Infrared weak small target detection method and device based on firm threshold function

Abstract

The present invention discloses an infrared dim target detection method and device based on a firm threshold function. The method comprises: (1) constructing an original thermal infrared image sequence into a three-dimensional space-time tensor; (2) designing a high-pass filter, filtering the three-dimensional space-time tensor to obtain a high-pass filter tensor; (3) building an infrared dim target detection model based on component analysis; (4) constructing a sparsity estimation norm based on a firm threshold function and a low-rank estimation norm based on a Laplace operator; (5) establishing an infrared dim target detection model based on a firm threshold function; (6) designing an optimization solution algorithm based on ADMM, solving the detection model in step (5) to obtain a target detection result tensor; (7) converting the target detection result tensor into a target detection result sequence to realize infrared dim target detection. The method of the present invention can effectively realize the detection of infrared dim targets and improve the comprehensive detection performance.

Description

Technical Field

[0001] The invention relates to the field of image processing, and in particular to a method and a device for detecting infrared dim small targets based on a firm threshold function. Background Art

[0002] Infrared small target detection technology plays a key role in various military and civilian fields, including monitoring, navigation, missile tracking, and search and rescue. Given the advantages of infrared systems in night vision and adverse weather conditions, "small" and "weak" target detection is particularly important. However, low signal-to-noise ratio and complex and changing environmental conditions make this research problem challenging. Infrared targets usually have the characteristics of small size and weak signal, so the detection task is easily interfered by background and clutter noise; the long-range imaging of infrared detectors further exacerbates these problems.

[0003] At present, traditional detection methods are mainly divided into three categories: background filtering-based methods, local contrast measurement-based methods, and component analysis-based methods. Background filtering-based methods, such as top-hat transformation, focus on using the differences in spatial characteristics to enhance the target and suppress the background. Generally, methods based on local contrast measurement do not work well against complex backgrounds because the contrast measurement operator cannot adapt to the changing background structure. Component analysis-based methods aim to decompose the original image signal into background signal, target signal, and noise signal, etc., to separate the target from the background. However, component analysis-based methods are not robust enough in highly complex environments. In recent years, the emergence of deep learning has brought revolutionary changes to infrared dim target detection, and convolutional neural networks (CNNs) and their derivative methods have performed well in feature extraction. However, these methods require a large amount of labeled data for training and are computationally intensive, making them less practical in scenarios with limited resources. Summary of the invention

[0004] In view of the deficiencies in the prior art, the purpose of the present invention is to provide an infrared dim target detection method and device based on a firm threshold function, design a high-pass filter, and construct the original infrared image sequence as a high-pass filter tensor, preliminarily suppress the low-frequency signal in the image sequence, and lay a good data foundation for the subsequent low-rank sparse decomposition; for the target component, a sparsity estimation norm based on a firm threshold function is designed, which can dynamically adjust the sparsity of target signals of different intensities to achieve sparsity; for the background component, the low-rank estimation norm based on the Laplace operator is designed, which fully considers the importance of different textures and improves the accuracy of low-rank background estimation; further, an infrared dim target detection model based on a firm threshold function is established, which provides an effective solution for improving infrared dim target detection; after the effectiveness verification of the embodiment, the infrared dim target detection method based on the firm threshold function established by the present invention, and the alternating direction multiplier method is used to solve the infrared dim target detection model, so as to realize infrared dim target detection. Through the comprehensive verification of the embodiment, it is proved that the infrared dim target detection method based on the firm threshold function has excellent effects in improving detection performance and background suppression, and provides new ideas and methods for research and application in related fields.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] On the one hand, the present invention discloses an infrared dim small target detection method based on a firm threshold function, which comprises the following steps:

[0007] Step 1): Based on the original thermal infrared image sequence, stack the infrared image frames in sequence to construct a three-dimensional space-time tensor ;

[0008] Step 2): Design a high-pass filter to transform the three-dimensional space-time tensor Each frontal slice of is transformed into the frequency domain using a two-dimensional Fourier transform, then filtered using a high-pass filter, and then transformed into the spatial domain to obtain a high-pass filter tensor ;

[0009] Step 3): Based on the three-dimensional space-time tensor , using low-rank sparse decomposition theory, build an infrared dim small target detection model based on component analysis;

[0010] Step 4): Design a sparsity estimation norm based on the firm threshold function. The sparsity estimation norm includes three piecewise functions. and scaling parameters The adjustment improves the separation accuracy of target components;

[0011] Background tensor The sum of the values ​​of the Laplace functions corresponding to the singular values ​​of all frontal slices is used as the low-rank estimation norm based on the Laplace operator;

[0012] Step 5): Based on the infrared dim small target detection model based on component analysis established in step 3), a sparsity reweighted tensor is introduced; an infrared dim small target detection model based on a firm threshold function is established;

[0013] Step 6): Design an optimization solution algorithm based on ADMM, optimize and solve the infrared weak target detection model, and obtain the target detection result tensor ;

[0014] Step 7): Transform the target detection result tensor It is converted into a target detection result sequence T as the infrared weak target detection result to realize infrared weak target detection.

[0015] The present invention also discloses an infrared dim small target detection device based on a firm threshold function for implementing the method, which comprises:

[0016] A space-time tensor construction module is used to construct the original thermal infrared image sequence into a three-dimensional space-time tensor;

[0017] High-pass filter module, used to design high-pass filters for three-dimensional space-time tensors Perform high-pass filtering to obtain a high-pass filter tensor ;

[0018] Infrared small target detection model building module, used to build an infrared small target detection model based on component analysis;

[0019] The first design module is used to design the sparsity estimation norm based on the firm threshold function;

[0020] The second design module is used to design a low-rank estimation norm based on the Laplace operator;

[0021] The target detection model building module based on the firm threshold function is used to build an infrared weak target detection model based on the firm threshold function;

[0022] Model optimization solution module, used to solve and establish infrared weak target detection model based on firm threshold function;

[0023] The target detection result output module is used to output the target detection result image corresponding to each frame of infrared image in the infrared image sequence.

[0024] Compared with the prior art, the present invention has the following beneficial effects:

[0025] 1) For the target component, this paper designs a sparsity estimation norm based on the firm threshold function, which contains two parameters: and Together they determine the behavior range of the sparsity estimation norm, Controls the range of completely suppressed signals, The range of scaling processing is adjusted to allow smooth compression of medium-sized signal values. These two parameters help suppress unimportant noise while retaining important information during the target sparsity estimation process. For background components, the designed Laplace operator-based low-rank estimation norm fully considers the importance of different textures by performing Laplace operator transformation on the singular values ​​of the background tensor, thereby improving the accuracy of low-rank background estimation.

[0026] 2) In order to lay the data foundation for the infrared dim target detection model based on component analysis, a high-pass filter is designed to perform high-pass filtering on the three-dimensional space-time tensor, so as to obtain the initial suppression of low-frequency signals and enhancement of high-frequency signals in the high-pass filtered tensor; further, based on the sparsity estimation norm of the firm threshold function and the low-rank estimation norm based on the Laplace operator, an infrared dim target detection model based on the firm threshold function is established, which provides an effective solution for improving the detection of infrared dim targets; after the effectiveness verification of the embodiments, the infrared dim target detection method based on the firm threshold function established by the present invention can achieve satisfactory target detection capability, background suppression capability and comprehensive detection performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 Schematic diagram of the three-dimensional space-time tensor construction in the present invention;

[0028] Figure 2 It is a structural schematic diagram of an infrared dim small target detection device based on a firm threshold function in the present invention;

[0029] Figure 3 It is a schematic diagram of the firm threshold function;

[0030] Figure 4 This is a sample frame image of a thermal infrared image sequence used for experimental testing;

[0031] Figure 5 The thermal infrared small target detection result obtained by the method proposed by the present invention is an example frame of the thermal infrared image sequence;

[0032] Figure 6The original image of an example frame of a thermal infrared image and the thermal infrared weak small target detection result diagram detected by the method of the present invention, TWTVR, STT-TRNR, FGLR-MCP, AGPCNet and RPCANet. DETAILED DESCRIPTION

[0033] In order to make the purpose, technical solutions and advantages of the present invention clearer, the present invention is described in detail below in conjunction with specific embodiments. Specific embodiments are described below to simplify the present invention. However, it should be recognized that the present invention is not limited to the illustrated embodiments, and various modifications of the present invention are possible without departing from the basic principles, and these equivalent forms also fall within the scope defined by the claims attached to the present application.

[0034] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the accompanying drawings in the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0035] The basic steps of the infrared small target detection method based on frequency domain data spherification of the present invention in this embodiment mainly include:

[0036] Step 1: Based on the original thermal infrared image sequence, stack the infrared image frames in sequence to construct a three-dimensional space-time tensor ;

[0037] Specifically, Figure 1 As shown in the figure, based on the original thermal infrared image sequence, the infrared image frames are stacked in the time dimension to construct a three-dimensional space-time tensor. , the three-dimensional space-time tensor The height is , the width is , thickness is ;

[0038] Specifically in the embodiment, the constructed three-dimensional space-time tensor The size is ;

[0039] Step 2: Design a high-pass filter for the 3D space-time tensor Perform high-pass filtering to obtain a high-pass filter tensor ;

[0040] Specifically, design a high-pass filter: construct a two-dimensional grid in the frequency domain , grid center Set as the midpoint of the frequency domain, each frequency domain coordinate point To center point The distance is ,in, represents the frequency domain coordinates, and is the center of the frequency domain coordinate;

[0041] The high pass filter is designed as , is the cutoff frequency that controls the degree of high-frequency information retention; for a three-dimensional space-time tensor Each front slice , , using two-dimensional Fourier transform to frequency domain, we have , represents the Fourier transform operation, Represents a centering operation in the frequency domain; using a high-pass filter Filter each front slice, the expression is ; Finally, Transform from frequency domain to spatial domain, high-pass filter matrix for each frontal slice , and then, we get the high-pass filter tensor ; Specifically in the embodiment, Take it as 100.

[0042] Step 3: Based on the three-dimensional space-time tensor obtained in step 2 , using low-rank sparse decomposition theory, build an infrared dim small target detection model based on component analysis;

[0043] Specifically, based on the low-rank sparse decomposition theory, for the three-dimensional space-time tensor , build an infrared small target detection model based on component analysis:

[0044] (1)

[0045] in, represents the background tensor, represents the target tensor, represents the noise tensor, represents the rank estimation operator, express norm, represents the square of the Frobenius norm, and Represents the trade-off coefficient.

[0046] Step 4: Design a sparsity estimation norm based on the firm threshold function. The sparsity estimation norm includes three piecewise functions. and scaling parameters The adjustment improves the separation accuracy of target components;

[0047] Background tensor The sum of the values ​​of the Laplace functions corresponding to the singular values ​​of all frontal slices is used as the low-rank estimation norm based on the Laplace operator;

[0048] Specifically, this embodiment is based on Figure 3 The firm threshold function curve shown in the figure designs the sparsity estimation norm based on the firm threshold function. , the calculation formula is:

[0049] (2)

[0050] in, represents the symbolic function, Represents the threshold parameter, which is used to control the output value of the function within different input ranges. represents the scaling parameter, which adjusts the upper limit of the threshold range;

[0051] Design of low-rank estimation norm based on Laplace operator: for background tensor The singular values ​​of all positive slices are calculated by summing the corresponding Laplace functions and defining the low-rank estimation norm based on the Laplace operator. , the calculation formula is:

[0052] (3)

[0053] in, express The jth front slice of The i-th singular value of is the control parameter of the Laplace function;

[0054] Specifically in the embodiment, , .

[0055] Step 5: High-pass filter the tensor , based on the infrared dim small target detection model based on component analysis established in step 3), the sparsity reweighted tensor is introduced to establish the infrared dim small target detection model based on the firm threshold function;

[0056] Specifically, based on the infrared dim target detection model based on component analysis established in step 3) and the sparsity estimation norm based on the firm threshold function and the low-rank estimation norm based on the Laplace operator designed in step 4), the sparsity reweighted tensor is introduced. , a normal number Prevent the denominator from being zero; establish an infrared weak target detection model based on the firm threshold function:

[0057] (4)

[0058] in, represents the Hadamard product; specifically in the embodiment, .

[0059] Step 6: Design an optimization solution algorithm based on ADMM, optimize and solve the infrared weak target detection model, and obtain the target detection result tensor ;

[0060] Specifically, the alternating direction multiplier method is used to solve the model (4) in step 5), and the auxiliary variable is introduced , and the equivalent model is

[0061] (5)

[0062] The corresponding augmented Lagrangian function for:

[0063] (6)

[0064] in, is the penalty coefficient, is the Lagrange multiplier;

[0065] Decompose (6) into several sub-problems and update the variables alternately;

[0066] 6.1) The iteration formula is

[0067] (7)

[0068] in, represents the number of iterations, , and are all unitary matrices, represents the singular value matrix, represents the singular value contraction operator, and , Each singular value in ,have ;

[0069] 6.2) The iteration formula is

[0070] (8)

[0071] 6.3) The iteration formula is

[0072] (9)

[0073] in, is a soft threshold shrinkage operator, and , is the soft threshold;

[0074] 6.4) The iteration formula is

[0075] (10)

[0076] 6.5) The iteration formula is

[0077] (11)

[0078] 6.6) The iteration formula is

[0079] (12)

[0080] (13)

[0081] 6.7) The iteration formula is

[0082] (14)

[0083] in, represents the update coefficient, express The maximum value of

[0084] During the iteration process, the iteration stop condition is: relative error , Indicates the threshold value;

[0085] After the iteration is terminated, the target detection result tensor is finally obtained ;

[0086] Specifically in the embodiment, , , , , , , , , , represents the unit tensor, , Represents a zero tensor.

[0087] Step 7: Target detection result tensor It is converted into a target detection result sequence T as the infrared weak target detection result to realize infrared weak target detection.

[0088] Corresponding to the aforementioned embodiment of an infrared dim small target detection method based on a firm threshold function, the present invention further provides an embodiment of an infrared dim small target detection device based on spatiotemporal background reconstruction.

[0089] Figure 2 FIG. 1 is a block diagram of an infrared small target detection device based on a firm threshold function according to an exemplary embodiment. Figure 2 As shown, the device comprises:

[0090] A space-time tensor construction module is used to construct the original thermal infrared image sequence into a three-dimensional space-time tensor;

[0091] High-pass filter module, used to design high-pass filters for three-dimensional space-time tensors Perform high-pass filtering to obtain a high-pass filter tensor ;

[0092] Infrared small target detection model building module, used to build an infrared small target detection model based on component analysis;

[0093] The first design module is used to design the sparsity estimation norm based on the firm threshold function;

[0094] The second design module is used to design a low-rank estimation norm based on the Laplace operator;

[0095] The target detection model building module based on the firm threshold function is used to build an infrared weak target detection model based on the firm threshold function;

[0096] Model optimization solution module, used to solve and establish infrared weak target detection model based on firm threshold function;

[0097] The target detection result output module is used to output the target detection result image corresponding to each frame of infrared image in the infrared image sequence.

[0098] Regarding the device in the above embodiment, the specific manner in which each module performs operations has been described in detail in the embodiment of the method, and will not be elaborated here.

[0099] For the device embodiment, since it basically corresponds to the method embodiment, the relevant parts can refer to the partial description of the method embodiment. The device embodiment described above is only schematic. The various modules in the device are a kind of logical function division. There may be other division methods in actual implementation. For example, multiple modules can be combined or integrated into another unit. Another point is that the connection between the modules shown or discussed can be a communication connection through some interfaces, which can be electrical or other forms. Some or all of the modules can be selected according to actual needs to achieve the purpose of the present application. Ordinary technicians in this field can understand and implement it without paying creative labor. The following takes the disclosed real thermal infrared image sequence as an example to illustrate the specific implementation method to reflect the technical effect of the present invention. The specific steps in the embodiment will not be repeated.

[0100] Example

[0101] The accompanying drawings shown in the embodiments of the present invention can make the purpose, technical solutions and advantages of the present invention more clearly described. It should be noted that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. All equivalent replacements, improvements, etc. made within the method ideas and principles provided by the present invention should be included in the protection scope of the present invention.

[0102] In this embodiment, a public infrared image sequence is used to verify the effective performance of the infrared dim target detection method based on the firm threshold function. The data set contains 200 consecutive infrared images, and the size of each frame is 256×256. The sequence scene contains a drone flying slowly at low altitude, from near to far, and forms a clear contrast with the complex ground-sky scene. The texture of the ground scene is complex and contains a lot of clutter interference. Figure 4 shows an example frame of an infrared image sequence, Figure 5 is the infrared small target detection result obtained after detection by this method. From the detection results, it can be seen that the infrared small target detection method based on the firm threshold function proposed by this method can enhance the saliency of the target and effectively suppress non-target components, showing excellent target detection ability. In addition, from a quantitative perspective, the performance of the infrared small target detection method based on the firm threshold function is evaluated by the 3D-ROC evaluation index system, including , , , , , , , .

[0103] In order to more objectively verify the effectiveness of the method of the present invention, five thermal infrared dim target detection methods are selected for comparison with the method of the present invention. The comparison methods include TWTVR, STT-TRNR, FGLR-MCP, AGPCNet and RPCANet. Table 1 shows the indicators of the 3D-ROC evaluation system for infrared dim target detection results using the comparison methods and the method of the present invention. The bold values ​​and underlined values ​​represent the corresponding optimal performance and suboptimal performance, respectively.

[0104] TWTVR originated from Zhao E, Dong L, Li C, et al. Infrared maritime target detection based on temporal weight and total variation regularization under strong wave interferences[J]. IEEE Transactions on Geoscience and RemoteSensing, 2024.

[0105] STT-TRNR originates from Yi H, Yang C, Qie R, et al. Spatial-temporal tensor ringnorm regularization for infrared small target detection[J]. IEEE Geoscienceand Remote Sensing Letters, 2023, 20: 1-5.

[0106] FGLR-MCP originated from Liu T, Liu Y, Yang J, et al. Graph Laplacianregularization for fast infrared small target detection[J]. PatternRecognition, 2025, 158: 111077.

[0107] AGPCNet is derived from Zhang T, Cao S, Pu T, et al. AGPCNet: Attention-guidedpyramid context networks for infrared small target detection. arXiv 2021[J].arXiv preprint arXiv:2111.03580.

[0108] RPCANet is derived from Wu F, Zhang T, Li L, et al. RPCANet: Deep Unfolding RPCABased Infrared Small Target Detection[C] / / Proceedings of the IEEE / CVF WinterConference on Applications of Computer Vision. 2024: 4809-4818.

[0109] Figure 6 The original image of the infrared image example frame and the thermal infrared weak target detection result diagram after the method of the present invention, TWTVR, STT-TRNR, FGLR-MCP, AGPCNet and RPCANet detection, where the red frame indicates the correctly detected target area, the green circle marked area is the clutter area, and the blue frame indicates the area where the target cannot be successfully detected. Qualitative analysis: Figure 6 From the target detection results of the example frames, it can be seen that except for this method and TWTVR, other comparison methods have the problem of missed target detection. TWTVR has the worst background suppression ability, and there are a large number of background components in the target detection results; STT-TRNR, AGPCNet and AMFUNet also have a small amount of clutter components in the target detection results; in contrast, the infrared weak target detection method based on the firm threshold function proposed in the present invention has excellent non-target component suppression ability on the example frames, and can enhance the significance of weak targets. Quantitative analysis: From the quantitative evaluation index results shown in Table 1, the comparison method cannot achieve the goals of target enhancement and background suppression at the same time, resulting in the comprehensive performance of the target detector failing to meet the requirements of practical applications; in contrast, the target detection ability, background suppression ability and comprehensive ability of the method proposed in the present invention can achieve the best effect on the infrared image data set of the embodiment. Combined with the above qualitative analysis and quantitative analysis, the infrared weak target detection method based on the firm threshold function of the present invention has superior target detection ability, background suppression ability and comprehensive efficiency.

[0110] Table 1 - Quantitative indicators of the detection results of thermal infrared image example sequences using TWTVR, STT-TRNR, FGLR-MCP, AGPCNet, RPCANet and the method of the present invention

[0111]

[0112] The accompanying drawings shown in the embodiments of the present invention can make the purpose, technical solutions and advantages of the present invention more clearly described. It should be noted that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. All equivalent replacements, improvements, etc. made within the method ideas and principles provided by the present invention should be included in the protection scope of the present invention.

Claims

1. A method for detecting infrared small targets based on a firm threshold function, characterized in that: The steps include: Step 1): Based on the original thermal infrared image sequence, stack the infrared image frames in sequence to construct a three-dimensional space-time tensor ; Step 2): Design a high-pass filter to transform the three-dimensional space-time tensor Each frontal slice of is transformed into the frequency domain using a two-dimensional Fourier transform, then filtered using a high-pass filter, and then transformed into the spatial domain to obtain a high-pass filter tensor ; Step 3): Based on the three-dimensional space-time tensor , using low-rank sparse decomposition theory, build an infrared dim small target detection model based on component analysis; The step 3) is specifically as follows: Based on the low-rank sparse decomposition theory, for the three-dimensional space-time tensor , build an infrared small target detection model based on component analysis: ； （1） in, represents the background tensor, represents the target tensor, represents the noise tensor, represents the rank estimation operator, express norm, represents the square of the Frobenius norm, and represents the trade-off coefficient; Step 4): Design a sparsity estimation norm based on the firm threshold function. The sparsity estimation norm includes three piecewise functions. and scaling parameters The adjustment improves the separation accuracy of target components; Background tensor The sum of the values ​​of the Laplace functions corresponding to the singular values ​​of all frontal slices is used as the low-rank estimation norm based on the Laplace operator; Step 5): Based on the infrared dim small target detection model based on component analysis established in step 3), a sparsity reweighted tensor is introduced; an infrared dim small target detection model based on a firm threshold function is established; Step 6): Design an optimization solution algorithm based on ADMM, optimize and solve the infrared weak target detection model, and obtain the target detection result tensor ; Step 7): Transform the target detection result tensor It is converted into a target detection result sequence T as the infrared weak target detection result to realize infrared weak target detection.

2. The infrared small target detection method based on firm threshold function according to claim 1 is characterized in that: The step 1) is specifically as follows: Based on the original thermal infrared image sequence, the infrared image frames are stacked in the time dimension to construct a three-dimensional space-time tensor. , the three-dimensional space-time tensor The height is , the width is , thickness is .

3. The infrared small target detection method based on firm threshold function according to claim 2 is characterized in that: The step 2) is specifically as follows: Constructing a 2D grid in the frequency domain , grid center Set as the midpoint of the frequency domain, each frequency domain coordinate point To center point The distance is , in, represents the frequency domain coordinates, , ; Designing a high-pass filter , is the cutoff frequency that controls the degree of high-frequency information retention; for each positive slice of the three-dimensional space-time tensor , , using two-dimensional Fourier transform to frequency domain, we have , represents the Fourier transform operation, represents the centering operation in the frequency domain; Use a high pass filter Filter each front slice, the expression is ; Finally, Transform from frequency domain to spatial domain to obtain the high-pass filter matrix for each frontal slice , and then get the high-pass filter tensor .

4. The infrared small target detection method based on firm threshold function according to claim 3 is characterized in that: The step 4) is specifically as follows: Design of sparsity estimation norm based on firm threshold function : ； （2） in, represents the symbolic function, Represents the threshold parameter, which is used to control the output value of the function within different input ranges. represents the scaling parameter, which adjusts the upper limit of the threshold range; Design of low-rank estimation norm based on Laplace operator: for background tensor The singular values ​​of all positive slices are calculated by summing the corresponding Laplace functions and defining the low-rank estimation norm based on the Laplace operator. , the calculation formula is: ； （3） in, Represents the background tensor The jth front slice of The i-th singular value of is the control parameter of the Laplace function.

5. The infrared small target detection method based on firm threshold function according to claim 1 is characterized in that: The step 5) is specifically as follows: Based on the infrared small target detection model based on component analysis established in step 3), the sparsity reweighted tensor is introduced , a normal number Prevent the denominator from being zero; establish an infrared weak target detection model based on the firm threshold function: ； （4） in, Represents the Hadamard product.

6. The infrared small target detection method based on firm threshold function according to claim 5 is characterized in that: The step 6) is specifically as follows: The alternating direction multiplier method is used to solve the model (4) in step 5), introducing auxiliary variables , and the equivalent model is ； （5） The corresponding augmented Lagrangian function for: ； （6） in, is the penalty coefficient, is the Lagrange multiplier; Decompose equation (6) into several sub-problems and update the variables alternately; 6-1) The iteration formula is ； （7） in, represents the number of iterations, , and are all unitary matrices, represents the singular value matrix, represents the singular value contraction operator, and ,for Each singular value in ,have ; 6-2) The iteration formula is ； （8） 6-3) The iteration formula is ； （9） in, is a soft threshold shrinkage operator, and , is the soft threshold; 6-4) The iteration formula is ； （10） 6-5) The iteration formula is ； （11） 6-6) The iteration formula is ； （12） ； （13） 6-7) The iteration formula is ； （14） in, represents the update coefficient, express The maximum value of During the iteration process, the iteration stop condition is: relative error , Indicates the threshold value; At the end of the iteration, the target detection result tensor is finally obtained. .

7. The infrared small target detection method based on firm threshold function according to claim 1 is characterized in that: The step 7) is specifically as follows: The final target tensor Reconstructed into infrared target detection result sequence T to realize thermal infrared weak target detection.

8. An infrared small target detection device based on a firm threshold function for implementing the method of claim 1, characterized in that: include: A space-time tensor construction module is used to construct the original thermal infrared image sequence into a three-dimensional space-time tensor; High-pass filter module, used to design high-pass filters for three-dimensional space-time tensors Perform high-pass filtering to obtain a high-pass filter tensor ; Infrared small target detection model building module, used to build an infrared small target detection model based on component analysis; The first design module is used to design the sparsity estimation norm based on the firm threshold function; The second design module is used to design a low-rank estimation norm based on the Laplace operator; The target detection model building module based on the firm threshold function is used to build an infrared weak target detection model based on the firm threshold function; Model optimization solution module, used to solve and establish infrared weak target detection model based on firm threshold function; The target detection result output module is used to output the target detection result image corresponding to each frame of infrared image in the infrared image sequence.

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