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基于子空间结构正则化的L21非负矩阵分解高光谱解混

陈善学 刘荣华

陈善学, 刘荣华. 基于子空间结构正则化的L21非负矩阵分解高光谱解混[J]. 电子与信息学报, 2022, 44(5): 1704-1713. doi: 10.11999/JEIT210232
引用本文: 陈善学, 刘荣华. 基于子空间结构正则化的L21非负矩阵分解高光谱解混[J]. 电子与信息学报, 2022, 44(5): 1704-1713. doi: 10.11999/JEIT210232
CHEN Shanxue, LIU Ronghua. L21 Nonnegative Matrix Factorization for Hyperspectral Unmixing Based on Subspace Structure Regularization[J]. Journal of Electronics & Information Technology, 2022, 44(5): 1704-1713. doi: 10.11999/JEIT210232
Citation: CHEN Shanxue, LIU Ronghua. L21 Nonnegative Matrix Factorization for Hyperspectral Unmixing Based on Subspace Structure Regularization[J]. Journal of Electronics & Information Technology, 2022, 44(5): 1704-1713. doi: 10.11999/JEIT210232

基于子空间结构正则化的L21非负矩阵分解高光谱解混

doi: 10.11999/JEIT210232
基金项目: 国家自然科学基金(61271260),重庆市教委科学技术研究项目(KJ1400416)
详细信息
    作者简介:

    陈善学:男,1966年生,教授,研究方向为图像处理、数据压缩

    刘荣华:女,1995年生,硕士生,研究方向为高光谱图像解混

    通讯作者:

    刘荣华 1181396334@qq.com

  • 中图分类号: TN911.73

L21 Nonnegative Matrix Factorization for Hyperspectral Unmixing Based on Subspace Structure Regularization

Funds: The National Natural Science Foundation of China (61271260), The Science and Technology Research Project of Chongqing Municipal Education Commission (KJ1400416)
  • 摘要: 标准的非负矩阵分解(NMF)应用于高光谱解混时,容易受到噪声和异常值的干扰,解混效果较差。为了提高分解性能,该文将L21范数引入标准的NMF算法中,对模型进行了改进,从而提高算法的鲁棒性。其次,为了提高分解后丰度矩阵的稀疏性,将双重加权稀疏约束引入L21NMF模型中,使其中一个权值提高每个像元对应的丰度向量上的稀疏性,另一个权值提高每个端元对应的丰度向量上的稀疏性。同时,为了利用像元的全局空间分布信息,观察地物在不同图像中的真实分布情况,引入子空间结构正则项,提出了基于子空间结构正则化的L21非负矩阵分解(L21NMF-SSR)算法。通过在模拟数据集和真实数据集与其他经典算法的比较,验证了该算法具有更好的性能,同时具有去噪能力。
  • 图  1  模拟数据中的光谱曲线

    图  2  L21NMF-SSR在λ1值下的SAD和RMSE

    图  3  L21NMF-SSR在λ2α值下的SAD和RMSE

    图  4  不同算法在不同端元数目的性能比较

    图  5  L21NMF-SSR提取的端元特征与参考特征的对比

    图  6  不同算法的丰度图对比

    图  7  L21NMF-SSR提取端元特征与真实端元特征的对比

    图  8  不同算法在Urban数据集的丰度图对比

    表  1  L21NMF-SSR算法(算法1)

     输入:高光谱图像矩阵${\boldsymbol{Y}}$
     输出:端元矩阵${\boldsymbol{E}}$,丰度矩阵${\boldsymbol{A}}$和自表达矩阵${\boldsymbol{Z}}$
     步骤1:使用VCA-FCLS初始化${\boldsymbol{E}}$和${\boldsymbol{A}}$,利用LRR计算${\boldsymbol{Z}}$,且
         ${\boldsymbol{L}} = {\boldsymbol{Z}}$;
     步骤2:利用式(20)更新${\boldsymbol{E}}$;
     步骤3:用${{\boldsymbol{Y}}_f}$和${{\boldsymbol{E}}_f}$替换${\boldsymbol{Y}}$和${\boldsymbol{E}}$;
     步骤4:利用式(24)、式(26)更新${\boldsymbol{A}}$和${\boldsymbol{Z}}$;
     步骤5:用SVT更新${\boldsymbol{L}}$;
     步骤6:直到满足停止条件;
    下载: 导出CSV

    表  2  不同算法在不同信噪比级别下的SAD值的比较

    SNR(dB)L1/2-NMFRSNMFSRRNMFSSRNMFSSR-NMFL21NMF-SSR
    150.19330.18960.17950.16220.14470.1025
    200.14900.12930.11270.09390.06530.0528
    250.09980.09650.08980.08000.04910.0391
    300.09520.08530.06390.05610.02670.0160
    350.06120.05140.04620.02650.00940.0073
    下载: 导出CSV

    表  3  不同算法在不同信噪比级别下的RMSE值的比较

    SNR(dB)L1/2-NMFRSNMFSRRNMFSSRNMFSSR-NMFL21NMF-SSR
    150.36690.33520.32470.28210.26190.1796
    200.27540.24880.17930.16140.15410.0996
    250.11720.10670.11250.09260.06590.0560
    300.10930.09010.07240.06420.04620.0318
    350.08610.06230.05220.04560.03120.0186
    下载: 导出CSV

    表  4  不同算法在Jasper Ridge数据集的SAD值对比

    L1/2-NMFRSNMFSRRNMFSSRNMFSSR-NMFL21NMF-SSR
    树木0.12840.17210.13060.13380.11310.1224
    水体0.08160.10610.08620.11950.09580.0307
    土壤0.15330.15840.15450.11890.14450.1711
    道路0.11740.10500.12120.11230.07230.0494
    均值0.12020.12170.12310.12110.10640.0934
    下载: 导出CSV

    表  5  不同算法在Jasper Ridge数据集的RMSE值对比

    L1/2-NMFRSNMFSRRNMFSSRNMFSSR-NMFL21NMF-SSR
    RMSE 0.2126 0.2080 0.2124 0.1564 0.1415 0.1311
    下载: 导出CSV

    表  6  不同算法在Urban数据集的SAD值对比

    L1/2-NMFRSNMFSRRNMFSSRNMFSSR-NMFL21NMF-SSR
    沥青0.36290.26310.25150.26610.17340.1324
    玻璃0.32780.23890.28390.21960.20090.1574
    树木0.20180.19750.19560.14090.11060.1130
    屋顶0.14090.20640.17830.18510.14630.1194
    均值0.25840.22650.22730.20290.15780.1306
    下载: 导出CSV

    表  7  不同算法在Urban数据集的RMSE值对比

    L1/2-NMFRSNMFSRRNMFSSRNMFSSR-NMFL21NMF-SSR
    RMSE0.35670.34930.34110.32830.27870.2581
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-03-22
  • 修回日期:  2021-08-13
  • 网络出版日期:  2021-08-27
  • 刊出日期:  2022-05-25

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