移除波段。实验结果表明,该方法能在大幅降低高光谱图像维度,从而提高运算效率的同时,仍然得到精确的分解结果。
4.通常对混合像元分解方法的实验研究只局限于数量较为有限的免费数据,它们大多是由美国研制的成像仪拍摄,并且年代较为久远。本文在保留这些数据的同时,也对由国产成像仪拍摄于近几年的高光谱图像进行了实验,以验证混合像元分解方法在实际应用中的有效性。
Due to the resolution limitation of the sensors and the variability of the ground surface, the observation of one pixel in a hyperspectral remote sensing image may contain several disparate substances, causing it to be a "mixed pixel". In order to utilize the hyperspectral data, these mixed pixels have to be decomposed into a set of constituent spectra, called endmember signatures, and their corresponding proportions, called abundances. Mixed pixels exist in almost all hyperspectral images, thus how to unmix these pixels has become an important problem of hyperspectral imagery, for whose application in the identification and detection of ground targets. In recent years, new ideas and approaches for hyperspectral unmixing are springing up. Using unsupervised method to decompose mixed-pixels more efficiently and accurately has become a hotspot in the research area of remote sensing. As an advanced statistical approach, Nonnegative Matrix Factorization (NMF) has been frequently researched recently for hyperspectral unmixing, because it can ensure the nonnegativity of results. However, it has some disadvantages, such as large amount of local minima and high computational complexity. Focusing on the application of nonnegative matrix factorization in hyperspectral unmixing, this thesis has made a lot of research, and the main works and innovations are as follows:
1. A constrained NMF approach has been proposed. Because of the local minima in the objective function, the traditional NMF algorithm is sensitive to the initial value when being applied to hyperspectral unmixing. In order to solve the problem, a new approach based on constrained NMF is proposed for decomposition of mixed pixels by introducing constraints of abundance separation and smoothness into the objective function of NMF. The algorithm can also satisfy the abundance nonnegative and sum-to-one constraints, which are necessary for hyperspectral unmixing. Experimental results on simulated and real hyperspectral data demonstrate that the proposed approach can overcome the shortcoming of local minima, and obtain better results. Meanwhile, the algorithm performs well for noisy data, and can also be used for the unmixing of hyperspectral data in which pure pixels do not exist.
2. On account of the low computational speed of NMF, a multi-core parallel processing method is proposed to increase its efficiency. The method decomposes the constrained NMF algorithm to several blocks, and choose appropriate parallel strategy according to the features of hyperspectral imagery. Experimental results show that, the multi-core CPU is utilized sufficiently after the execution of parallel processing, and the computational speed of unmixing has got an obvious improvement.
3. The correlation between neighboring bands of hyperspectral imagery is very high, while NMF is a statistical approach, thus a large amount of redundant information will be processed if the original data is used directly. In order to solve this problem, a maximum-information-based band selection approach for NMF is proposed. It aims at preserving the maximum amount of information, and removes bands one by one iteratively. Experimental results show that, the proposed approach can obviously reduce the number of dimensions of hyperspectral imagery and increase the processing efficiency, and obtain accurate results at the same time.
4. Some general free datasets are usually used for the experimental research of hyperspectral unmixing. These datasets are mostly captured over a decade ago by U.S.-made devices. In this thesis, datasets lately obtained by China-made devices are also used for experiments, in order to evaluate the performance of algorithms for practical application.
引文
[1]T. M. Lillesand and R. W. Kiefer. Remote Sensing and Image Interpretation [M],4th ed. New York:John Wiley & Sons, Inc.,2000.
[2]C.-I. Chang. Hyperspectral Imaging:Techniques for Spectral Detection and Classification [M]. New York:Plenum,2003.
[3]C.-I. Chang. Hyperspectral Data Exploitation [M]. New York:John Wiley & Sons, Inc., 2007.
[4]童庆禧,张兵,郑兰芬.高光谱遥感--原理，技术与应用[M].北京：高等教育出版社,2006.
[5]童庆禧.遥感科学技术进展[J].地理学报，1994,49：616-624.
[6]张良培,张立福.高光谱遥感[M].武汉：武汉大学出版社,2005.
[7]浦瑞良,宫鹏.高光谱遥感及其应用[M].北京：高等教育出版社,2000.
[8]G. Vane and A. F. H. Gotez. Terrestrial imaging spectrometry:current status, future trends [J]. Remote Sensing of Environment,1993,44:117-126.
[9]G. R. Hunt. Near-infrared spectral of alternation minerals-potential for use in remote sensing [J]. IEEE Trans. Geosci. Remote Sens.,1979,44(12):974-1986.
[10]钱乐祥,泮学芹,赵芊.中国高光谱成像遥感应用研究进展[J].国土资源遥感，2004,2：1-6.
[11]张斧.成像光谱技术发展的科学背景和现状[J].激光与红外,1994,24(1)：23-26.
[12]朱述龙,张占睦.遥感图像获取与分析[M].北京：科学出版社,2000.
[13]束炯,王强,孙娟.高光谱遥感的应用研究[J].华东师范大学学报(自然科学版),2006,4：1-10.
[14]A. F. H. Gotez, G. Vane, and J. E. Solomon, et al. Imaging spectrometry for earth remote sensing [J]. Science,1985,228:1147-1153.
[15]李天宏,杨海宏,赵永平.成像光谱仪遥感现状与展望[J].遥感技术与应用，1997,12(2)：54-58.
[16]R. Green, M. Eastwood, and C. Sarture, et al. Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS) [J]. Remote Sensing of Environment,1998, 65(3):227-248.
[17]张钧萍,张哗,周廷显.成像光谱技术超谱图像分类研究现状与分析[J].中国空间科学技术，2001,1：37-44.
[18]A. F. H. Goetz and L. C. Rowan. Geological remote sensing [J]. Science,1981,211:781-791.
[19]童庆禧.电子光学遥感系统的过去，现在和未来[M].北京：科学出版社,1995.
[20]L. J. Richard, R. W. Basedow, and E. Zalweski, et al. HYDICE:an airborne system for hyperspectral imaging [C]. in:Proc of SPIE,1993,1937:173-179.
[21]耿修瑞,高光谱遥感图像目标探测与分类技术研究[D]. PhD thesis,中国科学院研究生院(遥感应用研究所),2005.
[22]贾森,非监督的高光谱图像解混技术研究[D]. PhD Thesis,浙江大学计算机学院,2007.
[23]张钧萍,张晔,基于多特征多分辨率融合的高光谱图像分类[J].红外与毫米波学报,2004,23(5)：345-348.
[24]Q. Du and C.-I. Chang. A linear constrained distance-based discriminant analysis for hyperspectral image classification [J]. Pattern Recognition,2001,34:361-373.
[25]Q. Du and H. Ren. Real-time constrained linear discriminant analysis to target detection and classification in hyperspectral imagery [J]. Pattern Recognition,2003,36:1-12.
[26]C.-I. Chang, T.-L.E. Sun, and M. L. G. Althouse. An unsupervised interference rejection approach to target detection and classification for hyperspectral imagery [J]. Opt. Engng., 1998,37(3):735-743.
[27]C.-I. Chang, X. Zhao, M. L. G. Althouse, and J.-J. Pan. Least squars subspace projection approach to mixed pixel classification in hyperspectral images [J]. IEEE Trans. Geosci. Remote Sens.,1998,36(3):898-912.
[28]C.-I. Chang, H. Ren and S. S. Chiang. Real-time processing algorithms for target detection and classification in hyperspectral imagery [J]. IEEE Trans. Geosci. Remote Sens.,2000, 39(4):760-768.
[29]N. Keshava and J. F. Mustard. Spectral unmixing [J]. IEEE Signal Process. Mag.,2001, 19(1):44-57.
[30]惠巍巍,衣德萍,廖彩霞.混合像元分解综述[J].林业科技情报,2007,39(1)：2-3.
[31]N. Keshava. A survey of spectral unmixing algorithms [J]. Lincoln Lab. J.,2003,14(1): 55-73.
[32]J. J. Cipar, E. C. Meidunas, and E. M. Bassett. A comparison of endmember extraction techniques [C]. in:Proc of SPIE,2002,4725:1-9.
[33]薛绮,匡纲要,李智勇.基于线性混合模型的高光谱图像端元提取[J].遥感技术与应用，2004,19(3)：197-201.
[34]李剑萍,郑有飞.气象卫星混合像元分解研究综述[J].中国农业气象,2000,21(2)：44-47.
[35]J.-F. Cardoso. Blind signal separation:statistical principles [C]. Proc of the IEEE, Special issue on Blind Identification and estimation,1998,9(10):2009-2025.
[36]A. Cichocki and S. Amari. Adaptive Blind Signal and Image Processing:Learning Algorithms and Applications [M]. New York:John Wiley & Sons,2002.
[37]J. M. P. Nascimento. Unsupervised Hyperspectral Unmixing [D]. PhD thesis,2006.
[38]S. Mei, M. He, Z. Wang, and D. Feng. Spatial purity based endmember extraction for spectral mixture analysis [J], IEEE Trans. Geosci. Remote Sens.,2010,48(9):3434-3444.
[39]D. M. Rogge, B. Rivard, J. Zhang, and J. Feng. Iterative spectral unmixing for optimizing per-pixel endmember sets [J]. IEEE Trans. Geosci. Remote Sens.,2006,44(12):3725-3735.
[40]M. Zortea, A. Plaza. Spatial preprocessing for endmember extraction [J]. IEEE Trans. Geosci. Remote Sens.,2009,47(8):2679-2693.
[41]J. Li. Wavelet-based feature extraction for improved endmember abundance estimation in linear unmixing of hyperspectral signals [J]. IEEE Trans. Geosci. Remote Sens.,2004,42(3): 644-649.
[42]C. Kwan, B. Ayhan, G. Chen, et al. A novel approach for spectral unmixing, classification, and concentration estimation of chemical and biological agents [J]. IEEE Trans. Geosci. Remote Sens.,2006,44(2):409-419.
[43]杨伟,陈晋,松下文经.基于相关系数匹配的混合像元分解算法[J].遥感学报，2008,12(3)：454-461.
[44]C.-I. Chang and D. C. Heinz. Constrained subpixel target detection for remotely sensed imagery [J]. IEEE Trans. Geosci. Remote Sens.,2000,38(3):1144-1159.
[45]王晓飞,张钧萍,张晔.高光谱图像混合像元分解算法[J].红办与毫米波学报,2010,29(3)：210-215.
[46]罗文斐,钟亮,张兵,高连如.高光谱图像端元提取的零空间光谱投影算法[J].红外与毫米泚学报，2010,29(4)：307-311.
[47]S. Jia and Y. Qian. Spectral and spatial complexity-based hyperspectral unmixing [J]. IEEE Trans. Geosci. Remote Sens.,2007,45(12):3867-3879.
[48]F. Schmidt, A. Schmidt, E. Tre guier, et al. Implementation strategies for hyperspectral unmixing using Bayesian source separation [J]. IEEE Trans. Geosci. Remote Sens.,2010, 48(11):4003.
[49]丛浩,张良培,李平湘.一种端元可变的混合像元分解方法[J].中国图像图形学报,2006,11(8)：1092-1096.
[50]吴柯,张良培,李平湘.一种端元变化的神经网络混合像元分解算法方法[J].遥感学报，2007,11(1)：20-26.
[51]J. Zhang, B. Rivard, A. Sanchez-Azofeifa. Derivative spectral unmixing of hyperspectral data applied to mixtures of lichen and rock [J]. IEEE Trans. Geosci. Remote Sens.,2004,42(9): 1934.
[52]N. Dobigeon, J.-Y. Tourneret, and C.-I. Chang. Semi-supervised linear spectral unmixing using a hierarchical Bayesian model for hyperspectral imagery [J]. IEEE Trans. Geosci. Remote Sens.,2008,56(7):2684.
[53]A. Huck, M. Guillaume, and J. Blanc-Talon. Minimum dispersion constrained nonnegative matrix factorization to unmix hyperspectral data [J]. IEEE Trans. Geosci. Remote Sens.,2010, 48(6):2590.
[54]A. Zare and P. Gader. PCE:piecewise convex endmember detection [J]. IEEE Trans. Geosci. Remote Sens.,2010,48(6):2620.
[55]J. E. Ball, L. M. Bruce, N. H. Younan, et al. Hyperspectral pixel unmixing via spectral band selection and singular value decomposition [J]. IEEE Geosci. Remote Sens. Lett.,2007,4(3): 382.
[56]N. Dobigeon, S. Moussaoui, M. Coulon, et al. Joint bayesian endmember extraction and linear unmixing for hyperspectral imagery [J]. IEEE Trans. Signal Process.,2009,57(11): 4355
[57]游晓斌,游先祥,相莹莹.混合像元及混合像元分析[J].北京林业大学学报，2003,25：28-32.
[58]S. Liangrocapart and M. Petrou. Mixed pixels classification [C]. in Proc of:SPIE Conference on Image and Signal Processing for Remote Sensing Ⅳ,1998,3500:72-83.
[59]吕长春,王忠武,钱少猛.混合像元分解模型综述[J].遥感信息.2003,3：55-60.
[60]C.-I. Chang. An information theoretic-based approach to spectral variability, similarity and discriminability for hyperspectral image analysis [J]. IEEE Trans. Inform. Theory,2000, 46(5):1927-1932.
[61]Marsh, S. E., Switzer, and P. Kowalik, et al. Resolving the percentage of component terrains within single resolution elements [J]. Photogrammetric Engineering and Remote Sensing, 2001,46(8):1079-1086.
[62]R. Singer. Near-infrared spectral reflectance of mineral mixtures:Systematic combinations of. pyroxenes, olivine, and iron oxides [J]. Journal of Geophysical Research,1981,86: 7967-7982.
[63]M. O. Smith, P. E. Johnstonn, and J. B. Adams. Quantitative determination of mineral types and abundances from reflectance spectra using principle components analysis [J]. Journal of Geophysical Research,1985,90:797-804.
[64]D. Manolakis, C. Siracusa, and G. Shaw. Hyperspectral subpixel target detection using linear mixing model [J]. IEEE Trans. Geosci. Remote Sens.,2001,39(7):1392-1409.
[65]Charles Ichoku, Arnon Karnieli. A review of mixture modeling techniques for subpixel land cover estimation [J]. Remote Sensing Reviews,2001,1(13):161-186.
[66]A. M. Cross. Subpixel measurement of tropical cover using AVHRR data [J]. Int. J Remote Sens.,1991,12(5):1119-1129.
[67]N. A. Quarmby. Linear mixture modeling applied to AVHRR data for crop area estimation [J]. Int. J Remote Sens,,1995,13(3):415-425.
[68]A. R. Huete. Separation of soil-plant spectral mixture by factor analysis [J]. Remote Sensing of Environment,1986,19(3):237-251.
[69]D. S. Lu, M. Batistella. Linear mixture model applied to Amazonian vegetation classification [J]. Remote Sensing of Environment,2003,87:456-469.
[70]S. Wold. Principle Component Analysis [J]. Chemometrics and Intelligent Laboratory Systems,1987,2(11):37-52.
[71]A. A. Green, M. Berman, P. Switzer, et al. A transformation for ordering multispectral data in terms of image quality with implications for noise removal [J]. IEEE Trans. Geosci. Remote Sens.,1988,26(1):65-74.
[72]J. B. Lee, A. S. Woodyatt, and M. Berman. Enhancement of high spectral resolution remote-sensing data by a noise-adjusted principal components transform [J]. IEEE Trans. Geosci. Remote Sens.,1990,28(3):295-304.
[73]C.-I. Chang and Q. Du. Estimation of number of spectrally distinct signal sources in hyperspectral imagery [J]. IEEE Trans. Geosci. Remote Sens.,2004,42(3):608-619.
[74]J. M. Bioucas-Dias and J. M. P. Nascimento. Hyperspectral subspace identification [J]. IEEE Trans. Geosci. Remote Sens.,2008,46(8):2435-2445.
[75]J. Li and J. M. Bioucas-Dias. Minimum volume simplex analysis:a fast algorithm to unmix hyperspectral data [C]. in Proc. IGARSS, Boston, MA,2008,3:250-253, July.
[76]J. Boardman. Automating spectral unmixing of AVIRIS data using convegeometry concepts [C]. in JPL Pub.93-26, AVIRIS Workshop,1993,1:11-14.
[77]M. E. Winter. N-find:an algorithm for fast autonomous spectral endmember determination in hyperspectral data [C]. in Proc. SPIEconf. on Imaging Spectrometry V,1999,3753:266-275.
[78]J. Nascimento and J. Bioucas-Dias. Vertex component analysis:a fast algorithm to unmix hyperspectral data [J]. IEEE Trans. Geosci. Remote Sens.,2002,43(4):898-910.
[79]C.-I. Chang, C-C Wu, W. Liu, and Y-C Ouyang. A new growing method for simplex-based endmember extraction algorithm [J]. IEEE Trans. Geosci. Remote Sens.,2006,44(10): 2804-2819.
[80]X. Tao, B. Wang, and L. Zhang. A new approach based on orthogonal bases of data space to decomposition of mixed pixels for hyperspectral imagery [J]. Science China Series F: Information Sciences,2009,52(5):843-857.
[81]C.-I Chang, X.-L. Zhao, M. L. G. Althouse, and J. J. Pan. Least squares subspace projection approach to mixed pixel classification for hyperspectral image [J]. IEEE Trans. Geosci. Remote Sens.,1998,36(3):898-912.
[82]D. C. Heinz and C.-I. Chang. 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.
[83]L. Miao, H. Qi, and H. Szu. A Maximum Entropy Approach to Unsupervised Mixed-Pixel Decomposition [J]. IEEE Trans. Geosci. Remote Sens.,2007,16(4):1008-1021.
[84]A. Hyvarinen, J. Karhunen, and E. Oja. Independent Component Analysis [M]. New York: Wiley,2001.
[85]A. Hyvarinen. Fast and robust fixed-point algorithms for independent component analysis [J]. IEEE Trans. Neural Networks,1999,10(3):626-634.
[86]J. Nascimento and J. Bioucas-Dias. Does independent component analysis play a role in unmixing hyperspectral data? [J]. IEEE Trans. Geosci. Remote Sens.,2005,43(4):175-187.
[87]S. Moussaoui, H. Hauksdottir, F. Schmidt, C. Jutten, J. Chanussot, D. Brie, S. Doute, and J. A. Benediktsson. On the decomposition of mars hyperspectral data by ICA and bayesian positive source separation [J]. Neurocomputing,2008,71:2194-2208.
[88]D. D. Lee and H. S. Seung. Learning the parts of objects by non-negative matrix factorization [J]. Nature,1999,401:788-791.
[89]D. D. Lee and H. S. Seung. Algorithms for non-negative matrix factorization [J]. Adv. Neural Inform. Process. Syst.,2000,13:556-562.
[90]R. N. Clark, G.A. Swayze, A. Gallagher, T.V. King, and W.M. Calvin. The U.S. geological survey digital spectral library:Version 1:0.2 to 0.3 microns [R]. U.S. Geol. Surv., Open File Rep.,1993.
[91]Available at http://cobweb.ecn.purdue.edu/-biehl/MultiSpec/[OL].
[92]Available at http://www.tec.army.mil/Hypercube [OL].
[93]Available at http://aviris.jpl.nasa.gov/html/aviris.freedata.html [OL].
[94]W. Liu, N. Zheng, and X. Li. Review on nonnegative matrix factorization [R]. Technical Report of Institute of Artificial Intelligence and Robotics, Xi'an Jiaotong University, P. R. China,2004.
[95]D. Donoho and V. Stodden. When does non-negative matrix factorization give a correct decomposition into parts [OL].2003. Available:http://www.stanford.edu/-vcs/papers/ NMFCDP.pdf
[96]P. O. Hoyer. Non-negative sparse coding [C]. in Proc. of the 2002 12th IEEE Workshop NNSP,2002,557-565.
[97]P. O. Hoyer. Non-negative matrix factorization with sparseness constraints [J]. J. Machine Learn. Res.,2004,5:1457-1469.
[98]V. P. Pauca, J. Piper, and R. J. Plemmons. Nonnegative matrix factorization for spectral data analysis [J]. Lin. Alg. Appl,2006,416:29-47.
[99]P. Sajda, S. Du, and L. Parra. Recovery of constituent spectra using non-negative matrix factorization [C]. in Proc. SPIE, San Diego, CA,2003,5207:321-331.
[100]C.-Y. Liou and K. O. Yang. Unsupervised classification of remote sensing imagery with non-negative matrix factorization [C]. in Proc. ICONIP,2005,280-285.
[101]J. Piper, V. P. Pauca, and R. J. Plemmons, and M. Giffin. Object characterization from spectral data using nonnegative matrix factorization [C]. in Proc. AMOS Tech. Conf., Maui, HI,2004
[102]W. Liu and N. Zheng. Learning sparse features for classification by mixture models [J]. Patt. Recog. Lett.,2004,25:155-161.
[103]W. Liu, N. Zheng, and X. Li. Relative gradient speeding up additive updates for nonnegative matrix factorization [J]. Neurocomputing,2004,57:493-499.
[104]M. W. Berry, M. Browne, and A. N. Langville, et al. Algorithm and applications for approximate nonnegative matrix factorization [J]. Comp. Stat. Data Anal.,2007,52:155-173.
[105]Z. Chen and A. Cichocki. Nonnegative matrix factorization woth temporal smoothness and/or spatial decorrelation constraints. in Laboratory for Advanced Brain Signal Processing, RIKEN, Tech. Rep [OL]. Available:http://www.bsp.brain.riken.jp/ publications/2005/nips_nmf24-07.pdf
[106]A. Cichocki, S. Amari, and R. Zdunek, et al. Extended SMART algorithms for non-negative matrix factorization [J], Lect. Notes Comp. Sci.,2006,4029:548-562.
[107]R. Albright, J. Cox and D. Duling, et al. Algorithms, initializations, and convergence of the nonnegative matrix factorization [C]. in 12th ACM SIGKDD Int'l Conf. Knowledge Discovery and Data Mining (KDD'06).
[108]L. Miao and H. Qi. Endmember extraction from highly mixed data using minimum volume constrained nonnegative matrix factorization [J]. IEEE Trans. Geosci. Remote Sens.,2007, 45(3):765-777.
[109]S. Jia and Y. Qian. Constrained nonnegative matrix factorization for hyperspectral unmixing [J]. IEEE Trans. Geosci. Remote Sens.,2009,47(1):161-173.
[110]C-J. Lin. Projected gradient methods for non-negative matrix factorization [J]. Neural Comp., 2007,19(10):2756-2779.
[111]S. Wild, J. Curry, and A. Dougherty. Improving non-negative matrix factorization through structured initialization [J]. Patt. Recog.,2004,37:2217-2232.
[112]C. Boutsidis and E. Gallopoulos. SVD based initialization:A head start for nonnegative matrix factorization [J]. Patt. Recog.,2008,41:1350-1362.
[113]S. Kullback and R. A. Leibler. On information and sufficiency [J]. Ann. Math. Stat.,1951,22: 79-86.
[114]S. Kullback. Information theory and statistics [M], New York:John Wiley and Sons,1959.
[115]C.-I. Chang. Spectral information divergence for hyperspectral image analysis [C]. in Proc. IGARSS, Hamburg, Germany,1999,1:509-511.
[116]A. Plaza, P. Martinez, R. Perez, and J. Plaza. A quantitative and comparative analysis of endmember extraction algorithms from hyperspectral data [J]. IEEE Trans. Geosci. Remote Sens.,2004,42(3):650-663.
[117]D. Landgrebe. Multispectral data analysis:A signal theory perspective [R]. West Lafayette: School of Electrical & Computer Engineering, Purdue University,1998,56-89,.
[118]R. N. Clark and G. A. Swayze. Evolution in imaging spectroscopy analysis and sensor signal-to-noise:an examination of how far we have come. in The 6th Annual JPL Airborne Earth Science Workshop,1996 [OL]. Available:http://speclab.cr.usgs.gov/PAPERS. imspec.evol/aviris.evolution.html
[119]M. A. Heroux, P. Raghavan, and H. D. Simon. Parallel processing for scientific computing [M]. Cambridge:Cambridge University Press,2007.
[120]K. Asanovic, R. Bodik, B. C. Catanzaro, et al. The landscape of parallel computing research: A view from Berkeley [R]. EECS Dept., Univ. California, Berkeley, CA, Tech. Rep. No. UCB/EECS-2006-183,2006.
[121]Intel. Teraflops Research Chip [OL]. Available:http://techresearch.intel.com/articles/ Tera-Scale/1449.htm
[122]G. Amdahl. Validity of the single processor approach to achieving large-scale computing capabilities [C]. Proc. AFIPS Conference,1967,30:483-485.
[123]S. A. Robila, and L. G. Maciak. Considerations on parallelizing nonnegative matrix factorization foe hyperspectral data unmixing [J]. IEEE Geosci. Remote Sens. Lett.,2009, 6(1):57-61.
[124]A. Plaza, D. Valencia, J. Plaza, and C.-I. Chang. Parallel implementation of endmember extraction algorithms from hyperspectral data [J]. IEEE Geosci. Remote Sens. Lett.,2006, 3(3):334-338.
[125]A. Martinez-Uso, F. Pla, J. M. Sotoca, and P. Garcia-Sevilla. Clustering-based hyperspectral band selection using information measures [J]. IEEE Trans. Geosci. Remote Sens.,2007, 45(12):4158-4171.
[126]C.-I. Chang and S. Wang. Constrained band selection for hyperspectral imagery [J]. IEEE Trans. Geosci. Remote Sens.,2006,44(6):1575-1585.
[127]C. Sheffield. Selecting band combinations from multispectral data [J]. Photogramm. Eng. Remote Sens.,1985,51:681-687.
[128]J. C. Price. Spectral band selection for visible-near infrared remote sensing:Spectral-spatial resolution tradeoffs [J]. IEEE Trans. Geosci. Remote Sens.,1997,35:1277-1285.
[129]N. Keshava. Distance metrics and band selection in hyperspectral processing with applications to material identification and spectral libraries [J]. IEEE Trans. Geosci. Remote Sens.,2004,42(7):1552-1565.
[130]B. Guo, S. R. Gunn, R. I. Damper, and J. D. B. Nelson. Band selection for hyperspectral image classification using mutual information [J]. IEEE Geosci. Remote Sens. Lett.,2006, 3(4):522-526.
[131]F. Melgani and L. Bruzzone. Classification of hyperspectral remote sensing images with support vector machines [J]. IEEE Trans. Geosci. Remote Sens.,2004,42(8):1778-1790.
[132]S. Serpico and L. Bruzzone. A new search algorithm for feature selection in hyperspectral remote sensing images [J]. IEEE Trans. Geosci. Remote Sens.,2001,39(7):1360-1367.
[133]G. Petrie, P. Heasler, and T. Warner. Optimal band selection strategies for hyperspectral data sets [C]. in Proc. IGARSS, Seattle, WA,1998,1582-1584.
[134]P. Groves and P. Bajcsy. Methodology for hyperspectral band and classification model selection [C]. in Proc. IEEE Workshop Adv. Tech. Anal. Remotely Sensed Data, Greenbelt, MD,2003,120-128.
[135]C.-I. Chang, Q. Du, T.-L. Sun, and M. Althouse. A joint band prioritization and band-decorrelation approach to band selection for hyperspectral image classification [J]. IEEE Trans. Geosci. Remote Sens.,1999,37(6):2631-2641.
[136]M. Velez-Reyes and L. Jimenez. Subset selection analysis for the reduction of hyperspectral imagery [C]. in Proc IGARSS, Seattle, WA,1998,3:1577-1581.
[137]P. Bajcsy and P. Groves. Methodology for hyperspectral band selection [J]. Photogramm. Eng. Remote Sens. J.,2004,70(7):793-802.
[138]S. D. Stearns, B. E. Wilson, and J. R. Peterson. Dimensionality reduction by optimal band selection for pixel classification of hyperspectral imagery [J]. Applicat. Digital Image Processing ⅩⅥ,1993,2028:118-127.
[2]C.-I. Chang. Hyperspectral Imaging:Techniques for Spectral Detection and Classification [M]. New York:Plenum,2003.
[3]C.-I. Chang. Hyperspectral Data Exploitation [M]. New York:John Wiley & Sons, Inc., 2007.
[4]童庆禧,张兵,郑兰芬.高光谱遥感--原理，技术与应用[M].北京：高等教育出版社,2006.
[5]童庆禧.遥感科学技术进展[J].地理学报，1994,49：616-624.
[6]张良培,张立福.高光谱遥感[M].武汉：武汉大学出版社,2005.
[7]浦瑞良,宫鹏.高光谱遥感及其应用[M].北京：高等教育出版社,2000.
[8]G. Vane and A. F. H. Gotez. Terrestrial imaging spectrometry:current status, future trends [J]. Remote Sensing of Environment,1993,44:117-126.
[9]G. R. Hunt. Near-infrared spectral of alternation minerals-potential for use in remote sensing [J]. IEEE Trans. Geosci. Remote Sens.,1979,44(12):974-1986.
[10]钱乐祥,泮学芹,赵芊.中国高光谱成像遥感应用研究进展[J].国土资源遥感，2004,2：1-6.
[11]张斧.成像光谱技术发展的科学背景和现状[J].激光与红外,1994,24(1)：23-26.
[12]朱述龙,张占睦.遥感图像获取与分析[M].北京：科学出版社,2000.
[13]束炯,王强,孙娟.高光谱遥感的应用研究[J].华东师范大学学报(自然科学版),2006,4：1-10.
[14]A. F. H. Gotez, G. Vane, and J. E. Solomon, et al. Imaging spectrometry for earth remote sensing [J]. Science,1985,228:1147-1153.
[15]李天宏,杨海宏,赵永平.成像光谱仪遥感现状与展望[J].遥感技术与应用，1997,12(2)：54-58.
[16]R. Green, M. Eastwood, and C. Sarture, et al. Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS) [J]. Remote Sensing of Environment,1998, 65(3):227-248.
[17]张钧萍,张哗,周廷显.成像光谱技术超谱图像分类研究现状与分析[J].中国空间科学技术，2001,1：37-44.
[18]A. F. H. Goetz and L. C. Rowan. Geological remote sensing [J]. Science,1981,211:781-791.
[19]童庆禧.电子光学遥感系统的过去，现在和未来[M].北京：科学出版社,1995.
[20]L. J. Richard, R. W. Basedow, and E. Zalweski, et al. HYDICE:an airborne system for hyperspectral imaging [C]. in:Proc of SPIE,1993,1937:173-179.
[21]耿修瑞,高光谱遥感图像目标探测与分类技术研究[D]. PhD thesis,中国科学院研究生院(遥感应用研究所),2005.
[22]贾森,非监督的高光谱图像解混技术研究[D]. PhD Thesis,浙江大学计算机学院,2007.
[23]张钧萍,张晔,基于多特征多分辨率融合的高光谱图像分类[J].红外与毫米波学报,2004,23(5)：345-348.
[24]Q. Du and C.-I. Chang. A linear constrained distance-based discriminant analysis for hyperspectral image classification [J]. Pattern Recognition,2001,34:361-373.
[25]Q. Du and H. Ren. Real-time constrained linear discriminant analysis to target detection and classification in hyperspectral imagery [J]. Pattern Recognition,2003,36:1-12.
[26]C.-I. Chang, T.-L.E. Sun, and M. L. G. Althouse. An unsupervised interference rejection approach to target detection and classification for hyperspectral imagery [J]. Opt. Engng., 1998,37(3):735-743.
[27]C.-I. Chang, X. Zhao, M. L. G. Althouse, and J.-J. Pan. Least squars subspace projection approach to mixed pixel classification in hyperspectral images [J]. IEEE Trans. Geosci. Remote Sens.,1998,36(3):898-912.
[28]C.-I. Chang, H. Ren and S. S. Chiang. Real-time processing algorithms for target detection and classification in hyperspectral imagery [J]. IEEE Trans. Geosci. Remote Sens.,2000, 39(4):760-768.
[29]N. Keshava and J. F. Mustard. Spectral unmixing [J]. IEEE Signal Process. Mag.,2001, 19(1):44-57.
[30]惠巍巍,衣德萍,廖彩霞.混合像元分解综述[J].林业科技情报,2007,39(1)：2-3.
[31]N. Keshava. A survey of spectral unmixing algorithms [J]. Lincoln Lab. J.,2003,14(1): 55-73.
[32]J. J. Cipar, E. C. Meidunas, and E. M. Bassett. A comparison of endmember extraction techniques [C]. in:Proc of SPIE,2002,4725:1-9.
[33]薛绮,匡纲要,李智勇.基于线性混合模型的高光谱图像端元提取[J].遥感技术与应用，2004,19(3)：197-201.
[34]李剑萍,郑有飞.气象卫星混合像元分解研究综述[J].中国农业气象,2000,21(2)：44-47.
[35]J.-F. Cardoso. Blind signal separation:statistical principles [C]. Proc of the IEEE, Special issue on Blind Identification and estimation,1998,9(10):2009-2025.
[36]A. Cichocki and S. Amari. Adaptive Blind Signal and Image Processing:Learning Algorithms and Applications [M]. New York:John Wiley & Sons,2002.
[37]J. M. P. Nascimento. Unsupervised Hyperspectral Unmixing [D]. PhD thesis,2006.
[38]S. Mei, M. He, Z. Wang, and D. Feng. Spatial purity based endmember extraction for spectral mixture analysis [J], IEEE Trans. Geosci. Remote Sens.,2010,48(9):3434-3444.
[39]D. M. Rogge, B. Rivard, J. Zhang, and J. Feng. Iterative spectral unmixing for optimizing per-pixel endmember sets [J]. IEEE Trans. Geosci. Remote Sens.,2006,44(12):3725-3735.
[40]M. Zortea, A. Plaza. Spatial preprocessing for endmember extraction [J]. IEEE Trans. Geosci. Remote Sens.,2009,47(8):2679-2693.
[41]J. Li. Wavelet-based feature extraction for improved endmember abundance estimation in linear unmixing of hyperspectral signals [J]. IEEE Trans. Geosci. Remote Sens.,2004,42(3): 644-649.
[42]C. Kwan, B. Ayhan, G. Chen, et al. A novel approach for spectral unmixing, classification, and concentration estimation of chemical and biological agents [J]. IEEE Trans. Geosci. Remote Sens.,2006,44(2):409-419.
[43]杨伟,陈晋,松下文经.基于相关系数匹配的混合像元分解算法[J].遥感学报，2008,12(3)：454-461.
[44]C.-I. Chang and D. C. Heinz. Constrained subpixel target detection for remotely sensed imagery [J]. IEEE Trans. Geosci. Remote Sens.,2000,38(3):1144-1159.
[45]王晓飞,张钧萍,张晔.高光谱图像混合像元分解算法[J].红办与毫米波学报,2010,29(3)：210-215.
[46]罗文斐,钟亮,张兵,高连如.高光谱图像端元提取的零空间光谱投影算法[J].红外与毫米泚学报，2010,29(4)：307-311.
[47]S. Jia and Y. Qian. Spectral and spatial complexity-based hyperspectral unmixing [J]. IEEE Trans. Geosci. Remote Sens.,2007,45(12):3867-3879.
[48]F. Schmidt, A. Schmidt, E. Tre guier, et al. Implementation strategies for hyperspectral unmixing using Bayesian source separation [J]. IEEE Trans. Geosci. Remote Sens.,2010, 48(11):4003.
[49]丛浩,张良培,李平湘.一种端元可变的混合像元分解方法[J].中国图像图形学报,2006,11(8)：1092-1096.
[50]吴柯,张良培,李平湘.一种端元变化的神经网络混合像元分解算法方法[J].遥感学报，2007,11(1)：20-26.
[51]J. Zhang, B. Rivard, A. Sanchez-Azofeifa. Derivative spectral unmixing of hyperspectral data applied to mixtures of lichen and rock [J]. IEEE Trans. Geosci. Remote Sens.,2004,42(9): 1934.
[52]N. Dobigeon, J.-Y. Tourneret, and C.-I. Chang. Semi-supervised linear spectral unmixing using a hierarchical Bayesian model for hyperspectral imagery [J]. IEEE Trans. Geosci. Remote Sens.,2008,56(7):2684.
[53]A. Huck, M. Guillaume, and J. Blanc-Talon. Minimum dispersion constrained nonnegative matrix factorization to unmix hyperspectral data [J]. IEEE Trans. Geosci. Remote Sens.,2010, 48(6):2590.
[54]A. Zare and P. Gader. PCE:piecewise convex endmember detection [J]. IEEE Trans. Geosci. Remote Sens.,2010,48(6):2620.
[55]J. E. Ball, L. M. Bruce, N. H. Younan, et al. Hyperspectral pixel unmixing via spectral band selection and singular value decomposition [J]. IEEE Geosci. Remote Sens. Lett.,2007,4(3): 382.
[56]N. Dobigeon, S. Moussaoui, M. Coulon, et al. Joint bayesian endmember extraction and linear unmixing for hyperspectral imagery [J]. IEEE Trans. Signal Process.,2009,57(11): 4355
[57]游晓斌,游先祥,相莹莹.混合像元及混合像元分析[J].北京林业大学学报，2003,25：28-32.
[58]S. Liangrocapart and M. Petrou. Mixed pixels classification [C]. in Proc of:SPIE Conference on Image and Signal Processing for Remote Sensing Ⅳ,1998,3500:72-83.
[59]吕长春,王忠武,钱少猛.混合像元分解模型综述[J].遥感信息.2003,3：55-60.
[60]C.-I. Chang. An information theoretic-based approach to spectral variability, similarity and discriminability for hyperspectral image analysis [J]. IEEE Trans. Inform. Theory,2000, 46(5):1927-1932.
[61]Marsh, S. E., Switzer, and P. Kowalik, et al. Resolving the percentage of component terrains within single resolution elements [J]. Photogrammetric Engineering and Remote Sensing, 2001,46(8):1079-1086.
[62]R. Singer. Near-infrared spectral reflectance of mineral mixtures:Systematic combinations of. pyroxenes, olivine, and iron oxides [J]. Journal of Geophysical Research,1981,86: 7967-7982.
[63]M. O. Smith, P. E. Johnstonn, and J. B. Adams. Quantitative determination of mineral types and abundances from reflectance spectra using principle components analysis [J]. Journal of Geophysical Research,1985,90:797-804.
[64]D. Manolakis, C. Siracusa, and G. Shaw. Hyperspectral subpixel target detection using linear mixing model [J]. IEEE Trans. Geosci. Remote Sens.,2001,39(7):1392-1409.
[65]Charles Ichoku, Arnon Karnieli. A review of mixture modeling techniques for subpixel land cover estimation [J]. Remote Sensing Reviews,2001,1(13):161-186.
[66]A. M. Cross. Subpixel measurement of tropical cover using AVHRR data [J]. Int. J Remote Sens.,1991,12(5):1119-1129.
[67]N. A. Quarmby. Linear mixture modeling applied to AVHRR data for crop area estimation [J]. Int. J Remote Sens,,1995,13(3):415-425.
[68]A. R. Huete. Separation of soil-plant spectral mixture by factor analysis [J]. Remote Sensing of Environment,1986,19(3):237-251.
[69]D. S. Lu, M. Batistella. Linear mixture model applied to Amazonian vegetation classification [J]. Remote Sensing of Environment,2003,87:456-469.
[70]S. Wold. Principle Component Analysis [J]. Chemometrics and Intelligent Laboratory Systems,1987,2(11):37-52.
[71]A. A. Green, M. Berman, P. Switzer, et al. A transformation for ordering multispectral data in terms of image quality with implications for noise removal [J]. IEEE Trans. Geosci. Remote Sens.,1988,26(1):65-74.
[72]J. B. Lee, A. S. Woodyatt, and M. Berman. Enhancement of high spectral resolution remote-sensing data by a noise-adjusted principal components transform [J]. IEEE Trans. Geosci. Remote Sens.,1990,28(3):295-304.
[73]C.-I. Chang and Q. Du. Estimation of number of spectrally distinct signal sources in hyperspectral imagery [J]. IEEE Trans. Geosci. Remote Sens.,2004,42(3):608-619.
[74]J. M. Bioucas-Dias and J. M. P. Nascimento. Hyperspectral subspace identification [J]. IEEE Trans. Geosci. Remote Sens.,2008,46(8):2435-2445.
[75]J. Li and J. M. Bioucas-Dias. Minimum volume simplex analysis:a fast algorithm to unmix hyperspectral data [C]. in Proc. IGARSS, Boston, MA,2008,3:250-253, July.
[76]J. Boardman. Automating spectral unmixing of AVIRIS data using convegeometry concepts [C]. in JPL Pub.93-26, AVIRIS Workshop,1993,1:11-14.
[77]M. E. Winter. N-find:an algorithm for fast autonomous spectral endmember determination in hyperspectral data [C]. in Proc. SPIEconf. on Imaging Spectrometry V,1999,3753:266-275.
[78]J. Nascimento and J. Bioucas-Dias. Vertex component analysis:a fast algorithm to unmix hyperspectral data [J]. IEEE Trans. Geosci. Remote Sens.,2002,43(4):898-910.
[79]C.-I. Chang, C-C Wu, W. Liu, and Y-C Ouyang. A new growing method for simplex-based endmember extraction algorithm [J]. IEEE Trans. Geosci. Remote Sens.,2006,44(10): 2804-2819.
[80]X. Tao, B. Wang, and L. Zhang. A new approach based on orthogonal bases of data space to decomposition of mixed pixels for hyperspectral imagery [J]. Science China Series F: Information Sciences,2009,52(5):843-857.
[81]C.-I Chang, X.-L. Zhao, M. L. G. Althouse, and J. J. Pan. Least squares subspace projection approach to mixed pixel classification for hyperspectral image [J]. IEEE Trans. Geosci. Remote Sens.,1998,36(3):898-912.
[82]D. C. Heinz and C.-I. Chang. 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.
[83]L. Miao, H. Qi, and H. Szu. A Maximum Entropy Approach to Unsupervised Mixed-Pixel Decomposition [J]. IEEE Trans. Geosci. Remote Sens.,2007,16(4):1008-1021.
[84]A. Hyvarinen, J. Karhunen, and E. Oja. Independent Component Analysis [M]. New York: Wiley,2001.
[85]A. Hyvarinen. Fast and robust fixed-point algorithms for independent component analysis [J]. IEEE Trans. Neural Networks,1999,10(3):626-634.
[86]J. Nascimento and J. Bioucas-Dias. Does independent component analysis play a role in unmixing hyperspectral data? [J]. IEEE Trans. Geosci. Remote Sens.,2005,43(4):175-187.
[87]S. Moussaoui, H. Hauksdottir, F. Schmidt, C. Jutten, J. Chanussot, D. Brie, S. Doute, and J. A. Benediktsson. On the decomposition of mars hyperspectral data by ICA and bayesian positive source separation [J]. Neurocomputing,2008,71:2194-2208.
[88]D. D. Lee and H. S. Seung. Learning the parts of objects by non-negative matrix factorization [J]. Nature,1999,401:788-791.
[89]D. D. Lee and H. S. Seung. Algorithms for non-negative matrix factorization [J]. Adv. Neural Inform. Process. Syst.,2000,13:556-562.
[90]R. N. Clark, G.A. Swayze, A. Gallagher, T.V. King, and W.M. Calvin. The U.S. geological survey digital spectral library:Version 1:0.2 to 0.3 microns [R]. U.S. Geol. Surv., Open File Rep.,1993.
[91]Available at http://cobweb.ecn.purdue.edu/-biehl/MultiSpec/[OL].
[92]Available at http://www.tec.army.mil/Hypercube [OL].
[93]Available at http://aviris.jpl.nasa.gov/html/aviris.freedata.html [OL].
[94]W. Liu, N. Zheng, and X. Li. Review on nonnegative matrix factorization [R]. Technical Report of Institute of Artificial Intelligence and Robotics, Xi'an Jiaotong University, P. R. China,2004.
[95]D. Donoho and V. Stodden. When does non-negative matrix factorization give a correct decomposition into parts [OL].2003. Available:http://www.stanford.edu/-vcs/papers/ NMFCDP.pdf
[96]P. O. Hoyer. Non-negative sparse coding [C]. in Proc. of the 2002 12th IEEE Workshop NNSP,2002,557-565.
[97]P. O. Hoyer. Non-negative matrix factorization with sparseness constraints [J]. J. Machine Learn. Res.,2004,5:1457-1469.
[98]V. P. Pauca, J. Piper, and R. J. Plemmons. Nonnegative matrix factorization for spectral data analysis [J]. Lin. Alg. Appl,2006,416:29-47.
[99]P. Sajda, S. Du, and L. Parra. Recovery of constituent spectra using non-negative matrix factorization [C]. in Proc. SPIE, San Diego, CA,2003,5207:321-331.
[100]C.-Y. Liou and K. O. Yang. Unsupervised classification of remote sensing imagery with non-negative matrix factorization [C]. in Proc. ICONIP,2005,280-285.
[101]J. Piper, V. P. Pauca, and R. J. Plemmons, and M. Giffin. Object characterization from spectral data using nonnegative matrix factorization [C]. in Proc. AMOS Tech. Conf., Maui, HI,2004
[102]W. Liu and N. Zheng. Learning sparse features for classification by mixture models [J]. Patt. Recog. Lett.,2004,25:155-161.
[103]W. Liu, N. Zheng, and X. Li. Relative gradient speeding up additive updates for nonnegative matrix factorization [J]. Neurocomputing,2004,57:493-499.
[104]M. W. Berry, M. Browne, and A. N. Langville, et al. Algorithm and applications for approximate nonnegative matrix factorization [J]. Comp. Stat. Data Anal.,2007,52:155-173.
[105]Z. Chen and A. Cichocki. Nonnegative matrix factorization woth temporal smoothness and/or spatial decorrelation constraints. in Laboratory for Advanced Brain Signal Processing, RIKEN, Tech. Rep [OL]. Available:http://www.bsp.brain.riken.jp/ publications/2005/nips_nmf24-07.pdf
[106]A. Cichocki, S. Amari, and R. Zdunek, et al. Extended SMART algorithms for non-negative matrix factorization [J], Lect. Notes Comp. Sci.,2006,4029:548-562.
[107]R. Albright, J. Cox and D. Duling, et al. Algorithms, initializations, and convergence of the nonnegative matrix factorization [C]. in 12th ACM SIGKDD Int'l Conf. Knowledge Discovery and Data Mining (KDD'06).
[108]L. Miao and H. Qi. Endmember extraction from highly mixed data using minimum volume constrained nonnegative matrix factorization [J]. IEEE Trans. Geosci. Remote Sens.,2007, 45(3):765-777.
[109]S. Jia and Y. Qian. Constrained nonnegative matrix factorization for hyperspectral unmixing [J]. IEEE Trans. Geosci. Remote Sens.,2009,47(1):161-173.
[110]C-J. Lin. Projected gradient methods for non-negative matrix factorization [J]. Neural Comp., 2007,19(10):2756-2779.
[111]S. Wild, J. Curry, and A. Dougherty. Improving non-negative matrix factorization through structured initialization [J]. Patt. Recog.,2004,37:2217-2232.
[112]C. Boutsidis and E. Gallopoulos. SVD based initialization:A head start for nonnegative matrix factorization [J]. Patt. Recog.,2008,41:1350-1362.
[113]S. Kullback and R. A. Leibler. On information and sufficiency [J]. Ann. Math. Stat.,1951,22: 79-86.
[114]S. Kullback. Information theory and statistics [M], New York:John Wiley and Sons,1959.
[115]C.-I. Chang. Spectral information divergence for hyperspectral image analysis [C]. in Proc. IGARSS, Hamburg, Germany,1999,1:509-511.
[116]A. Plaza, P. Martinez, R. Perez, and J. Plaza. A quantitative and comparative analysis of endmember extraction algorithms from hyperspectral data [J]. IEEE Trans. Geosci. Remote Sens.,2004,42(3):650-663.
[117]D. Landgrebe. Multispectral data analysis:A signal theory perspective [R]. West Lafayette: School of Electrical & Computer Engineering, Purdue University,1998,56-89,.
[118]R. N. Clark and G. A. Swayze. Evolution in imaging spectroscopy analysis and sensor signal-to-noise:an examination of how far we have come. in The 6th Annual JPL Airborne Earth Science Workshop,1996 [OL]. Available:http://speclab.cr.usgs.gov/PAPERS. imspec.evol/aviris.evolution.html
[119]M. A. Heroux, P. Raghavan, and H. D. Simon. Parallel processing for scientific computing [M]. Cambridge:Cambridge University Press,2007.
[120]K. Asanovic, R. Bodik, B. C. Catanzaro, et al. The landscape of parallel computing research: A view from Berkeley [R]. EECS Dept., Univ. California, Berkeley, CA, Tech. Rep. No. UCB/EECS-2006-183,2006.
[121]Intel. Teraflops Research Chip [OL]. Available:http://techresearch.intel.com/articles/ Tera-Scale/1449.htm
[122]G. Amdahl. Validity of the single processor approach to achieving large-scale computing capabilities [C]. Proc. AFIPS Conference,1967,30:483-485.
[123]S. A. Robila, and L. G. Maciak. Considerations on parallelizing nonnegative matrix factorization foe hyperspectral data unmixing [J]. IEEE Geosci. Remote Sens. Lett.,2009, 6(1):57-61.
[124]A. Plaza, D. Valencia, J. Plaza, and C.-I. Chang. Parallel implementation of endmember extraction algorithms from hyperspectral data [J]. IEEE Geosci. Remote Sens. Lett.,2006, 3(3):334-338.
[125]A. Martinez-Uso, F. Pla, J. M. Sotoca, and P. Garcia-Sevilla. Clustering-based hyperspectral band selection using information measures [J]. IEEE Trans. Geosci. Remote Sens.,2007, 45(12):4158-4171.
[126]C.-I. Chang and S. Wang. Constrained band selection for hyperspectral imagery [J]. IEEE Trans. Geosci. Remote Sens.,2006,44(6):1575-1585.
[127]C. Sheffield. Selecting band combinations from multispectral data [J]. Photogramm. Eng. Remote Sens.,1985,51:681-687.
[128]J. C. Price. Spectral band selection for visible-near infrared remote sensing:Spectral-spatial resolution tradeoffs [J]. IEEE Trans. Geosci. Remote Sens.,1997,35:1277-1285.
[129]N. Keshava. Distance metrics and band selection in hyperspectral processing with applications to material identification and spectral libraries [J]. IEEE Trans. Geosci. Remote Sens.,2004,42(7):1552-1565.
[130]B. Guo, S. R. Gunn, R. I. Damper, and J. D. B. Nelson. Band selection for hyperspectral image classification using mutual information [J]. IEEE Geosci. Remote Sens. Lett.,2006, 3(4):522-526.
[131]F. Melgani and L. Bruzzone. Classification of hyperspectral remote sensing images with support vector machines [J]. IEEE Trans. Geosci. Remote Sens.,2004,42(8):1778-1790.
[132]S. Serpico and L. Bruzzone. A new search algorithm for feature selection in hyperspectral remote sensing images [J]. IEEE Trans. Geosci. Remote Sens.,2001,39(7):1360-1367.
[133]G. Petrie, P. Heasler, and T. Warner. Optimal band selection strategies for hyperspectral data sets [C]. in Proc. IGARSS, Seattle, WA,1998,1582-1584.
[134]P. Groves and P. Bajcsy. Methodology for hyperspectral band and classification model selection [C]. in Proc. IEEE Workshop Adv. Tech. Anal. Remotely Sensed Data, Greenbelt, MD,2003,120-128.
[135]C.-I. Chang, Q. Du, T.-L. Sun, and M. Althouse. A joint band prioritization and band-decorrelation approach to band selection for hyperspectral image classification [J]. IEEE Trans. Geosci. Remote Sens.,1999,37(6):2631-2641.
[136]M. Velez-Reyes and L. Jimenez. Subset selection analysis for the reduction of hyperspectral imagery [C]. in Proc IGARSS, Seattle, WA,1998,3:1577-1581.
[137]P. Bajcsy and P. Groves. Methodology for hyperspectral band selection [J]. Photogramm. Eng. Remote Sens. J.,2004,70(7):793-802.
[138]S. D. Stearns, B. E. Wilson, and J. R. Peterson. Dimensionality reduction by optimal band selection for pixel classification of hyperspectral imagery [J]. Applicat. Digital Image Processing ⅩⅥ,1993,2028:118-127.