Chinese Optics, Volume. 16, Issue 5, 1066(2023)
Infrared small target detection via L1−2 spatial-temporal total variation regularization
Figures & Tables(10)
Fig. 1. The detection results of the proposed algorithm in different scenes
Fig. 2. The ROC curves of different image sequences at different parameter
不同步长
Fig. 3. The detection results of the representative frames in Sequence 1-6 by the six tested methods
Fig. 4. The 3D detection results of the representative frames in Sequence 6
Table 1. The solution of
\begin{document}$ {L_{1 - 2}} $\end{document} View tableView in ArticleTable 1. The solution of
\begin{document}$ {L_{1 - 2}} $\end{document} 输入 ：红外图像序列${f_1},{f_2}, \cdots ,{f_P} \in { {\mathcal{R} }^{m \times n} }$ $L$ ${\lambda _1},{\lambda _2},\alpha .$ 输出 ：背景张量${ { {\mathcal{B} } }^k}$ ${ { {\mathcal{T} } }^k}$ ${ {\mathcal{N} }^k}.$ 初始化 ：输入图像序列转化为原始张量${ {\mathcal{F} } },$ $\rho = 1.1,$ ${ {\mathcal{B} }^0} = { {\boldsymbol{ {\mathcal{T} } } }^0} = { {\mathcal{N} }^0} = 0,{\mathcal{Y} }_1^0 = {\mathcal{Y} }_2^0 = 0,$ ${ {\mathcal{W} }^0} = {\mathcal{I} }$ $p$ $p = 0.8,$ ${\mu _0} = 1\times10^{-2},{\mu _{\max } } = 1\times10^7,k = 0.$ 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；
Table 2. The characteristic of the experimental data
View tableView in ArticleTable 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
Table 3. Quantitative evaluation results of the tested methods for the representative images of sequences 1-3
View tableView in ArticleTable 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
Table 4. Quantitative evaluation results of the tested methods for the representative images of sequences 4-6
View tableView in ArticleTable 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
Table 5. Runtime comparison of different algorithms
(s) View tableView in ArticleTable 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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De-min ZHAO, Yang SUN, Zai-ping LIN, Wei XIONG. Infrared small target detection via L1−2 spatial-temporal total variation regularization[J]. Chinese Optics, 2023, 16(5): 1066
Paper Information
Category: Original Article
Received: Nov. 8, 2022
Accepted: --
Published Online: Oct. 27, 2023
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