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基于L1−2时空域总变分正则项的红外弱小目标检测算法

赵德民 孙扬 林再平 熊伟

赵德民, 孙扬, 林再平, 熊伟. 基于L1−2时空域总变分正则项的红外弱小目标检测算法[J]. 中国光学(中英文), 2023, 16(5): 1066-1080. doi: 10.37188/CO.2022-0229
引用本文: 赵德民, 孙扬, 林再平, 熊伟. 基于L1−2时空域总变分正则项的红外弱小目标检测算法[J]. 中国光学(中英文), 2023, 16(5): 1066-1080. doi: 10.37188/CO.2022-0229
ZHAO De-min, SUN Yang, LIN Zai-ping, XIONG Wei. Infrared small target detection via L1−2 spatial-temporal total variation regularization[J]. Chinese Optics, 2023, 16(5): 1066-1080. doi: 10.37188/CO.2022-0229
Citation: ZHAO De-min, SUN Yang, LIN Zai-ping, XIONG Wei. Infrared small target detection via L1−2 spatial-temporal total variation regularization[J]. Chinese Optics, 2023, 16(5): 1066-1080. doi: 10.37188/CO.2022-0229

基于L1−2时空域总变分正则项的红外弱小目标检测算法

doi: 10.37188/CO.2022-0229
基金项目: 国家自然科学基金(No. 91738302)
详细信息
    作者简介:

    赵德民(1992—),男,湖南常德人,硕士研究生,工程师,主要研究方向为控制工程、图像处理。E-mail:421071849@qq.com

    孙 扬(1992—),男,湖南岳阳人,博士,讲师,主要研究方向为图像处理、红外目标检测。E-mail:sunyang_kd@163.com

    林再平(1982—),男,湖南长沙人,博士,副研究员,主要研究方向为空间信息处理、目标检测。E-mail:linzaiping@sina.com

    熊 伟(1971—),男,山东临邑人,博士,博士生导师,研究员,主要从事信息系统建模仿真与评估等方面研究。E-mail:13331094335@163.com

  • 中图分类号: TP391.4

Infrared small target detection via L1−2 spatial-temporal total variation regularization

Funds: Supported by National Natural Science Foundation of China (No. 91738302)
More Information
  • 摘要:

    针对红外图像序列中复杂背景干扰下容易出现的高虚警问题,提出一种基于${L_{1 - 2}}$时空域总变分正则项的红外弱小目标检测算法。首先,将红外图像序列转化为时空域红外张量块,该步骤可利用张量的高维数据结构优势关联图像序列中的时空域信息。然后,利用加权Schatten $p$范数和${L_{1 - 2}}$时空域总变分正则项对低秩背景成分进行重构,以保留背景中起伏剧烈的边缘和角点,提高稀疏目标的重构精度。最后,将目标张量恢复为图像序列,利用自适应阈值分割方法得到最终的目标图像。与另外5种检测算法进行对比实验,结果显示,该方法的虚警率较Maxemeidan算法、Tophat算法、LIRDNet算法、DNANet算法以及WSNMSTIPT算法平均分别下降了71.4%、71.1%、68.5%、74.3%和20.47%;而在检测实时性方面,该算法耗时为Maxemeidan算法、DNANet算法以及WSNMSTIPT算法的42.4%、82.9%和28.7%。实验结果验证了该方法在检测性能上的优越性,表明该算法能够显著提高复杂背景干扰下的目标检测精度和效率。

     

  • 图 1  本文方法在不同典型场景下的检测结果

    Figure 1.  The detection results of the proposed algorithm in different scenes

    图 2  不同步长L下6组测试序列的ROC曲线

    Figure 2.  The ROC curves of different image sequences at different parameter $L$

    图 3  不同检测方法的红外弱小目标检测结果

    Figure 3.  The detection results of the representative frames in Sequence 1-6 by the six tested methods

    图 4  序列六的三维图像对比示意图

    Figure 4.  The 3D detection results of the representative frames in Sequence 6

    图 5  序列1-6的ROC曲线对比图

    Figure 5.  ROC curves of the detection results of Sequences 1-6

    表  1  $ {L_{1 - 2}} $STTV模型的求解

    Table  1.   The solution of $ {L_{1 - 2}} $ STTV model

    输入:红外图像序列${f_1},{f_2}, \cdots ,{f_P} \in { {\mathcal{R} }^{m \times n} }$,帧数步长$L$,正则化参数${\lambda _1},{\lambda _2},\alpha .$
    输出:背景张量${ { {\mathcal{B} } }^k}$,目标张量${ { {\mathcal{T} } }^k}$,噪声张量${ {\mathcal{N} }^k}.$
    初始化:输入图像序列转化为原始张量${ {\mathcal{F} } },$$\rho = 1.1,$
    ${ {\mathcal{B} }^0} = { {\boldsymbol{ {\mathcal{T} } } }^0} = { {\mathcal{N} }^0} = 0,{\mathcal{Y} }_1^0 = {\mathcal{Y} }_2^0 = 0,$${ {\mathcal{W} }^0} = {\mathcal{I} }$,Schattern $p$范数指数$p = 0.8,$${\mu _0} = 1\times10^{-2},{\mu _{\max } } = 1\times10^7,k = 0.$
    迭代循环: 收敛误差条件不满足时,执行
    1. 根据式(12)更新背景张量${ {\mathcal{B} }^{k + 1} }$;
    2. 根据式(22)、(23)、(24)更新${ {\mathcal{Z} }^{k + 1} }$;
    3. 根据式(27)更新目标张量${ {\mathcal{T} }^{k + 1} }$;
    4. 根据式(29)更新噪声张量${ {\mathcal{N} }^{k + 1} }$;
    5. 根据式(30)、(31)更新拉格朗日乘子和$ {\mu ^{k + 1}} $;
    6. 根据式(32)更新背景权重张量${ {\mathcal{W} }^{k + 1} }$;
    7. 判断下列收敛条件是否满足:
    ${ {\left\| { {\mathcal{F} } - {\mathcal{B} } - {\mathcal{T} } - {\mathcal{N} } } \right\|_F^2} \mathord{\left/ {\vphantom { {\left\| { {\mathcal{F} } - {\mathcal{B} } - {\mathcal{T} } - {\mathcal{N} } } \right\|_F^2} {\left\| {\mathcal{F} } \right\|_F^2} } } \right. } {\left\| {\mathcal{F} } \right\|_F^2} } \leqslant \varepsilon$
    满足则跳出循环,输出结果,否则执行步骤8;
    8. 迭代次数$k = k + 1$,返回步骤1;
    下载: 导出CSV

    表  2  实验数据特性

    Table  2.   The characteristic of the experimental data

    序号帧数尺寸背景特性目标SCR
    1120250×200天空场景,卷云层和噪声干扰2.24
    2120200×150天空场景,云层和噪声干扰4.35
    3120128×128地面场景,高亮背景干扰2.13
    4120200×158天空场景,高亮云层干扰0.94
    5120256×256地面场景,高亮杂波干扰1.76
    6120256×256地面场景,高亮杂波干扰1.01
    下载: 导出CSV

    表  3  不同方法在序列1至序列3的评价指标

    Table  3.   Quantitative evaluation results of the tested methods for the representative images of sequences 1-3

    算法序列1的第24帧序列2的第92帧序列3的第60帧
    LSNRGBSFSCRGCGLSNRGBSFSCRGCGLSNRGBSFSCRGCG
    Maxmedian0.530.731.972.721.882.526.582.610.820.713.194.48
    Tophat0.910.631.602.531.351.071.801.681.051.321.461.11
    LIRDNet1.042.4316.894.931.298.2731.853.850.941.704.682.75
    DNANet0.991.416.884.882.3712.3039.253.190.982.134.522.12
    WSNMSTIPT1.061.7213.357.75InfInfInf7.811.091.505.493.66
    本文算法1.122.9822.827.67InfInfInf8.871.102.5114.435.75
    下载: 导出CSV

    表  4  不同方法在序列4至序列6的评价指标

    Table  4.   Quantitative evaluation results of the tested methods for the representative images of sequences 4-6

    算法序列4的第76帧序列5的第72帧序列6的第117帧
    LSNRGBSFSCRGCGLSNRGBSFSCRGCGLSNRGBSFSCRGCG
    Maxmedian2.352.0512.946.301.391.2911.588.950.882.6212.594.80
    Tophat2.291.525.693.751.270.944.975.301.021.113.072.77
    LIRDNetNaNInfNaN0.00InfInfInf20.06NaNInfNaN0.00
    DNANetNaNInfNaN0.00NaNInfNaN0.00NaNInfNaN0.00
    WSNMSTIPTInfInfInf7.272.505.0273.5314.651.9314.64100.256.85
    本文算法InfInfInf15.85InfInfInf23.16InfInfInf12.33
    下载: 导出CSV

    表  5  算法运行时间比较

    Table  5.   Runtime comparison of different algorithms (s)

    算法序列1序列2序列3序列4序列5序列6
    Tophat1.931.651.152.202.162.70
    Maxmedian174.39110.1858.47114.21205.67209.48
    LIRDNet19.9239.1316.6438.4576.3683.62
    DNANet31.2665.4133.4258.24130.19126.58
    WSNMSTIPT79.8780.4166.2074.34527.15459.19
    本文算法20.8147.6924.8351.82109.69114.93
    下载: 导出CSV
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  • 收稿日期:  2022-11-08
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