基于<i>L</i><sub>1−2</sub>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

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

赵德民^{1, 2,},
孙扬^3, ,,
林再平^3,,
熊伟^1,

1.
航天工程大学, 北京150001
2.
航天东方红卫星有限公司, 北京100080
3.
国防科技大学电子科学学院, 湖南长沙 410073

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
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出版历程
- 收稿日期: 2022-11-08
- 修回日期: 2022-12-01
- 网络出版日期: 2023-04-14

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

ZHAO De-min^{1, 2
,},
SUN Yang^{3
, ,},
LIN Zai-ping^3
,,
XIONG Wei^1
,

1.
Aerospace Engineering University, Beijing 150001, China
2.
DFH Satellite Corporation, Beijing 100080, China
3.
College of Electronic Science and Technology, National University of Defense Technology, Changsha 410073, China

Funds: Supported by National Natural Science Foundation of China (No. 91738302)

More Information

Corresponding author: sunyang_kd@163.com

摘要

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。
- 红外弱小目标 /
- 时空域信息 /
- 时空域总变分正则 /
- 张量主成分分析 /
- 低秩和稀疏重构
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 Schatten p-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.

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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

下载: 全尺寸图片幻灯片

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 $L$

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

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
算法	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

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
算法	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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