Research of Infrared Dim and Small Target Detection Algorithms Based on Low-Rank and Sparse Decomposition

Reference	Constraints of background components	Publish year	Constraint term
［15］	Low-rank constraints of background patch image	2013	Nuclear norm
［16］		2017	Partial sum of singular values
［17］		2018	Weighted nuclear norm
［19］		2018	γ norm
［21］		2019	Schatten 1/2 norm
［25］	Low-rank constraints of background tensor	2019	Tensor nuclear norm
［28］		2019	Partial sum of tensor nuclear norm
［33］			nonconvex tensor rank surrogate via Laplace function
［30］		2018	Weighted tensor nuclear norm
［31］		2019	Weighted Schatten p norm
［36］		2022	Improved tensor nuclear norm
［38］		2021	METTR norm
［22］		2017	Sum of nuclear norm
［40］	Total variation constraints	2017	Isotropic total variation
［41］		2020	Tensor nonlocal total variation
［42］		2022	Hyper total variation
［44］		2019	3D anisotropic total variation

Table 2. Comparison of target component constraints

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Table 2. Comparison of target component constraints

Reference	Constraints of target component	Publish year	Sparse constraints term /methods for extracting prior
［16］	Sparse constraints of target component	2017	L₁norm with non-negative constraint
［19］		2018	Weighted L₁ norm
［45］		2018	Weighted L₁ norm
［46］		2019	L_p-Norm
［47］	Weighting factor for the target component	2016	Steering kernel
［48］		2017	Variation weighted information entropy
［49］		2020	Local image entropy
［41］		2020	Structure tensor
［50］		2021	Double window local contrast measure
［51］		2022	Structure tensor and direction derivative
［33］		2020	Local contrast energy
［36］		2022	Local visual saliency

Table 3. Comparison of joint temporal information constraints

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Table 3. Comparison of joint temporal information constraints

Reference	Representation of infrared image	Publish year	Utilization of temporal information
［52］	Matrix	2020	temporal extension of sequence image and temporal low-rank and sparse decomposition
［53］		2019	Spatial-temporal patch image
［54］		2016	Temporal consistency constraint for target component
［55］		2022	Temporal consistency constraint for target component
［56］	Tensor	2020	holistic spatial-temporal tensor
［57］		2020	spatial-temporal patch tensor
［58］		2022	holistic spatial-temporal tensor
［59］		2022	non-overlapping spatial-temporal patch tensor

Table 4. Comparison of G_SCRG and F_BSF

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Table 4. Comparison of G_SCRG and F_BSF

Algorithm	Scene 1		Scene 2		Scene 3		Scene 4		Scene 5
Algorithm	G_SCRG	F_BSF	G_SCRG	F_BSF	G_SCRG	F_BSF	G_SCRG	F_BSF	G_SCRG	F_BSF
LCM	2.19	0.41	41.41	1.30	1.39	0.53	2.55	1.18	4.99	0.60
Max_mean	0.47	0.43	0.39	0.25	1.22	0.66	1.02	1.49	0.97	0.67
IPI	11.07	9.83	2.00	1.23	inf	inf	inf	inf	68.44	35.12
Nipps	52.90	35.37	20.74	9.34	inf	inf	8.13	26.43	inf	inf
NRAM	37.87	24.45	inf	inf	inf	inf	inf	inf	inf	inf
PSTNN	inf	inf	inf	inf	inf	inf	inf	inf	inf	inf
ECA_STT	19.06	12.43	58.56	28.69	391.38	106.10	0.96	0.90	3.46	1.57
RIPT	inf	inf	inf	inf	inf	inf	inf	inf	13.19	6.19
ASTTV_NTLA	inf	inf	inf	inf	inf	inf	5.06	6.85	389.68	204.11

Table 5. Single frame computation time

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Table 5. Single frame computation time

Algorithm	Scene 1	Scene 2	Scene 3	Scene 4	Scene 5
LCM	00.16	0.80	0.15	0.16	0.15
Max_mean	0.004	0.013	0.003	0.003	0.005
IPI	4.72	31.86	4.84	5.14	5.51
Nipps	11.82	115.36	6.23	12.65	11.12
NRAM	1.98	35.01	0.891	1.54	1.91
PSTNN	0.27	3.00	0.55	0.64	0.69
ECA_STT	6.63	4.60	40.61	7.10	7.14
RIPT	2.98	14.99	2.19	3.82	5.5
ASTTV_NTLA	1.72	9.75	1.18	1.86	1.84

Table 6. Comparison of computational complexity

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Table 6. Comparison of computational complexity

Algorithm	Computational complexity
Max_mean	$O (M N)$
LCM	$O (K^{3} M N)$
IPI	$O (m n^{2})$
NRAM	$O (m n^{2})$
NIPPS	$O (m n^{2})$
ECA_STT	$O (n_{1} n_{2} n_{3} l o g n_{3} + n_{1} n_{2}^{2} ⌈(n_{3} + 1) / 2⌉)$
RIPT	$O (n_{1} n_{2} n_{3} (n_{1} n_{2} + n_{1} n_{3} + n_{2} n_{3}))$
PSTNN	$O (n_{1} n_{2} n_{3} l o g n_{3} + n_{1} n_{2}^{2} ⌈(n_{3} + 1) / 2⌉)$
ASTTV_NTLA	$O (n_{1} n_{2} n_{3} 2 l o g n_{3} + n_{1} n_{2}^{2} ⌈(n_{1} n_{2} n_{3}^{2} + 1) / 2⌉)$

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Junhai Luo, Hang Yu. Research of Infrared Dim and Small Target Detection Algorithms Based on Low-Rank and Sparse Decomposition[J]. Laser & Optoelectronics Progress, 2023, 60(16): 1600004

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