Infrared small target detection method based on nonconvex low-rank Tuck decomposition

Jun-Gang YANG; Ting LIU; Yong-Xian LIU; Bo-Yang LI; Ying-Qian WANG; Wei-Dong SHENG; Wei AN

doi:10.11972/j.issn.1001-9014.2025.02.017

Journal of Infrared and Millimeter Waves, Volume. 44, Issue 2, 297(2025)

Infrared small target detection method based on nonconvex low-rank Tuck decomposition

Jun-Gang YANG1... Ting LIU1,2,*, Yong-Xian LIU1,**, Bo-Yang LI1, Ying-Qian WANG1, Wei-Dong SHENG1 and Wei AN1 |Show fewer author(s)

Author Affiliations

¹College of Electronic Science and Technology，National University of Defense Technology，Changsha 410073，China

²College of Automation and Electronic Information，Xiangtan University，Xiangtan 411100，China

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Abstract Get PDF(in Chinese)

Figures & Tables(11)

Fig. 1. The overall flow chart of the proposed method

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Fig. 2. Comparison of ADMM algorithm and sGSADMM algorithm：（a）ADMM algorithm；（b）sGSADMM algorithm

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Fig. 3. The convergence curve of the proposed method on Sequence 6

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Fig. 4. The qualitative experimental results of the proposed method and eight compared methods on Sequences 1-3（red rectangular box represents targets，blue oval represents background clutters and false alarm）

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Fig. 5. The qualitative experimental results of the proposed method and eight compared methods on Sequences 4-6（where red rectangular box represents targets，blue oval represents background clutters and false alarm）

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Fig. 6. 3D ROC curves for the proposed method and compared methods on Sequences 1-6. Each row from left to right represents 3D ROC，2D ROC $(F_{a}, P_{d})$ ，2D ROC $(τ, P_{d})$ ，2D ROC $(τ, F_{a})$

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Table 0. [in Chinese]

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Table 0. [in Chinese]

算法1 本文的NFTD-sGSADMM算法
1.输入. 红外图像序列， $O$ ， $B^{0} = S^{0} = 0$ ，L，H， $λ_{1}$ ， $λ_{2}$ ， $ρ_{0} = 0.01$ ， $ρ_{m a x} = 1 e 7$ ， $μ = 1.5$ ， $ζ = 1 e - 6$
2.重复以下步骤，直到满足停止条件：
步骤1. 根据式（11）更新 $U_{n}$
步骤2. 根据式（14）更新 $W_{n}$
步骤3. 根据式（16）更新 $B$
步骤4. 根据式（19）更新 $G$
步骤5. 根据式（21）更新 $S$
步骤6. 根据式（16）更新 $B$
步骤7. 根据式（14）更新 $W_{n}$
步骤8. 根据式（11）更新 $U_{n}$
步骤9 根据式（22）更新 ${\{δ_{n}\}}_{n = 1}^{N}$ ， $Γ$ ， $Λ$
步骤10. 根据式（23）更新 $ρ$
步骤11. 检查是否达到收敛条件 $\frac{{‖O - B - S‖}_{F}^{2}}{{‖O‖}_{F}^{2}} \leq ζ$
3.输出. 背景图像 $B$ ，目标图像 $S$

Table 1. AUC metrics for different L and H values in sequence 1

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Table 1. AUC metrics for different L and H values in sequence 1

L	H	$A U C_{(F_{a}, F_{d})}$	$A U C_{(τ, P_{d})}$	$A U C_{(τ, F_{a})}$	$A U C_{O A}$	$A U C_{S N P R}$
3	8	0.9916	0.9683	0.0020	1.9579	484.15
4	8	0.9999	0.9966	0.0020	1.9945	498.30
5	8	0.9999	0.9995	0.0020	1.9974	499.75
6	8	0.9999	0.8608	0.0022	1.8585	391.27
7	8	0.9999	0.7980	0.0037	1.7942	215.68
8	8	0.9999	0.7980	0.0052	1.7927	153.46
L	H	$A U C_{(F_{a}, F_{d})}$	$A U C_{(τ, P_{d})}$	$A U C_{(τ, F_{a})}$	$A U C_{O A}$	$A U C_{S N P R}$
5	2	0.9999	0.8804	0.1133	1.7670	7.7705
5	4	0.9999	0.8529	0.0335	1.8193	25.460
5	6	0.9999	0.8176	0.0078	1.8097	104.82
5	8	0.9999	0.9995	0.0020	1.9974	499.75
5	10	0.9999	0.9974	0.0020	1.9953	498.70

Table 2. Evaluation of detection performance of different methods on Sequences 1-6.

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Table 2. Evaluation of detection performance of different methods on Sequences 1-6.

场景	NRAM	ECASTT	MSLSTIPT	ASTTV-NTLA	IMNN-LWEC	SRSTT	4D-TT	NFTD-sGSADMM
	0.9999	0.9958	0.9999	0.9999	0.9999	0.9958	0.9999	0.9999	0.9999
	0.9941	0.9835	0.9577	0.9000	0.9863	0.9936	0.7863	0.8059	0.9995
序列1	0.0512	0.0020	0.0082	0.0752	0.0300	0.0020	0.0020	0.0020	0.0020
	1.9428	1.9773	1.9494	1.8247	1.9562	1.9874	1.7842	1.8038	1.9974
	19.416	491.75	116.79	11.968	32.877	496.80	393.15	402.95	499.75
	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999
	0.7902	0.7157	0.9682	0.9866	0.9431	0.8569	0.7667	0.8882	0.9830
序列2	0.0270	0.0020	0.0022	0.2867	0.0439	0.0020	0.0020	0.0020	0.0020
	1.7631	1.7136	1.9659	1.6998	1.8991	1.8548	1.7646	1.8861	1.9809
	29.267	357.85	440.09	3.4412	21.483	428.45	383.35	444.10	491.50
	0.9999	0.9999	0.9998	0.9999	0.9999	0.9915	0.9999	0.9999	0.9999
	0.9617	0.9549	0.7065	0.8255	0.8176	0.9056	0.8216	0.8176	0.9667
序列3	0.0309	0.0020	0.0051	0.0643	0.0455	0.0022	0.0020	0.0020	0.0020
	1.9307	1.9528	1.7012	1.7611	1.7720	1.8949	1.8195	1.8155	1.9646
	31.123	477.45	138.53	12.838	17.969	411.64	410.80	408.80	483.35
	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999	0.9999
	0.9667	0.9353	0.9766	0.9471	0.9984	0.9863	0.9510	0.9392	0.9947
序列4	0.0247	0.0020	0.0034	0.0741	0.0204	0.0020	0.0020	0.0020	0.0020
	1.9419	1.9332	1.9731	1.8729	1.9779	1.9842	1.9489	1.9371	1.9926
	39.138	467.65	287.24	12.781	48.941	493.15	475.50	469.60	497.35
	0.9999	0.8999	0.9995	0.9999	0.9999	0.9916	0.9999	0.9999	0.9999
	0.9878	0.7855	0.7130	0.9846	0.9976	0.9853	0.9667	0.9627	0.9911
序列5	0.0479	0.0022	0.0099	0.3427	0.1384	0.0020	0.0020	0.0020	0.0020
	1.9398	1.6832	1.7026	1.6418	1.8591	1.9749	1.9646	1.9606	1.9890
	20.622	357.05	72.020	2.8731	7.2081	492.65	483.35	481.35	495.55
	0.9999	0.9874	0.9999	0.9999	0.9999	0.9833	0.9999	0.9999	0.9999
	1.0000	0.7614	0.8175	0.9000	0.9976	0.9290	0.8529	0.9392	0.9812
序列6	0.0521	0.0021	0.0075	0.1386	0.1776	0.0021	0.0020	0.0020	0.0020
	1.9478	1.7467	1.8099	1.7613	1.8199	1.9102	1.8508	1.9371	1.9791
	19.194	362.57	109.00	6.4935	5.6171	442.38	426.45	469.60	490.60

Table 3. Performance evaluation related to ablation experiments

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Table 3. Performance evaluation related to ablation experiments

场景	FTD-sGSADMM	NFTD-ADMM	NFTD-sGSADMM
	0.9833	0.9999	0.9999	0.9999
	0.8888	0.9881	0.9865	0.9947
序列4	0.0020	0.0020	0.0020	0.0020
	1.8701	1.9860	1.9844	1.9926
	444.40	494.05	493.25	497.35
	0.9999	0.9958	0.9999	0.9999
	0.9941	0.9751	0.9814	0.9911
序列5	0.0199	0.0020	0.0020	0.0020
	1.9741	1.9689	1.9793	1.9890
	49.955	487.55	490.70	495.55
	0.9999	0.9749	0.9916	0.9999
	0.9314	0.9411	0.9600	0.9812
序列6	0.0217	0.0020	0.0020	0.0020
	1.9096	1.9140	1.9496	1.9791
	42.922	470.55	480.00	490.60

Table 4. Time comparison of the proposed method and compared methods in six scenes.

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Table 4. Time comparison of the proposed method and compared methods in six scenes.

	序列1	序列2	序列3	序列4	序列5	序列6
Top-hat	0.0043s	0.0042s	0.0042s	0.0042s	0.0050s	0.0041s
NRAM	1.3736s	0.9492s	1.3235s	1.4354s	1.2867s	1.3546s
ECASTT	4.7305s	4.8508s	4.7872s	4.7385s	4.9369s	4.6887s
MSLSTIPT	2.1905s	2.2949s	2.2691s	2.2357s	2.2702s	2.2541s
ASTTV-NTLA	1.9818s	1.8454s	1.8661s	1.7746s	1.8840s	1.8520s
IMNN-LWEC	2.5232s	2.5428s	2.5530s	2.6821s	2.5472s	2.7229s
SRSTT	13.994s	12.236s	13.235s	14.389s	14.287s	14.566s
4D-TT	0.9129s	0.9272s	0.9319s	0.9310s	0.9881s	0.9635s
NFTD-sGSADMM	0.1807s	0.1795s	0.2418s	0.1778s	0.4583s	0.4309s

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Jun-Gang YANG, Ting LIU, Yong-Xian LIU, Bo-Yang LI, Ying-Qian WANG, Wei-Dong SHENG, Wei AN. Infrared small target detection method based on nonconvex low-rank Tuck decomposition[J]. Journal of Infrared and Millimeter Waves, 2025, 44(2): 297

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Paper Information

Category: Interdisciplinary Research on Infrared Science

Received: Jun. 12, 2024

Accepted: --

Published Online: Mar. 14, 2025

The Author Email: LIU Ting (liuting@nudt.edu.cn), LIU Yong-Xian (yongxian23@nudt.edu.cn)

DOI:10.11972/j.issn.1001-9014.2025.02.017

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 0. [in Chinese]

Table 0. [in Chinese]

Table 1. AUC metrics for different L and H values in sequence 1

Table 1. AUC metrics for different L and H values in sequence 1

Table 2. Evaluation of detection performance of different methods on Sequences 1-6.

Table 2. Evaluation of detection performance of different methods on Sequences 1-6.

Table 3. Performance evaluation related to ablation experiments

Table 3. Performance evaluation related to ablation experiments

Table 4. Time comparison of the proposed method and compared methods in six scenes.

Table 4. Time comparison of the proposed method and compared methods in six scenes.

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