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一种高精度并行主偏度分析算法及其在遥感图像中的应用

王大虎 刘畅 王健 姚锴 张振

王大虎, 刘畅, 王健, 姚锴, 张振. 一种高精度并行主偏度分析算法及其在遥感图像中的应用[J]. 电子与信息学报, 2023, 45(10): 3492-3501. doi: 10.11999/JEIT220960
引用本文: 王大虎, 刘畅, 王健, 姚锴, 张振. 一种高精度并行主偏度分析算法及其在遥感图像中的应用[J]. 电子与信息学报, 2023, 45(10): 3492-3501. doi: 10.11999/JEIT220960
WANG Dahu, LIU Chang, WANG Jian, YAO Kai, ZHANG Zhen. A High Precision Parallel Principal Skewness Analysis Algorithm and Its Application to Remote Sensing Images[J]. Journal of Electronics & Information Technology, 2023, 45(10): 3492-3501. doi: 10.11999/JEIT220960
Citation: WANG Dahu, LIU Chang, WANG Jian, YAO Kai, ZHANG Zhen. A High Precision Parallel Principal Skewness Analysis Algorithm and Its Application to Remote Sensing Images[J]. Journal of Electronics & Information Technology, 2023, 45(10): 3492-3501. doi: 10.11999/JEIT220960

一种高精度并行主偏度分析算法及其在遥感图像中的应用

doi: 10.11999/JEIT220960
详细信息
    作者简介:

    王大虎:男,博士生,研究方向为雷达信号处理、遥感图像处理

    刘畅:男,研究员,研究方向为雷达信号处理、雷达图像处理、多任务合成孔径雷达系统

    王健:男,博士生,研究方向为立体SAR、雷达信号处理、雷达图像处理

    姚锴:男,博士生,研究方向为雷达信号处理、雷达波形设计

    张振:男,助理研究员,研究方向为图像处理、无人机系统

    通讯作者:

    刘畅 cliu@aircas.ac.cn

  • 中图分类号: TN911.7

A High Precision Parallel Principal Skewness Analysis Algorithm and Its Application to Remote Sensing Images

  • 摘要: 主偏度分析(PSA)作为主成分分析(PCA)的一种3阶推广,常用于盲图像分离、SAR图像去噪以及高光谱特征提取等。但现有PSA算法只能得到近似解,这会影响图像后续处理的精度。针对这一问题,该文在现有PSA算法基础上,提出了一种高精度并行主偏度分析(PPSA)算法。PPSA算法充分考虑数据结构,选用协偏度张量的全部切片的特征向量作为迭代的初始值,可以准确地得到实际解。仿真实验以及实际遥感图像实验验证了PPSA算法的有效性与优越性。
  • 图  1  不同初始值,PSA, MPSA算法求解结果

    图  2  不同初始值,NPSA算法求解结果

    图  3  PPSA算法求解结果

    图  4  源图像以及各种算法处理结果

    图  5  原始数据以及各种算法处理结果

    图  6  高光谱Cuprite数据彩色图像

    图  8  PPSA算法对高光谱图像Cuprite的偏度比较

    图  7  4种算法运行时间对比图

    算法1 PPSA算法
     输入:输入数据${\boldsymbol{R}} \in {{\boldsymbol{R}}^{L \times N} }$
     输出:输出变换矩阵${\boldsymbol{U}}$, ${\boldsymbol{Y}} = {{\boldsymbol{U}}^{\rm{T}}}\tilde {\boldsymbol{R}}$
     (1) 白化数据,得到$\tilde {\boldsymbol{R}}$
     (2) 根据式(1)计算m阶$L $维张量${\boldsymbol{S}}$
     (3) 计算张量${\boldsymbol{S}}$切片的所有特征向量,记为V% main loop: %
     (4) ${\text{for }}i = 1:{L^2}{\text{ do}} $
     (5)   k = 0
     (6)   ${\boldsymbol{u}}_i^{(k)} = {\boldsymbol{V}}(:,i)$
     (7)   while stop conditions are not meet do
     (8)     ${\boldsymbol{u}}_i^{(k + 1)} = {\boldsymbol{S}}{ \times _1}{\boldsymbol{u}}_i^{(k + 1)}{ \times _3}{\boldsymbol{u}}_i^{(k + 1)}$
     (9)     ${\boldsymbol{u}}_i^{(k + 1)} = {\boldsymbol{u}}_i^{(k + 1)}/{\left\| {{\boldsymbol{u}}_i^{(k + 1)} } \right\|_2}$
     (10)   end while
     (11)   ${{\boldsymbol{U}}_{:i} } = {\boldsymbol{u}}_i^{(k + 1)}$
     (12) end for
    下载: 导出CSV

    表  1  不同初始化方法的比较,选取n个初始值计算100 000次的结果

    随机选取$n$个初始值随机选取$n$个正交初始值单个切片的特征向量作为初始值
    2490278907398270
    3128645308098029
    474503537397222
    523611556585831
    6836517150430
    78928135851
    82712919981
    982917004
    下载: 导出CSV

    表  2  不同初始化方法的比较,选取n × n个初始值计算100 000次的结果

    随机选取$ n \times n $个初始值随机选取$ n \times n $正交初始值全部切片的特征向量作为初始值
    2908339818499997
    3884019283099999
    4882259002999989
    5856468845199994
    6796737009699988
    7793826915699974
    8775766854699991
    9643386657099938
    下载: 导出CSV

    表  3  FastICA, PSA, MPSA, NPSA, MSDP和PPSA算法评估结果

    指标FastICAPSAMPSANPSAMSDPPPSA


    1


    ISI0.67570.06810.05510.02530.02030.0203
    TMSE3.2856×10–112.5547×10–112.5548×10–113.8168×10–111.8645×10–111.8645×10–11
    $ \rho $0.95440.99540.99540.99920.99980.9998
    0.98890.99920.99880.999970.99920.9992
    0.99681.00001.00001.00001.00001.0000
    PSNR66.169676.610577.744983.635085.912985.9129
    70.032572.644873.795474.435874.487074.4870
    79.257990.990190.432491.166791.328591.3285
    T(s)0.00420.00110.00100.00432.85940.0032
    2ISI0.48440.14420.15240.07870.07450.0745
    TMSE3.2241×10–112.6798×10–112.6337×10–112.5154×10–111.9555×10–141.9555×10–14
    $ \rho $0.97490.99670.99670.99950.99970.9997
    0.99000.99050.99070.99200.99210.9921
    0.99700.99990.99981.00001.00001.0000
    PSNR69.188674.938975.670883.458883.767483.7674
    73.714373.118674.353170.121870.601770.6017
    76.917589.046690.468394.077694.782394.7823
    T(s)0.00520.00110.00100.00423.10460.0021
    3ISI0.29650.04050.04520.00410.00060.0006
    TMSE2.6603×10–102.6628×10–101.9986×10–103.4050×10–101.7480×10–101.7480×10–10
    $ \rho $0.97560.99660.99620.99971.00001.0000
    0.99500.99940.99951.00001.00001.0000
    0.99690.99980.99991.00001.00001.0000
    PSNR69.922883.255978.820691.466996.638896.6388
    61.812361.149258.887261.229764.021264.0212
    82.332787.541690.474994.042495.191095.1910
    T(s)0.00480.00120.00090.00332.97860.0022
    下载: 导出CSV

    表  4  不同算法的平均峰值信噪比和平均绝对误差(计算10次运行的平均结果)

    组合 评估指标FastICAPSANPSAPPSA均值滤波中值滤波
    1PSNR64.329383.629283.987984.111562.089260.9464
    MAE0.07190.01270.01200.01190.17490.1957
    2PSNR61.356281.470581.881581.971162.769762.3189
    MAE0.16310.01710.01630.01610.15740.1659
    3PSNR68.668478.820078.882478.955564.031464.6669
    MAE0.06660.02450.02430.02410.13060.1233
    (注释:组合1中${E_{{\text{gs}}}}$=0, $\delta _{{\text{gs}}}^{\text{2}}$=100, ${E_{{\text{gm}}}}$=2, $\delta _{{\text{gm}}}^{\text{2}}$=80;组合2中${E_{{\text{gs}}}}$=0, $\delta _{{\text{gs}}}^{\text{2}}$=80, ${E_{{\text{gm}}}}$=2, $\delta _{{\text{gm}}}^{\text{2}}$=60;组合3中${E_{{\text{gs}}}}$=0, $\delta _{{\text{gs}}}^{\text{2}}$=60, ${E_{{\text{gm}}}}$=2, $\delta _{{\text{gm}}}^{\text{2}}$=40)
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-07-18
  • 修回日期:  2022-11-13
  • 录用日期:  2022-12-20
  • 网络出版日期:  2022-12-23
  • 刊出日期:  2023-10-31

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