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一种基于协同稀疏和全变差的高光谱线性解混方法

陈允杰 葛魏东 孙乐

陈允杰, 葛魏东, 孙乐. 一种基于协同稀疏和全变差的高光谱线性解混方法. 自动化学报, 2018, 44(1): 116-128. doi: 10.16383/j.aas.2018.c160414
引用本文: 陈允杰, 葛魏东, 孙乐. 一种基于协同稀疏和全变差的高光谱线性解混方法. 自动化学报, 2018, 44(1): 116-128. doi: 10.16383/j.aas.2018.c160414
CHEN Yun-Jie, GE Wei-Dong, SUN Le. A Novel Linear Hyperspectral Unmixing Method Based on Collaborative Sparsity and Total Variation. ACTA AUTOMATICA SINICA, 2018, 44(1): 116-128. doi: 10.16383/j.aas.2018.c160414
Citation: CHEN Yun-Jie, GE Wei-Dong, SUN Le. A Novel Linear Hyperspectral Unmixing Method Based on Collaborative Sparsity and Total Variation. ACTA AUTOMATICA SINICA, 2018, 44(1): 116-128. doi: 10.16383/j.aas.2018.c160414

一种基于协同稀疏和全变差的高光谱线性解混方法

doi: 10.16383/j.aas.2018.c160414
基金项目: 

国家自然科学基金 61601236

国家自然科学基金 61672291

江苏省自然科学基金 BK20150923

国家自然科学基金 61571230

国家自然科学基金 61471199

详细信息
    作者简介:

    陈允杰  南京信息工程大学数学与统计学院教授.2008年获得南京理工大学模式识别与智能系统博士学位.主要研究方向为数值计算, 模式识别, 图像分析.E-mail:priestcyj@nuist.edu.cn

    葛魏东  南京信息工程大学硕士研究生.主要研究方向为高光谱遥感图像解混.E-mail:15295748192@163.com

    通讯作者:

    孙乐  南京信息工程大学计算机与软件学院讲师.2014年获得南京理工大学模式识别与智能系统博士学位.主要研究方向为高光谱遥感图像解混、分类和目标识别.本文通信作者.E-mail:sunlecncom@163.com

A Novel Linear Hyperspectral Unmixing Method Based on Collaborative Sparsity and Total Variation

Funds: 

National Natural Science Foundation of China 61601236

National Natural Science Foundation of China 61672291

Natural Science Foundation of Jiangsu Province BK20150923

National Natural Science Foundation of China 61571230

National Natural Science Foundation of China 61471199

More Information
    Author Bio:

     Professor at the College of Math and Statistics, Nanjing University of Information Science and Technology. He received his Ph. D. degree from Nanjing University of Science and Technology in 2008. His research interest covers image processing, pattern recognition, and numerical analysis

     Master student at the College of Math and Statistics, Nanjing University of Information Science and Technology. His main research interest is image processing of hyperspectral unmixing

    Corresponding author: SUN Le  Lecturer at the School of Computer and Software, Nanjing University of Information Science and Technology. He received his Ph. D. degree from Nanjing University of Science and Technology in 2014. His research interest covers image processing especially for hyperspectral imagery, including unmixing, classification, and restoration. Corresponding author of this paper
  • 摘要: 稀疏分解是高光谱图像(Hyperspectral image,HSI)解混中的常用方法,为了克服传统稀疏解混方法只重视挖掘空间相关性而忽视稀疏性精确刻画的缺点,本文提出一种新的基于协同稀疏和全变差(Total variation,TV)相结合的高光谱空谱联合线性解混方法,从而进一步提高解混的精度.该方法基于已知光谱库的高光谱稀疏线性回归模型,利用TV正则项对高光谱邻域像元间的相关性进行约束;同时,协同稀疏性被用来刻画丰度系数的行稀疏性,从而表明协同稀疏先验对空谱联合解混精度的提高至关重要;最后采用交替方向乘子法求解模型.模拟高光谱数据实验结果定量地验证本文方法能够比现有同类方法获得更精确的解混结果,同时真实高光谱数据实验结果定性地验证了本文方法的有效性.
    1)  本文责任编委 辛景民
  • 图  1  基于协同稀疏和TV正则项的高光谱线性解混方法的流程图

    Fig.  1  Flowchart of the method based on collaborative sparsity and total variation

    图  2  5个端元在光谱库中的谱线

    Fig.  2  Spectral characteristic curves of five endmembers

    图  3  模拟数据图以及其中5个端元的真实丰度图

    Fig.  3  Simulated image and five true fractional abundances of endmembers in the simulated dataset

    图  4  不同噪声下CLSUnSAL-TV算法得到的关于参数$\lambda$和$\lambda_{\text{TV}}$的SRE函数图

    Fig.  4  SRE (dB) as a function of parameters $\lambda$ and $\lambda_{\text{TV}}$ obtained by CLSUnSAL-TV algorithm in different noise levels

    图  5  信噪比为40 dB情况下6种算法解混得到的丰度图

    Fig.  5  Reconstructed abundances of six methods for simulated dataset when SNR = 40 (dB)

    图  6  Cuprite数据的RGB伪彩合成图(波段15、23、117)

    Fig.  6  The false color image of AVIRIS Cuprite (band 15、23、117)

    图  7  对真实数据使用6种方法解混得到的丰度图

    Fig.  7  Reconstructed abundances of six methods for real dataset

    表  1  6种方法在最优参数($\lambda, \lambda_{\text{TV}}, \mu$)时对模拟数据集解混得到的SRE (dB), RMSE ($10^{-2}$)以及所需时间$t$ (s)

    Table  1  SRE, RMSE ($10^{-2}$), the running time (seconds), and optimal parameters of the six unmixing methods for the simulated dataset

    Constraint SNR (dB) NCLS SUnSAL CLSUnSAL NCLS-TV SUnSAL-TV 本文方法
    SRE $-$6.605 2.810 5.781 6.325 9.752 9.887
    不添加 RMSE 7.39 2.50 1.77 1.67 1.14 1.11
    "和为一" 20 $t$ 27.893 15.895 46.083 288.623 344.225 312.128
    约束 $\lambda$ 0 0.01 1 0 0.005 0.5
    $\lambda_{\text{TV}}$ 0 0 0 0.01 0.01 0.05
    $\mu$ 0.01 0.05 0.02 0.05 0.05 0.03
    SRE 0.910 6.155 9.501 10.054 14.153 15.095
    不添加 RMSE 3.11 1.70 1.16 1.09 0.68 0.61
    "和为一" 30 $t$ 12.322 27.303 52.105 110.546 114.569 91.574
    约束 $\lambda$ 0 0.01 1 0 0.005 0.5
    $\lambda_{\text{TV}}$ 0 0 0 0.01 0.01 0.05
    $\mu$ 0.01 0.05 0.02 0.05 0.05 0.03
    SRE 5.497 11.150 17.850 18.772 22.003 23.625
    不添加 RMSE 1.83 0.96 0.41 0.40 0.27 0.23
    "和为一" 40 $t$ 7.2 30.76 17.406 122.905 129.609 97.493
    约束 $\lambda$ 0 0.01 0.5 0 0.0005 0.1
    $\lambda_{\text{TV}}$ 0 0 0 0.05 0.005 0.005
    $\mu$ 0.01 0.05 0.08 0.04 0.04 0.05
    SRE 2.339 2.861 5.826 7.033 10.069 10.123
    添加 RMSE 2.64 2.50 1.75 1.54 1.08 1.06
    "和为一" 20 $t$ 36.146 22.197 58.385 28.750 351.530 320.872
    约束 $\lambda$ 0 0.1 1 0 0.0005 0.05
    $\lambda_{\text{TV}}$ 0 0 0 0.05 0.1 0.05
    $\mu$ 0.01 0.05 0.05 0.05 0.5 0.3
    SRE 5.955 6.176 9.680 13.424 14.619 15.272
    添加 RMSE 1.74 1.70 1.53 0.74 0.64 0.60
    "和为一" 30 $t$ 18.981 31.524 62.153 119.349 125.995 124.671
    约束 $\lambda$ 0 0.05 1 0 0.005 0.5
    $\lambda_{\text{TV}}$ 0 0 0 0.01 0.01 0.005
    $\mu$ 0.01 0.05 0.02 0.8 0.8 0.02
    SRE 10.633 11.317 19.010 22.344 22.390 23.998
    添加 RMSE 1.01 0.94 0.39 0.26 0.25 0.22
    "和为一" 40 $t$ 11.571 35.470 27.047 128.115 140.698 109.489
    约束 $\lambda$ 0 0.01 0.5 0 0.0005 0.1
    $\lambda_{\text{TV}}$ 0 0 0 0.05 0.005 0.005
    $\mu$ 0.01 0.05 0.03 0.05 0.1 0.04
    下载: 导出CSV
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  • 收稿日期:  2016-05-23
  • 录用日期:  2016-12-10
  • 刊出日期:  2018-01-20

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