XU Jin-huan1, SHEN Yu1, LIU Peng-fei2, XIAO Liang1
1. Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, China;
2. School of Computer Science, School of Software, Nanjing University of Posts and Telecommunications, Nanjing, Jiangsu 210023, China
Abstract：Sparse multinomial logistic regression(SMLR) is an important supervised classification method for hyperspectral images(HSI).However,because the traditional SMLR based pixel-wise classifiers only use the spectral signatures,the good robustness and high classification accuracy are hardly achieved with a small number of samples without considering the spatial information of HSI.By using the kernel tricks,the kernel sparse multinomial logistic regression(KSMLR) method can partly overcome this limitation,however the resulted misclassification errors are still expected to be further reduced.According to the statistical analysis of classification errors resulted in KSMLR,we propose a novel two stage framework which combines KSMLR and error rejection for HSI classification.The proposed model,named KSMRL-TVL1,adopts the L1 norm to measure the heavy-tailed property of the classification errors so as to build the data fidelity term,and uses the total variation(TV) regularization term to measure the local spatial smoothness of the hidden probability field.The experiments on Indian Pines dataset and University of Pavia dataset show that the proposed method can better improve the robustness and classification accuracy.
[1] 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,2006.166-238. TONG Qing-xi,ZHANG Bing,ZHENG Lan-fen.Hyperspectral Remote Sensing[M].Beijing:Higher Education Press,2006.166-238.(in Chinese)
[2] 吴泽彬,韦志辉,孙乐,等.基于迭代加权L1正则化的高光谱混合像元分解[J].南京理工大学学报,2011,35(4):431-435. WU Ze-Bin,WEI Zhi-hui,SUN Le,et al.Hyperspectral unmixing based on iterative weighted L1 regularization[J].Journal of Nanjing University of Science and Technology,2011,35(4):431-435.(in Chinese)
[3] 宋相法,焦李成.基于稀疏表示及光谱信息的高光谱遥感图像分类[J].电子与信息学报,2012,34(2):268-272. SONG Xiang-fa,JIAO Li-cheng.Classification of hyperspectral remote sensing image based on sparse representation and spectral information[J].Journal of Electronics and Information Technology,2012,34(2):268-272.(in Chinese)
[4] DU Bo,ZHANG Liang-pei.Random-selection-based anomaly detector for hyperspectral imagery[J].IEEE Transactions on Geoscience and Remote Sensing,2011,49(5):1578-1589.
[5] MELGANI F,BRUZZONE L.Classification of hyperspectral remote sensing images with support vector machines[J].IEEE Transactions on Geoscience and Remote Sensing,2004,42(8):1778-1790.
[6] BOHNING D.Multinomial logistic regression algorithm[J].Annals of the Institute of Statistical Mathematics,1992,44(1):197-200.
[7] CHEN Y,NASRABADI N M,TRAN T D.Hyperspectral image classification using dictionary based sparse representation[J].IEEE Transactions on Geoscience and Remote Sensing,2011,49(10):3973-3985.
[8] KRISHNAPURAM B,CARIN L,FIGUEIREDO M A T,Hartemink A J.Sparse multinomial logistic regression:fast algorithms and generalization bounds[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2005,27(6):957-968.
[9] BIOUCAS-DIAS J M,FIGUEIREDO M.Logistic regression via variable splitting and augmented lagrangian tools[R].Instituto Superior T'ecnico,TULisbon,2009.
[10] 孙乐,吴泽彬,冯灿,等.一种新的两分类器融合的空谱联合高光谱分类方法[J].电子学报,2015,43(11):2210-2217. SUN L,WU Ze-bin,FENG Can,et al.A novel two-classifier fusion method for spectral-spatial hyperspectral classification[J].Acta Electronica Sinica,2015,43(11):2210-2217.(in Chinese)
[11] GURRAM P,KWON H.Contextual SVM Using Hilbert Space Embedding for Hyperspectral Classification[J].IEEE Geoscience and Remote Sensing Letters,2013,10(5):1031-1035.
[12] 倪鼎,马洪兵.基于近邻协同的高光谱图像谱-空联合分类[J].自动化学报,2015,41(2):273-284. NI Ding,MA Hong-bing.Spectral-spatial classification of hyperspectral images based on neighborhood collaboration[J].Acta Automatica Sinica,2015,41(2):273-284.(in Chinese)
[13] CAMPS-VALLS G,GOMEZ-CHOVA L,MUNOZ-MARI J,et al.Composite kernels for hyperspectral image classification[J].IEEE Geoscience & Remote Sensing Letters,2006,3(1):93-97.
[14] DU Bo,ZHANG Liang-pei,ZHANG Le-fei,et al.A discriminative manifold learning based dimension reduction method for hyperspectral classification[J].International Journal of Fuzzy Systems,2012,14(2):272-277.
[15] SHI Qian,ZHANG Liang-pei,DU Bo.Semisupervised discriminative locally enhanced alignment for hyperspectral image classification[J].IEEE Transactions on Geoscience and Remote Sensing,2013,51(9):4800-4815.
[16] HUANG Xin,LU Qi-kai,ZHANG Liang-pei,et al.New postprocessing methods for remote sensing image classification:a systematic study[J].IEEE Transactions on Geoscience and Remote Sensing,2014,52(11):7140-7159.
[17] TARABALKA Y,FAUVEL M,CHANUSSOT J,et al.SVM-and MRF-based method for accurate classification of hyperspectral images[J].IEEE Geoscience and Remote Sensing Letters,2010,7(4):736-740.
[18] LI J,BIOUCAS-DIAS J M,PLAZA A.Semisupervised hyperspectral image segmentation using multinomial logistic regression with active learning[J].IEEE Transactions on Geoscience and Remote Sensing,2010,48(11):4085-4098.
[19] LI J,BIOUCAS-DIAS J M,PLAZA A.Spectral-spatial hyperspectral image segmentation using subspace multinomial logistic regression and Markov random fields[J].IEEE Transactions on Geoscience and Remote Sensing,2012,50(3):809-823.
[20] ZHANG Bing,LI Shan-shan,JIA Xiu-ping,et al.Adaptive Markov random field approach for classification of hyperspectral imagery[J].IEEE Geoscience and Remote Sensing Letters,2011,8(5):973-977.
[21] SUN Le,WU Ze-bin,LIU Jian-jun,et al.Supervised spectral-spatial hyperspectral image classification with weighted Markov random fields[J].IEEE Transactions on Geoscience and Remote Sensing,2014,53(3):1490-1503.
[22] IORDACHE M D,BIOUCAS-DIAS J M,PLAZA A.Total variation spatial regularization for sparse hyperspectral unmixing[J].IEEE Transactions on Geoscience and Remote Sensing,2012,50(11):4484-4502.
[23] ESSER E.Applications of Lagrangian-Based Alternating Direction Methods and Connections to Split Bregman[R].CAM Report,2009.
[24] GOLDSTEIN T,OSHER S.The split bregman method for L1-regularized problems[J].SIAM Journal on Imaging Sciences,2009,2(2):323-343.
[25] WU Chun-lin,TAI Xue-cheng.Augmented Lagrangian method,dual methods,and split Bregman iteration for ROF,vectorial TV,and high order models[J].SIAM Journal on Imaging Sciences,2010,3(3):300-339.
[26] IORDACHE M D,BIOUCAS-DIAS J M,PLAZA A.Total variation spatial regularization for sparse hyperspectral unmixing[J].IEEE Transactions on Geoscience and Remote Sensing,2012,50(11):4484-4502.
[27] CHEN Y,NASRABADI N M,TRAN T D.Hyperspectral image classification via kernel sparse representation[A].Processing of International Conference on Image Processing[C].Brussels,Belgium:IEEE Computer Society,2011.1233-1236.
[28] LI J,BIOUCAS-DIAS J M,PLAZA A.Exploiting spatial information in semi-supervised hyperspectral image segmentation[A].Proceedings of Hyperspectral Image and Signal Processing:Evolution in Remote Sensing[C].Reykjavik,Iceland:GRSS,2010.1-4.
[29] DU B,WANG Z,ZHANG L,et al.Exploring representativeness and informativeness for active learning[J].IEEE Transactions on Cybernetics,2017,47(1):14-26.
2018, Vol. 46 
