Infrared Dim and Small Target Detection Method and Device Based on Asymmetric Penalty Sparsity

Abstract

The present invention discloses an infrared dim and small target detection method and device based on asymmetric penalty sparsity. It includes: 1) constructing the image sequence to be detected into a three-dimensional spatio-temporal tensor; 2) performing principal component analysis to obtain the principal component tensor; 3) constructing an asymmetric penalty sparsity estimation function for the target; 4) constructing a tensor nuclear norm based on the Laplace operator; 5) establishing an infrared dim and small target detection model based on asymmetric penalty sparsity; 6) using an algorithm based on ADMM to solve the model established in step 5) to obtain the target detection result tensor; 7) converting it into a target detection result sequence to realize the detection of infrared dim and small targets. The infrared dim and small target detection method based on asymmetric penalty sparsity of the present invention can effectively improve the comprehensive detection performance of infrared dim and small targets.

Description

Technical Field

[0001] The present invention relates to the field of image processing, and particularly to an infrared small and weak target detection method and device based on asymmetric penalty sparsity. Background Art

[0002] At present, Infrared Searching and Tracking (IRST) systems have extensive applications in the fields of national defense and public safety, such as landmine detection, low-altitude security, missile tracking, and UAV defense. As one of the core technologies of IRST systems, infrared small and weak target detection plays a crucial role in achieving real-time early warning and precise tracking. However, due to the characteristics of long-distance imaging, the targets in infrared images usually exhibit the characteristics of "small size and weak signal", lacking clear shape, texture details, and other structured information. At the same time, the complex and changeable imaging environment makes the infrared images often accompanied by strong background interference and noise, such as dense clouds, ocean clutter, thermal radiation, etc. These factors make infrared small and weak target detection a challenging research topic.

[0003] In complex scenes, the key to achieving high-precision infrared small and weak target detection lies in: (1) background modeling and characterization, (2) target sparsity estimation, and (3) robustness and real-time performance. Currently, infrared small and weak target detection methods mainly include traditional detection methods and deep learning-based detection methods. Traditional detection methods design detection algorithms by using the prior characteristics of infrared images and the statistical characteristics of targets and backgrounds, including filtering-based methods, background modeling-based methods, low-rank sparse decomposition-based methods, local contrast metric-based methods, etc. Deep learning-based methods rely on the learning ability of large-scale data and can extract complex feature information, including convolutional neural network (CNN)-based methods, Transformer-based methods, etc. However, the existing methods cannot achieve the optimal performance simultaneously in terms of background suppression ability and target detection ability. Therefore, developing infrared small and weak target detection methods with higher robustness and generalization ability is still an important research direction. Summary of the Invention

[0004] Aiming at the deficiencies in the prior art, the purpose of the present invention is to provide an infrared small and weak target detection method and device based on asymmetric penalty sparsity.

[0005] The present invention constructs the infrared image sequence to be detected into a three-dimensional spatio-temporal tensor, makes full use of the spatio-temporal information of the infrared image sequence, and conducts infrared small and weak target detection based on low-rank sparse decomposition. For the three-dimensional spatio-temporal tensor conducts principal component analysis, determines the number of principal components to be retained by using singular value decomposition, and obtains the principal component tensor , it can achieve the preliminary suppression of clutter noise, retain most of the background components and target components, and lay a data foundation for subsequent low-rank sparse decomposition. Furthermore, construct an asymmetric penalty sparsity estimation function for the target to improve the accuracy of estimating the target sparsity; construct a tensor nuclear norm based on the Laplace operator to improve the accuracy of estimating the low-rank background. Thus, establish an infrared small target detection model based on asymmetric penalty sparsity to achieve infrared small target detection. Through the comprehensive verification of the embodiments, it proves the excellent effect of the infrared small target detection method based on asymmetric penalty sparsity in improving detection performance and background suppression, and provides new ideas and methods for the research and application in related fields.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] On the one hand, the present invention discloses an infrared small target detection method based on asymmetric penalty sparsity, including the following steps:

[0008] Step 1): Stack the thermal infrared image sequences to be detected in sequence along the time dimension to construct a three-dimensional spatio-temporal tensor ;

[0009] Step 2): Perform principal component analysis on the three-dimensional spatio-temporal tensor , use singular value decomposition to determine the number of principal components to be retained, and obtain the principal component tensor ;

[0010] Step 3): Construct an asymmetric penalty sparsity estimation function for the target , and estimate the sparsity of the target;

[0011] Step 4): Perform a fast Fourier transform on the background tensor contained in the principal component tensor, and calculate the sum of the numerical values of the Laplace functions of the singular values of all positive slices in the obtained tensor, and construct a tensor nuclear norm based on the Laplace operator , and estimate the low-rank characteristic of the background;

[0012] Step 5): Combine the asymmetric penalty sparsity estimation function of the target and the tensor nuclear norm based on the Laplace operator to establish an infrared small target detection model based on asymmetric penalty sparsity for the principal component tensor ;

[0013] Step 6): Use the optimization solution algorithm based on ADMM to solve the infrared small target detection model based on asymmetric penalty sparsity constructed in step 5) to obtain the target detection result tensor ;

[0014] Step 7): The target detection result tensor It is transformed into a target detection result sequence T, which is used as the infrared small and weak target detection result, thereby realizing the infrared small and weak target detection.

[0015] The present invention also discloses an infrared small and weak target detection device based on spatio-temporal background reconstruction for implementing the above method, which includes:

[0016] A spatio-temporal tensor construction module, which is used to construct the infrared image sequence to be detected into a three-dimensional spatio-temporal tensor;

[0017] A principal component analysis module, which is used to obtain a principal component tensor corresponding to the three-dimensional spatio-temporal tensor ;

[0018] A first design module, which is used to construct an asymmetric penalty sparsity estimation function of the target , and estimate the sparsity of the target component;

[0019] A second design module, which is used to perform a fast Fourier transform on the background tensor contained in the principal component tensor, calculate the sum of the numerical values of the Laplace functions of the singular values of all positive slices in the obtained tensor, construct a tensor nuclear norm based on the Laplace operator, and estimate the low-rank property of the background component;

[0020] A model establishment module based on asymmetric penalty sparsity, which is used to establish an infrared small and weak target detection model based on asymmetric penalty sparsity;

[0021] A model optimization and solution module, which is used to solve the infrared small and weak target detection model established based on asymmetric penalty sparsity;

[0022] A target detection result output module, which is used to output the target detection result map corresponding to each frame of the infrared image in the infrared image sequence.

[0023] Compared with the prior art, the beneficial effects of the present invention include:

[0024] 1) By constructing a spatio-temporal tensor, the present invention makes full use of the spatio-temporal information of the infrared image sequence, conducts principal component analysis, determines the number of principal components to be retained by using singular value decomposition, and obtains a principal component tensor , realizing the preliminary suppression of clutter noise in the original data signal, retaining most of the background components and target components, and laying a data foundation for subsequent low-rank sparse decomposition.

[0025] 2) The present invention designs a sparsity estimation step based on an asymmetric penalty function, effectively alleviating the problem that in the traditional sparsity estimation process, a unified penalty is imposed on signals of different intensities, resulting in the underestimation of signals. The designed method can handle target signals of different intensities more flexibly, ensuring that signal components are not over-penalized, effectively reducing information loss; at the same time, it can prevent smaller signals from being ignored. Therefore, the designed sparsity estimation method based on an asymmetric penalty function provides an effective solution for improving the sparsity target estimation accuracy in infrared small target detection. The infrared small and weak target detection model based on asymmetric penalty sparsity established by the present invention can achieve satisfactory target detection ability, background suppression ability and comprehensive detection performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 It is a schematic diagram of constructing a three-dimensional spatio-temporal tensor in the present invention;

[0027] Figure 2 It is a schematic structural diagram of an infrared small and weak target detection device based on asymmetric penalty sparsity in the present invention;

[0028] Figure 3 It is an example frame image of a thermal infrared image sequence for experimental testing;

[0029] Figure 4 It is the thermal infrared small and weak target detection result obtained by the method proposed by the present invention for an example frame of the thermal infrared image sequence;

[0030] Figure 5 It is the original image of an example frame of a thermal infrared image and its thermal infrared small and weak target detection result diagrams detected by the method of the present invention, AGPCNet, AMFUNet, GSWLCM, MDWCM, IPCE and FGLR-MCP. The green box indicates target loss, the red box indicates the target area, and the orange dashed box indicates clutter interference. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0031] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be described in detail below 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 described 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 appended claims of this application.

[0032] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0033] The basic steps of the infrared dim small target detection method based on frequency domain data sphering in the present invention mainly include:

[0034] Step 1: Stack the original thermal infrared image sequences to be detected in sequence in the time dimension to construct a three-dimensional spatio-temporal tensor ;

[0035] Specifically, as Figure 1 shown, stack the original thermal infrared image sequences to be detected in the time dimension direction to construct a three-dimensional spatio-temporal tensor , The size of is denotes the width of denotes the height of denotes the thickness of

[0036] Specifically in the embodiment, the size of the constructed three-dimensional spatio-temporal tensor is .

[0037] Step 2: Perform principal component analysis on the three-dimensional spatio-temporal tensor , determine the number of principal components to be retained by using singular value decomposition, and obtain the principal component tensor ;

[0038] Specifically, expand the three-dimensional spatio-temporal tensor into a two-dimensional matrix , denotes the expansion operator, The size of is in width and in height;

[0039] Determine the number of principal components by using singular value decomposition, , where and denote the unitary matrices obtained by singular value decomposition, denotes the singular value matrix of denotes the th singular value of Define as the comparison coefficient, traverse from small to large in the index list When is first satisfied, determine the number of principal components as the current

[0040] Perform principal component analysis on the transpose of the matrix to reduce its dimensionality to principal components, obtaining as principal components, getting

[0041] (1)

[0042] Among them, is the coefficient matrix of the first principal components, is the score matrix;

[0043] The principal component reconstruction process is as follows:

[0044] (2)

[0045] Among them, represents the score vector corresponding to the th principal component, represents the coefficient vector corresponding to the th principal component, represents the th column vector of the reconstructed principal component matrix, represents the reconstructed principal component matrix; Reconstruct to the size of the original three-dimensional spatio-temporal tensor to obtain the principal component tensor , having ;

[0046] Specifically in the embodiment, is taken as 0.2.

[0047] Step 3: Construct an asymmetric penalty sparsity estimation function for the target to estimate the sparsity of the target;

[0048] Specifically, the asymmetric penalty function is defined as

[0049] (3)

[0050] Among them, represents the asymmetry degree control factor, represents the smoothing factor that controls the smoothness of the function and the penalty intensity near zero;

[0051] From formula (3), construct the asymmetric penalty sparsity estimation function for the target as

[0052] (4)

[0053] Among them, Denote the target tensor;

[0054] Specifically in the embodiment, Take it as 0.001, Take it as 4.

[0055] Step 4: Construct the tensor nuclear norm based on the Laplace operator , and estimate the low-rank property of the background;

[0056] Specifically, perform a fast Fourier transform on the background tensor to obtain the tensor , and calculate the sum of the numerical values of the Laplace functions of the singular values of all positive slices, which is defined as the tensor nuclear norm based on the Laplace operator , and the calculation formula is:

[0057] (5)

[0058] Wherein, represents the tensor obtained after the fast Fourier transform of the background tensor , represents the i-th positive slice of the k-th singular value of is the control parameter of the Laplace operator, which is a positive constant;

[0059] Specifically in the embodiment, Take it as 0.001.

[0060] Step 5: Combine the asymmetric penalty sparsity estimation function of the target and the tensor nuclear norm based on the Laplace operator to establish an infrared small and weak target detection model based on the asymmetric penalty sparsity of the principal component tensor ;

[0061] Specifically, combine the asymmetric penalty sparsity estimation function of the target in step 3) and the tensor nuclear norm based on the Laplace operator in step 4), and model the principal component tensor as a linear combination of the background tensor , the target tensor and the noise tensor , and model the low-rank sparse decomposition process of the principal component tensor as

[0062] (6)

[0063] Introduce a sparsity reweighting strategy, and the sparsity reweighted tensor is calculated as , wherein, Denote positive constants to prevent the denominator from being zero; thus, the principal component tensor is obtained. The infrared dim small target detection model based on the asymmetric penalty sparsity:

[0064] (7)

[0065] Among them, and denote the weight coefficients, denotes the square of the Frobenius norm, denotes the Hadamard product.

[0066] Step 6: Use the optimization solution algorithm based on ADMM to solve the infrared dim small target detection model based on the asymmetric penalty sparsity constructed in step 5) to obtain the target detection result tensor ;

[0067] Specifically, use the alternating direction method of multipliers (ADMM) algorithm to solve the model (7) in step 5), introduce the auxiliary variable , and obtain the equivalent model as

[0068] (8)

[0069] The corresponding augmented Lagrangian function is:

[0070] (9)

[0071] Among them, is the penalty coefficient, is the Lagrange multiplier;

[0072] Decompose the solution problem of equation (9) into several sub-problems, and alternately update each variable according to equations (10) to (17) until the iteration ends;

[0073] The iteration formula of the auxiliary variable is:

[0074] (10)

[0075] Among them, represents the number of iterations, , and are both unitary matrices, represents the singular value matrix, represents the singular value shrinkage operator, and there is , For each singular value in ;

[0076] Background tensor The iterative formula is as follows:

[0077] (11)

[0078] Target tensor The iterative formula is

[0079] (12)

[0080] Among them, the intermediate parameter , is the soft-thresholding shrinkage operator, and there is , is the soft threshold;

[0081] Sparsity reweighted tensor The iterative formula is

[0082] (13)

[0083] Noise tensor The iterative formula is

[0084] (14)

[0085] Lagrange multiplier The iterative formula is

[0086] (15)

[0087] (16)

[0088] Penalty coefficient The iterative formula is

[0089] (17)

[0090] Among them, represents the update coefficient, represents the maximum value of;

[0091] During the iteration process, when any of the following conditions is met, the iteration stops: (1) Relative error ; (2) During two adjacent iteration processes does not change;

[0092] When the iteration stops, the final target tensor is obtained;

[0093] Specifically in the embodiment, , , , , , , , , represents the unit tensor, , represents the three-dimensional zero tensor.

[0094] Step 7: Convert the finally obtained target tensor into the target detection result sequence T as the infrared small and weak target detection result, realizing the infrared small and weak target detection.

[0095] Corresponding to the foregoing embodiment of an infrared small and weak target detection method based on asymmetric penalty sparsity, the present invention also provides an embodiment of an infrared small and weak target detection device based on spatio-temporal background reconstruction.

[0096] Figure 2 is a block diagram of an infrared small and weak target detection device shown according to an exemplary embodiment, as Figure 2 shown, the device includes:

[0097] A spatio-temporal tensor construction module for constructing the infrared image sequence to be detected into a three-dimensional spatio-temporal tensor;

[0098] A principal component analysis module for obtaining the principal component tensor corresponding to the three-dimensional spatio-temporal tensor ;

[0099] A first design module for constructing an asymmetric penalty sparsity estimation function of the target and estimating the sparsity of the target component;

[0100] A second design module for performing a fast Fourier transform on the background tensor included in the principal component tensor and calculating the sum of the numerical values of the Laplace functions of the singular values of all positive slices in the obtained tensor, constructing a tensor nuclear norm based on the Laplace operator, and estimating the low rankness of the background component;

[0101] An asymmetric penalty sparsity-based model establishment module for establishing an infrared small and weak target detection model based on asymmetric penalty sparsity;

[0102] A model optimization and solution module for solving the infrared small and weak target detection model established based on asymmetric penalty sparsity;

[0103] A target detection result output module for outputting the target detection result map corresponding to each frame of the infrared image in the infrared image sequence.

[0104] Regarding the device in the above embodiments, the specific manners in which each module performs operations have been described in detail in the embodiments related to the method, and will not be elaborated herein.

[0105] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to the descriptions of the method embodiments. The device embodiments described above are only illustrative. The various modules in the device are a logical function division, and in actual implementation, there may be other division methods. For example, multiple modules can be combined or integrated into another unit. Another point is that the connections between the modules shown or discussed can be communication connections 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 solution of the present application. Those of ordinary skill in the art can understand and implement it without creative efforts. Hereinafter, a publicly available real thermal infrared image sequence will be used as an example to illustrate the specific implementation manners to reflect the technical effects of the present invention, and the specific steps in the embodiments will not be repeated.

[0106] Embodiment

[0107] The accompanying drawings of the embodiments of the present invention can make the purpose, technical solutions and advantages of the present invention more clearly understood. 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. Any equivalent replacement, improvement, etc. made within the method ideas and principles provided by the present invention should be included in the protection scope of the present invention.

[0108] In this embodiment, the effectiveness of the infrared small and weak target detection method based on asymmetric penalty sparsity will be verified through a publicly available infrared image sequence. The publicly available infrared image sequence contains 150 consecutive infrared image frames, and the resolution of each frame is 256×256. The sequence contains a moving unmanned aerial vehicle target, which has a significant gray-scale contrast with the complex background; the data set is based on the ground background and contains randomly distributed high-brightness points, texture structures and other linear high-brightness structures; in addition, there are strong clutter and non-Gaussian noise components in the images. Figure 3 Shows an example frame of the infrared image sequence, Figure 4 which is the infrared small and weak target detection result obtained after the detection by this method. From the detection result, it can be intuitively observed that this method can significantly enhance the target, while effectively suppressing background interference and noise components, showing excellent target detection ability. In order to more comprehensively and objectively evaluate the performance of the infrared small and weak target detection method based on asymmetric penalty sparsity, from a quantitative perspective, the detection performance of the algorithm is evaluated through the 3D-ROC evaluation index system, as follows:

[0109] Table 1 - 3D-ROC Evaluation Index System

[0110]

[0111] To more objectively verify the effectiveness of the method of the present invention, six infrared small target detection methods are selected for comparison with the method of the present invention. The comparison methods include AGPCNet, AMFUNet, GSWLCM, MDWCM, IPCE, and FGLR-MCP. Table 2 shows the index situation of the 3D-ROC evaluation system for the infrared small target detection results using the comparison methods and the method of the present invention. The bold numerical values and underlined numerical values respectively represent the corresponding best performance and sub-optimal performance.

[0112] AGPCNet is from Zhang T, Cao S, Pu T, et al. AGPCNet: Attention-guided pyramid context networks for infrared small target detection. arXiv 2021[J]. arXiv preprint arXiv:2111.03580.

[0113] AMFUNet is from Chung W Y, Lee I H, Park C G. Lightweight infrared small target detection network using full-scale skip connection U-Net[J]. IEEE Geoscience and Remote Sensing Letters, 2023, 20: 1-5.

[0114] GSWLCM is from Qiu Z, Ma Y, Fan F, et al. Global sparsity-weighted local contrast measure for infrared small target detection[J]. IEEE Geoscience and Remote Sensing Letters, 2022, 19: 1-5.

[0115] MDWCM is from Lu R, Yang X, Li W, et al. Robust infrared small target detection via multidirectional derivative-based weighted contrast measure[J]. IEEE Geoscience and Remote Sensing Letters, 2020, 19: 1-5.

[0116] IPCE is from Zhang C, He Y, Tang Q, et al. Infrared small target detection via interpatch correlation enhancement and joint local visual saliency prior[J]. IEEE Transactions on Geoscience and Remote Sensing, 2021, 60: 1-14.

[0117] FGLR-MCP is from Liu T, Liu Y, Yang J, et al. Graph Laplacian regularization for fast infrared small target detection[J]. Pattern Recognition, 2025, 158: 111077.

[0118] Figure 5 The original image of the example frame of the infrared image and the thermal infrared small target detection result maps detected by the method of the present invention, AGPCNet, AMFUNet, GSWLCM, MDWCM, IPCE and FGLR-MCP. From Figure 5It can be seen from the target detection result images that problems of target loss occurred in AGPCNet, MDWCM, IPCE, and FGLR-MCP. There is more clutter in the detection results of GSWLCM and AMFUNet. In contrast, the infrared dim and small target detection method based on asymmetric penalty sparsity proposed by the present invention can well suppress components such as background and noise, and enhance the saliency of dim and small targets. In addition, according to the index results of the 3D-ROC evaluation system shown in Table 2, the compared methods cannot well achieve target enhancement and background suppression, resulting in insufficient comprehensive performance. In contrast, the target detection ability, background suppression ability, and comprehensive ability of the method proposed by the present invention can basically obtain satisfactory results. Through the above qualitative analysis and quantitative analysis, the infrared dim and small target detection method based on asymmetric penalty sparsity proposed by the present invention has superior target detection ability, background suppression ability, and comprehensive effectiveness.

[0119] Table 2 - Quantitative indicators of the detection results of the thermal infrared image instance sequence using AGPCNet, AMFUNet, GSWLCM, MDWCM, IPCE, FGLR-MCP, and the method of the present invention

[0120]

[0121] The description of 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 understood. 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. Any equivalent replacement, improvement, etc. made within the method ideas and principles provided by the present invention shall be included in the protection scope of the present invention.

Claims

1. An infrared dim and small target detection method based on asymmetric penalty sparsity, characterized in that It includes the following steps: Step 1): Stack the sequence of thermal infrared images to be detected in the time dimension in turn to construct a three-dimensional spatio-temporal tensor ; Step 2): Perform principal component analysis on the three-dimensional space-time tensor to determine the number of principal components to be retained using singular value decomposition, and obtain the principal component tensor ; Step 3): Construct an asymmetric penalty sparsity estimation function for the target to estimate the sparsity of the target; , and estimate the sparsity of the target; Specifically, step 3) is as follows: Asymmetric penalty function It is defined as: （3） Among them, represents the asymmetry degree control factor, represents the smoothing factor that controls the smoothness of the function and the penalty intensity near the zero point; Construct the asymmetric penalty sparsity estimation function of the target according to formula (3). be （4） Among them, represents the target tensor; Step 4): Perform a fast Fourier transform on the background tensor contained in the principal component tensor, calculate the sum of the numerical values of the Laplace functions of the singular values of all positive slices in the obtained tensor, and construct a tensor nuclear norm based on the Laplace operator , and estimate the low-rank property of the background; Step 5): Combine the target asymmetric penalty sparsity estimation function and the tensor nuclear norm based on the Laplace operator to establish a principal component tensor infrared small and weak target detection model based on asymmetric penalty sparsity; Specifically, step 5) is as follows: Combining the target asymmetric penalty sparsity estimation function in step 3) and the Laplace operator-based tensor nuclear norm in step 4), the principal component tensor is modeled as a linear combination of the background tensor , the target tensor , and the noise tensor . The low-rank sparse decomposition process of the principal component tensor is modeled as: （6） Introduce a sparsity reweighting strategy, and the sparsity reweighted tensor is calculated as , where represents a positive constant to prevent the denominator from being zero; thus, the infrared small and dim target detection model based on asymmetric penalty sparsity of the principal component tensor is obtained: （7） Among them, and represent weight coefficients, represents the square of the Frobenius norm, represents the Hadamard product; Step 6): Use the optimization algorithm based on ADMM to solve the infrared small and weak target detection model based on the asymmetric penalty sparsity constructed in Step 5) to obtain the target detection result tensor ; Step 7): Convert the target detection result tensor into a target detection result sequence T, which serves as the infrared dim and small target detection result, thereby realizing the infrared dim and small target detection.

2. The infrared small and weak target detection method based on asymmetric penalty sparsity according to claim 1, characterized in that The step 1) is as follows: Stack the original thermal infrared image sequence to be detected along the time dimension to construct a three-dimensional spatio-temporal tensor , The size of , denotes the width of denotes the height of denotes the thickness of 3. The infrared dim and small target detection method based on asymmetric penalty sparsity according to claim 2, characterized in that Specifically, step 2) is as follows: Expand the three-dimensional spatio-temporal tensor into a two-dimensional matrix , denotes the expansion operator, and its size is ; Determine the number of principal components using singular value decomposition, , where, and represent unitary matrices obtained from singular value decomposition, represents the singular value matrix of; represents the -th singular value of, define to represent the comparison coefficient, traverse from smallest to largest in the index list , when first satisfying , determine the number of principal components as the current ; For the matrix transpose perform principal component analysis, and reduce to principal components to obtain （1） Among them, is the coefficient matrix of the first principal components, is the score matrix; The main component reconstruction process is as follows: （2） Among them, represents the score vector corresponding to the th principal component, represents the coefficient vector corresponding to the th principal component, represents the th column vector of the reconstructed principal component matrix, represents the reconstructed principal component matrix; is reconstructed into the size of the original three-dimensional spatio-temporal tensor to obtain the principal component tensor , and there is .

4. The infrared small and weak target detection method based on asymmetric penalty sparsity according to claim 3, characterized in that Specifically, step 4) is as follows: Perform a fast Fourier transform on the background tensor to obtain a tensor . Calculate the sum of the numerical values of the Laplace functions of the singular values of all positive slices, which is defined as the tensor nuclear norm based on the Laplace operator . The calculation formula is as follows: （5） Among them, represents the background tensor the tensor obtained after performing the fast Fourier transform, represents the i-th positive slice of the k-th singular value of is the control parameter of the Laplace operator.

5. The infrared dim and small target detection method based on asymmetric penalty sparsity according to claim 1, wherein Specifically, step 6) is as follows: Use the ADMM algorithm to solve the model (7) in step 5), and introduce auxiliary variables , and the equivalent model is obtained as follows: （8） The augmented Lagrangian function corresponding to the equivalent model is as follows: （9） Among them, is the penalty coefficient, is the Lagrange multiplier; Decompose the solution problem of equation (9) into several sub-problems, and alternately update each variable according to equations (10) to (17) until the iteration ends; Auxiliary variable The iterative formula is as follows: （10） Among them, represents the number of iterations, , and are both unitary matrices, represents the singular value matrix, represents the singular value shrinkage operator, and there is , each singular value in , there is ; Background tensor The iterative formula is as follows: （11） Target tensor The iterative formula for （12） Among them, the intermediate parameter is , is the soft threshold shrinkage operator, and there is , is the soft threshold; Sparsity Reweighted Tensor The iterative formula is （13） Noise tensor The iterative formula for （14） Lagrange multiplier The iterative formula for （15） （16） Penalty coefficient The iteration formula is （17） Among them, represents the update coefficient, represents the maximum value of; During the iteration process, the iteration stop condition is: relative error , or during two adjacent iteration processes does not change; When the iteration stops, the final target tensor is obtained .

6. The infrared small and weak target detection method based on asymmetric penalty sparsity according to claim 1, wherein Specifically, step 7) is as follows: The finally obtained target tensor is reconstructed into an infrared target detection result map, obtaining a sequence T of small target detection result maps, thus realizing the detection of small thermal infrared targets.

7. An infrared small and weak target detection device based on asymmetric penalty sparsity for implementing the method according to claim 1, characterized in that, It includes: A spatio-temporal tensor construction module, which is used to construct the infrared image sequence to be detected into a three-dimensional spatio-temporal tensor; A principal component analysis module, configured to obtain a principal component tensor corresponding to a three-dimensional spatio-temporal tensor ; The first design module is used to construct an asymmetric penalty sparsity estimation function of the target to estimate the sparsity of the target component. , and estimate the sparsity of the target component. A second design module, which is used to perform a fast Fourier transform on the background tensor contained in the main component tensor, calculate the sum of the numerical values of the Laplace functions of the singular values of all positive slices in the obtained tensor, construct a tensor nuclear norm based on the Laplace operator, and estimate the low rankness of the background component; A model establishment module based on asymmetric penalty sparsity, which is used to establish an infrared small and weak target detection model based on asymmetric penalty sparsity; A model optimization and solution module, which is used to solve the established infrared small and weak target detection model based on asymmetric penalty sparsity; A target detection result output module, which is used to output the target detection result map corresponding to each frame of the infrared image in the infrared image sequence.

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