Infrared small target detection via L1−2 spatial-temporal total variation regularization
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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。Abstract:To solve the high false alarms caused by complex background clutters in infrared small-target detection, a novel detection method based on
${L_{1 - 2}}$ spatial-temporal total variation regularization is proposed. First, the input infrared image sequence is transformed into a Spatial-Temporal Infrared Patch-Tensor (STIPT) structure. This step can associate the spatial and temporal information by using the high dimensional data structures in the tensor domain. Then, weighted Schattenp -norm and${L_{1 - 2}}$ spatial-temporal total variation regularization are incorporated to recover the low-rank background component to preserve the strong edges and corners, which can improve the accuracy of sparse target component recovery. Finally, the STIPT structure can be transformed into an infrared image sequence by the inverse operator, and an adaptive threshold segmentation is used to obtain the real target. The method is verified using a contrast test with other five methods, and the experimental results show that the false alarm rate by this method decreases to 71.4%, 71.7%, 68.5%, 74.3% and 20.47% compared with the Maxemeidan, Tophat, LIRDNet, DNANet and WSNMSTIPT algorithms. The time cost also decreased to 42.4%, 82.9% and 28.7% of that of the Maxemeidan, DNANet and WSNMSTIPT. The extensive experimental results demonstrate the superiority of this method in detection performance, which can greatly improve the accuracy and efficiency of target detection with complex background clutters. -
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
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；
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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 1 120 250×200 天空场景，卷云层和噪声干扰 2.24 2 120 200×150 天空场景，云层和噪声干扰 4.35 3 120 128×128 地面场景，高亮背景干扰 2.13 4 120 200×158 天空场景，高亮云层干扰 0.94 5 120 256×256 地面场景，高亮杂波干扰 1.76 6 120 256×256 地面场景，高亮杂波干扰 1.01
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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 LSNRG BSF SCRG CG LSNRG BSF SCRG CG LSNRG BSF SCRG CG Maxmedian 0.53 0.73 1.97 2.72 1.88 2.52 6.58 2.61 0.82 0.71 3.19 4.48 Tophat 0.91 0.63 1.60 2.53 1.35 1.07 1.80 1.68 1.05 1.32 1.46 1.11 LIRDNet 1.04 2.43 16.89 4.93 1.29 8.27 31.85 3.85 0.94 1.70 4.68 2.75 DNANet 0.99 1.41 6.88 4.88 2.37 12.30 39.25 3.19 0.98 2.13 4.52 2.12 WSNMSTIPT 1.06 1.72 13.35 7.75 Inf Inf Inf 7.81 1.09 1.50 5.49 3.66 本文算法 1.12 2.98 22.82 7.67 Inf Inf Inf 8.87 1.10 2.51 14.43 5.75
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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 LSNRG BSF SCRG CG LSNRG BSF SCRG CG LSNRG BSF SCRG CG Maxmedian 2.35 2.05 12.94 6.30 1.39 1.29 11.58 8.95 0.88 2.62 12.59 4.80 Tophat 2.29 1.52 5.69 3.75 1.27 0.94 4.97 5.30 1.02 1.11 3.07 2.77 LIRDNet NaN Inf NaN 0.00 Inf Inf Inf 20.06 NaN Inf NaN 0.00 DNANet NaN Inf NaN 0.00 NaN Inf NaN 0.00 NaN Inf NaN 0.00 WSNMSTIPT Inf Inf Inf 7.27 2.50 5.02 73.53 14.65 1.93 14.64 100.25 6.85 本文算法 Inf Inf Inf 15.85 Inf Inf Inf 23.16 Inf Inf Inf 12.33
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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 Tophat 1.93 1.65 1.15 2.20 2.16 2.70 Maxmedian 174.39 110.18 58.47 114.21 205.67 209.48 LIRDNet 19.92 39.13 16.64 38.45 76.36 83.62 DNANet 31.26 65.41 33.42 58.24 130.19 126.58 WSNMSTIPT 79.87 80.41 66.20 74.34 527.15 459.19 本文算法 20.81 47.69 24.83 51.82 109.69 114.93
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