An Infrared Dim and Small Target Detection Method and Device Based on Hypergraph

Abstract

The present invention discloses a method and device for detecting infrared dim and small targets based on hypergraphs. The method includes: 1) constructing the image sequence to be detected into a three-dimensional spatio-temporal tensor; 2) establishing a low-rank sparse tensor decomposition model; 3) designing a tensor nuclear norm based on Laplace; 4) designing a hypergraph Laplacian regularization term; 5) establishing a spatio-temporal tensor decomposition model based on the hypergraph regularization term; 6) using an algorithm based on ADMM to solve the model established in step 5) to obtain a target detection result tensor; (7) converting the obtained target detection result tensor into a target detection result sequence as the infrared dim and small target detection result, thereby realizing the detection of infrared dim and small targets. The method for detecting infrared dim and small targets based on hypergraphs in the present invention can effectively improve the 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 a method and device for detecting small and weak infrared targets based on a hypergraph. Background Art

[0002] Thermal infrared imaging has characteristics such as all-weather operation, strong penetration, thermal sensitivity, and strong concealment, and has been widely used in fields such as military reconnaissance, maritime search and rescue, and operation and maintenance of photovoltaic power stations. Due to long-distance imaging, the target imaging area is small and the signal intensity is weak, existing in the form of small and weak targets in infrared sequence images. At the same time, the complex background of infrared images often contains various interferences, such as dense clouds, ocean clutter, etc. In addition, as one of the core technologies of infrared search and tracking systems, the detection of small and weak infrared targets poses requirements for improving detection accuracy and optimizing operation efficiency to meet the needs of practical applications. Therefore, it is urgent to study the method for detecting small and weak targets in infrared sequence images, which has important value and significance for ensuring national defense security and public safety.

[0003] Currently, the technology for detecting small and weak infrared targets has become a research hotspot in academia and industry, and its method system is mainly divided into the following categories: detection methods based on background filtering, local contrast measurement, machine learning, deep learning, and component analysis. The method based on background filtering suppresses background information through filtering technology to highlight the target signal; however, since the background model is difficult to accurately describe the background characteristics in complex scenarios, this method performs poorly in scenarios with rapidly changing backgrounds or complex clutter environments, limiting its practicality. The method based on local contrast measurement mainly relies on the characteristic differences between the target and the background in the local area, such as gradients, textures, etc.; although it has good detection effects in some static scenarios, it is highly sensitive to complex backgrounds and noise clutter, vulnerable to environmental conditions, and difficult to maintain robustness in variable scenarios. The method based on machine learning distinguishes the target from the background by constructing a classifier, usually relying on manually designed features; however, the quality of feature design directly determines the detection performance. At the same time, the algorithm has a high dependence on training samples and has poor robustness in unseen scenarios. The method based on deep learning can autonomously extract multi-level features to improve detection accuracy; however, this method usually requires a large amount of labeled data and has a high computational complexity, making it difficult to be applied in real time in resource-constrained scenarios. The method based on component analysis separates the target and the background by decomposing each component in the image, and its performance highly depends on the accurate modeling of the intrinsic characteristics of each component; in dealing with noise and complex backgrounds, this method shows certain advantages, but its computational complexity and dependence on the model also pose challenges to practical applications.

[0004] Therefore, developing an infrared small and weak target detection method with higher robustness, real-time performance, and generalization ability remains an important research direction in this field. Summary of the Invention

[0005] Aiming at the deficiencies in the prior art, the purpose of the present invention is to provide a method and device for detecting small and weak infrared targets based on hypergraphs. By constructing the infrared image sequence to be detected into a three-dimensional spatio-temporal tensor, making full use of the spatio-temporal information of the infrared image sequence, and carrying out low-rank sparse spatio-temporal tensor decomposition. Through the construction of the tensor nuclear norm based on Laplace calculation, the importance of different features in the background can be distinguished and different weights can be assigned, so as to achieve a more accurate characterization of the low-rank characteristics. Considering the flexibility of the hypergraph, the image sequence to be detected is constructed into a hypergraph structure, which can capture more complex correlations from multiple frames at the same time, better represent the cross-frame structure information, and further improve the accuracy of background estimation. Furthermore, a spatio-temporal tensor decomposition model based on hypergraph is established, which has excellent target detection ability and background suppression ability. Through the comprehensive verification of the embodiments, it is proved that the method for detecting small and weak infrared targets based on hypergraph has excellent effects in improving detection performance and background suppression, providing 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 a method for detecting small and weak infrared targets based on hypergraph, which is characterized by including the following steps:

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

[0009] Step 2): Use the three-dimensional spatio-temporal tensor to establish a low-rank sparse decomposition model based on the three-dimensional spatio-temporal tensor;

[0010] Step 3): Design a tensor nuclear norm based on Laplace to estimate the low-rank characteristics of the background;

[0011] Step 4): Construct each frame image of the thermal infrared image sequence to be detected into an image block tensor as a graph node, and use the node set to construct a hypergraph, and design a hypergraph Laplacian regularization term;

[0012] Step 5): Combine the tensor nuclear norm based on Laplace and the hypergraph Laplacian regularization term to establish a spatio-temporal tensor decomposition model based on hypergraph;

[0013] Step 6): Use the optimization solution algorithm based on ADMM to solve the spatio-temporal tensor decomposition model constructed in step 5) to obtain the target detection result tensor;

[0014] Step 7): Convert the obtained target detection result tensor into a target detection result sequence T as the infrared dim small target detection result, thus realizing the infrared dim small target detection.

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

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

[0017] A low-rank sparse decomposition model establishment module, configured to establish a low-rank sparse tensor decomposition model corresponding to the three-dimensional spatio-temporal tensor;

[0018] A Laplace-based tensor nuclear norm design module, configured to design a Laplace-based tensor nuclear norm;

[0019] A hypergraph construction module, configured to construct the image frame sequence to be detected into a hypergraph structure;

[0020] A hypergraph Laplacian regularization construction module, configured to construct a hypergraph Laplacian regularization term corresponding to the hypergraph structure;

[0021] A spatio-temporal tensor decomposition model establishment module based on hypergraph, configured to establish a spatio-temporal tensor decomposition model based on the hypergraph regularization term;

[0022] A model optimization and solution module, configured to use an ADMM-based optimization algorithm to solve the spatio-temporal tensor decomposition model based on the hypergraph regularization term;

[0023] A target detection result output module, configured to output the infrared dim small target detection result graph of each frame of the infrared image sequence.

[0024] Compared with the prior art, the beneficial effects of the present invention include:

[0025] 1) By constructing a three-dimensional spatio-temporal tensor, the present invention makes full use of the spatio-temporal information of the infrared image sequence, which helps to express the background signal and the target signal; and provides a tensor nuclear norm based on Laplace calculation, which can better characterize the low-rank characteristics of the background and is conducive to the effective separation of the background and the target.

[0026] 2) In order to fully explore and extract the spatio-temporal relationship between the image frames in the infrared sequence, the present invention designs a hypergraph structure, constructs the infrared image frames into image block tensors as the nodes of the hypergraph, and introduces time and space factors into the weights of the hyperedges, so as to capture more complex correlations from multiple frames simultaneously; by introducing the hypergraph Laplacian regularization term, in the spatio-temporal tensor decomposition model based on the low-rank sparse theory, satisfactory target detection ability, background suppression ability and comprehensive detection performance can be achieved. Description of the Drawings

[0027] Figure 1 It is a schematic diagram for constructing a three-dimensional space-time tensor in the present invention;

[0028] Figure 2 It is a schematic structural diagram of an infrared small and weak target detection device based on a hypergraph in the present invention;

[0029] Figure 3 It is a schematic diagram for constructing nodes of a hypergraph;

[0030] Figure 4 It is a schematic structural diagram of the constructed hypergraph;

[0031] Figure 5 It is an example frame image of a thermal infrared image sequence for experimental testing;

[0032] Figure 6 It is the detection result of a small and weak thermal infrared target obtained by the method proposed in the present invention for an example frame of a thermal infrared image sequence;

[0033] Figure 7 It is the original image of an example frame of a thermal infrared image and the detection result diagrams of small and weak thermal infrared targets detected by the methods of the present invention, MDWCM, MSLSTIPT, TWTVR, STT-TRNR, FGLR-MCP, AGPCNet, and RPCANet. The green box indicates target loss, the red box indicates the target area, and the orange dashed box indicates clutter interference. Detailed Embodiment

[0034] 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 reference to 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.

[0035] Below, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the drawings in the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of protection of the present invention.

[0036] The basic steps of the infrared small and weak target detection method based on frequency-domain data sphering in the present embodiment mainly include:

[0037] Step 1: Stack the thermal infrared image sequences to be detected in sequence according to the time dimension to construct a three-dimensional space-time tensor ;

[0038] Specifically, as Figure 1 shown, for the original thermal infrared image sequence, the original thermal infrared image sequence is stacked 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.

[0039] Specifically in the embodiment, the constructed three-dimensional spatio-temporal tensor has a size of .

[0040] Step 2: Using the three-dimensional spatio-temporal tensor , establish a low-rank and sparse decomposition model based on the three-dimensional spatio-temporal tensor; specifically, model the three-dimensional spatio-temporal tensor as a linear combination of the background tensor , the target tensor and the noise tensor . Considering the low-rank property of the background tensor and the sparse property of the target tensor, model the spatio-temporal tensor as

[0041] (1)

[0042] Wherein, denotes rank calculation, denotes norm, denotes the square of the Frobenius norm, and denote weight coefficients.

[0043] Step 3: Design a Laplace-based tensor nuclear norm to estimate the low-rank property of the background;

[0044] Specifically, perform a fast Fourier transform on the background tensor to obtain the tensor , calculate the sum of the numerical values of the Laplace function of the singular values of all the frontal slices of, and define it as the Laplace-based tensor nuclear norm , and the calculation formula is:

[0045] (5)

[0046] Wherein, is the background tensor The i-th positive slice after fast Fourier transform The j-th singular value of is the control parameter of the Laplace operator, which is a positive constant.

[0047] Specifically, in the embodiment is taken as 0.001.

[0048] Step 4: Construct each frame image of the thermal infrared image sequence to be detected into an image block tensor as a graph node, and use the node set to construct a hypergraph, and design a hypergraph Laplacian regularization term;

[0049] Specifically, as Figure 3 shown, construct the image frame into an image block tensor as a graph node, and the construction process is as follows: Use the image frame of the thermal infrared image sequence to be detected, and slide through a sliding window with a fixed size on in an S-shaped path to obtain non-overlapping image blocks, The value of and The values are the same, , represents the ceiling operator, and stack them as positive slices in turn to obtain the non-overlapping image block tensor of the image frame , as the graph node corresponding to the image frame ; Thus, the node set corresponding to the original thermal infrared image sequence is obtained; It means that there are image frames constructed into nodes;

[0050] Use the node set to construct a hypergraph. First, define the hyperedge set , where represents hyperedges, and each hyperedge has nodes, denoted as , , , ; For the fully connected nodes within the hyperedge , the weight between any two nodes and is defined as follows:

[0051] (6)

[0052] where represents the square of the 2-norm of the matrix, represents the th image frame corresponding to the th front slice, represents the th image frame corresponding to the th front slice, is the time interval factor,

[0053] Therefore, the weight of the hyperedge is expressed as:

[0054] (7)

[0055] Thus, the hypergraph is constructed, as Figure 4 shown; define the hypergraph Laplacian matrix which includes the node degree matrix the hyperedge degree matrix and the incidence matrix as follows:

[0056] (1) Node degree matrix is a diagonal matrix of the degree of each node, with size and the degree of each node is the sum of the weights of all hyperedges connected to that node:

[0057] (8)

[0058] where represent the degrees of nodes and respectively;

[0059] (2) Hyperedge degree matrix is a diagonal matrix with size representing the degree of each hyperedge, that is, the number of included nodes. If the hyperedge includes nodes, then the degree of the hyperedge is :

[0060] (9)

[0061] (3) Incidence matrix is a matrix that describes the relationship between points and hyperedges, with a size of If the node belongs to the hyperedge , then , otherwise it is 0. is

[0062] (10)

[0063] Therefore, the hypergraph Laplacian matrix of the hypergraph is defined as

[0064] (11)

[0065] The hypergraph Laplacian matrix is used to construct the hypergraph Laplacian regularization term:

[0066] (12)

[0067] Among them, represents the trace calculation of the matrix, represents the background matrix obtained after expanding the background tensor ; , represents the background matrix obtained after expanding the background tensor The height of the background matrix is , and the width is , , represents the expansion operator.

[0068] Specifically, in the embodiment, is taken as 2, is taken as 5, is taken as , is taken as 0.001, is taken as 0.8.

[0069] Step 5: Combine the Laplace-based tensor nuclear norm and the hypergraph Laplacian regularization term to establish a hypergraph-based spatio-temporal tensor decomposition model;

[0070] Specifically, introduce the sparsity reweighted tensor , represents a positive constant to prevent the denominator from being zero; use the norm to approximate the norm; the hypergraph-based spatio-temporal tensor decomposition model established by combining the Laplace-based tensor nuclear norm and the hypergraph Laplacian regularization term is

[0071] (13)

[0072] Among them, denotes the norm, , and denote the weight coefficients, denotes the Hadamard product;

[0073] Step 6: Use the ADMM-based optimization algorithm to solve the spatio-temporal tensor decomposition model constructed in step 5) to obtain the target detection result tensor;

[0074] Specifically, the alternating direction method of multipliers (ADMM) algorithm is used to solve model (13), introducing auxiliary variables and , and the equivalent model is

[0075] (14)

[0076] The corresponding augmented Lagrangian function is:

[0077] (15)

[0078] Among them, is the penalty coefficient, is the Lagrange multiplier;

[0079] The solution problem of equation (15) is decomposed into several sub-problems, and each variable is alternately updated according to equations (16) to (25) until the iteration ends;

[0080] The iteration formula for the auxiliary variable is:

[0081] (16)

[0082] Among them, denotes the number of iterations, , and are both unitary matrices, denotes the singular value matrix, denotes the singular value shrinkage operator, and there is , for each singular value in, there is ;

[0083] The iteration formula for the auxiliary variable is:

[0084] (17)

[0085] Wherein, represents the identity matrix, represents the hypergraph Laplacian matrix;

[0086] The background tensor has the iterative formula:

[0087] (18)

[0088] Wherein, , , which means respectively reconstructing the matrix and the matrix into tensors with dimensions of and tensor ;

[0089] The target tensor has the iterative formula:

[0090] (19)

[0091] Wherein, is the soft thresholding shrinkage operator, and there is , is the soft threshold;

[0092] The noise tensor has the iterative formula:

[0093] (20)

[0094] The sparsity reweighted tensor has the iterative formula:

[0095] (21)

[0096] The Lagrange multiplier has the iterative formula:

[0097] (22)

[0098] (23)

[0099] (24)

[0100] The penalty coefficient has the iterative formula:

[0101] (25)

[0102] Among them, represents the update coefficient, represents the maximum value of;

[0103] During the iteration process, the iteration stop condition is: when the relative error is less than the set error , the iteration terminates; or when the number of non-zero elements in the target tensor no longer changes, stop the iteration;

[0104] The target tensor obtained after the iteration stops is used as the target detection result tensor;

[0105] Specifically in the embodiment, , , , , , , , , , represents a three-dimensional zero tensor, , represents a two-dimensional zero matrix.

[0106] Step 7: Convert the obtained target detection result tensor into a target detection result sequence T as the infrared small and weak target detection result to implement infrared small and weak target detection.

[0107] Corresponding to the foregoing embodiment of an infrared small and weak target detection method based on a hypergraph, the present invention also provides an embodiment of an infrared small and weak target detection device based on spatio-temporal background reconstruction.

[0108] 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:

[0109] A three-dimensional spatio-temporal tensor construction module for constructing the infrared image sequence to be detected into a three-dimensional spatio-temporal tensor;

[0110] A low-rank sparse decomposition model establishment module for establishing a low-rank sparse tensor decomposition model corresponding to the three-dimensional spatio-temporal tensor;

[0111] A Laplace-based tensor nuclear norm design module for designing a Laplace-based tensor nuclear norm;

[0112] A hypergraph construction module for constructing the image frame sequence to be detected into a hypergraph structure;

[0113] A hypergraph Laplacian regularization construction module for constructing the hypergraph Laplacian regularization term corresponding to the hypergraph structure;

[0114] A spatio-temporal tensor decomposition model establishment module based on the hypergraph for establishing a spatio-temporal tensor decomposition model based on the hypergraph regularization term;

[0115] A model optimization and solution module for solving the spatio-temporal tensor decomposition model based on the hypergraph regularization term by using an optimization algorithm based on ADMM;

[0116] An object detection result output module for outputting the infrared small and weak target detection result map of each frame of the infrared image sequence.

[0117] 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 here.

[0118] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can refer to the partial descriptions of the method embodiments. The device embodiments described above are merely illustrative. The various modules in the device are a logical function division, and 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 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. The following takes the publicly available real thermal infrared image sequence 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.

[0119] Embodiment

[0120] The accompanying drawings description shown in the embodiments of the present invention can make the purpose, technical solution and advantages of the present invention introduced more clearly. It should be noted that the specific embodiments described here 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 idea and principle provided by the present invention shall be included within the protection scope of the present invention.

[0121] In this embodiment, the effectiveness verification of the infrared small and dim target detection method based on hypergraph will be carried out through a publicly available infrared image sequence. The publicly available infrared image sequence contains 150 consecutive infrared image frames, each with a size of 256×256. This sequence contains a slowly flying unmanned aerial vehicle (UAV), which forms a high contrast with the surrounding background. The dataset has the sky and forest as the background and contains linear highlighted roadside structures, etc. In addition, there are significant clutters and noises in the images. Figure 5 The following shows an example frame of the infrared image sequence. Figure 6 The following is the target detection result image obtained from the example frame of the infrared image sequence by the infrared small and dim target detection method based on hypergraph of the present invention. It can be visually observed from the detection result image that this method can improve the target saliency and effectively suppress the background and noise components. To more accurately and objectively evaluate the comprehensive performance of the infrared small and dim target detection method based on hypergraph, from a quantitative perspective, the detection performance of the algorithm is evaluated through the 3D-ROC evaluation index system as follows:

[0122] (1) Effectiveness of the detector

[0123]

[0124] (2) Target detection probability

[0125]

[0126] (3) Background suppression probability

[0127]

[0128] (4) Joint target detection ability

[0129]

[0130] (5) Joint background suppression ability

[0131]

[0132] (6) Joint target detection ability and background suppression ability

[0133]

[0134] (7) Target-background signal ratio

[0135]

[0136] (8) Comprehensive target detection ability

[0137]

[0138] To more objectively verify the effectiveness of the method of the present invention, seven infrared small and weak target detection methods were selected for comparison with the method of the present invention. The comparison methods include MDWCM, MSLSTIPT, TWTVR, STT-TRNR, FGLR-MCP, AGPCNet, and RPCANet. Table 1 shows the index situation of the 3D-ROC evaluation system for the infrared small and weak 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 optimal performance and sub-optimal performance.

[0139] 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.

[0140] MSLSTIPT is from Sun Y, Yang J, An W. Infrared dim and small target detection via multiple subspace learning and spatial-temporal patch-tensor model[J]. IEEE Transactions on Geoscience and Remote Sensing, 2020, 59(5): 3737-3752.

[0141] TWTVR is 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 Remote Sensing, 2024.

[0142] STT-TRNR is from Yi, Haiyang, et al. "Spatial-Temporal Tensor Ring Norm Regularization for Infrared Small Target Detection." IEEE Geoscience and Remote Sensing Letters 20 (2023): 1-5.

[0143] 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.

[0144] 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.

[0145] RPCANet is from Wu F, Zhang T, Li L, et al. RPCANet: Deep Unfolding RPCABased Infrared Small Target Detection[C] / / Proceedings of the IEEE / CVF Winter Conference on Applications of Computer Vision. 2024: 4809-4818.

[0146] Figure 7 The original image of the example frame of the infrared image and the thermal infrared small target detection result diagrams detected by the method of the present invention, MDWCM, MSLSTIPT, TWTVR, STT-TRNR, FGLR-MCP, AGPCNet and RPCANet. From Figure 7It can be seen from the target detection result images that the background suppression capabilities of STT-TRNR, TWTVR and MSLSTIPT are extremely weak, MDWCM, FGLR-MCP and AGPCNet have problems of target shrinkage or even target loss, and there are more clutter residues in the detection result images of RPCANet; in contrast, the infrared weak target detection method based on hypergraph proposed in the present invention can well suppress background, noise and other components, and enhance the significance of weak targets. In addition, according to the indicator results based on the 3D-ROC evaluation system shown in Table 1, the target detection ability, background suppression ability and comprehensive ability of the method proposed in the present invention can basically achieve optimal performance and suboptimal performance; in contrast, other methods have insufficient background suppression ability or insufficient target detection ability, resulting in an overall performance far worse than the method proposed in the present invention. Combining the above qualitative and quantitative analysis, the infrared weak target detection method based on hypergraph proposed in the present invention has superior target detection ability, background suppression ability and comprehensive effectiveness.

[0147] Table 1 Quantitative indicators of detection results of thermal infrared image example sequences using MDWCM, MSLSTIPT, TWTVR, STT-TRNR, FGLR-MCP, AGPCNet, RPCANet and the proposed method

[0148]

[0149] 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 hypergraph, characterized in that: The steps include: Step 1): Stack the thermal infrared image sequence to be detected in sequence according to the time dimension to construct a three-dimensional space-time tensor ; Step 2): Using the 3D space-time tensor , establish a low-rank sparse decomposition model based on three-dimensional space-time tensor; Step 2) is as follows: transform the three-dimensional space-time tensor Modeled as a background tensor , target tensor and the noise tensor Considering the low-rank characteristics of the background tensor and the sparse characteristics of the target tensor, the spatiotemporal tensor Modeled as: （1） in, represents the rank calculation, express norm, represents the square of the Frobenius norm, and represents the weight coefficient; Step 3): Design a Laplace-based tensor nuclear norm to estimate the low-rank characteristics of the background; Step 3) is as follows: The background tensor Perform fast Fourier transform to get the tensor ,calculate The numerical sum of the Laplace functions of the singular values ​​of all positive slices is defined as the Laplace-based tensor nuclear norm , the calculation formula is: （5） in, is the background tensor The i-th frontal slice after fast Fourier transformation The jth singular value of is the control parameter of the Laplace operator; Step 4): Each frame of the thermal infrared image sequence to be detected is constructed as an image block tensor as a graph node, and a hypergraph is constructed using the node set to design the hypergraph Laplace regularization term; Step 4) is as follows: The image frames of the thermal infrared image sequence to be detected The image block tensor is constructed as a graph node. The construction process is as follows: using the image frame of the thermal infrared image sequence to be detected , by fixing the size The sliding window is Slide in an S-shaped path to obtain non-overlapping image patches, The numerical value and The values ​​of are the same, , represents the round-up operator and stacks them as front slices to obtain the image frame Tensor of non-overlapping image patches , as the image frame Corresponding graph nodes ; Thus, the node set corresponding to the original thermal infrared image sequence is obtained ; Using Node Sets To construct a hypergraph, first define the hyperedge set ,in, express hyperedges, and each hyperedge has nodes, represented by , , , ; For the hyperedge within fully connected nodes, any two nodes and The weight between The definition is as follows: （6） in, represents the square of the matrix's bi-norm, Indicates Image frames The corresponding node No. A frontal slice. Indicates Image frames The corresponding node No. A frontal slice. is the time interval factor, , is a normal number to prevent the denominator from being zero; Therefore, the super edge Weight It is expressed as: （7） Thus, a hypergraph is constructed. , define the hypergraph Laplacian matrix , which contains the node degree matrix , hyperedge degree matrix , and the correlation matrix ,as follows: Node degree matrix is the diagonal matrix of the degree of each node, with size , the degree of each node is the sum of the weights of all hyperedges connected to that node: （8） in, , , Respectively represent nodes , and degree; Hyperedge degree matrix is a size of The diagonal matrix of （9） Incidence Matrix It is a matrix describing the relationship between points and hyperedges, and its size is , for （10） Hypergraph The hypergraph Laplacian matrix of Defined as （11） The hypergraph Laplacian matrix is ​​used to construct the hypergraph Laplacian regularization term: （12） in, represents the trace calculation of the matrix, , which means that the background tensor The background matrix obtained after expansion , background matrix The height is , the width is , Represents the spread operator; Step 5): Combine the Laplace-based tensor nuclear norm and the hypergraph Laplace regularization term to establish a hypergraph-based spatiotemporal tensor decomposition model; Step 5) is as follows: Introducing sparse reweighted tensors , Represents a positive constant to prevent the denominator from being zero; use Norm Approximation norm; the hypergraph-based spatiotemporal tensor decomposition model established by combining the Laplace-based tensor core norm and the hypergraph Laplace regularization term is: （13） in, express norm, , and represents the weight coefficient, represents the Hadamard product; Step 6): Using the ADMM-based optimization solution algorithm, solve the spatiotemporal tensor decomposition model 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 as the infrared small target detection result to realize infrared small target detection.

2. The infrared small target detection method based on hypergraph according to claim 1 is characterized in that: The step 1) comprises: stacking the original thermal infrared image sequence in the time dimension direction to construct a three-dimensional space-time tensor , The size is , express The width of express Height, express Thickness.

3. The infrared small target detection method based on hypergraph according to claim 1 is characterized in that: The step 6) is specifically as follows: The ADMM algorithm is used to solve the model (13), introducing auxiliary variables and , the equivalent model is: （14） The augmented Lagrangian function corresponding to the equivalent model for: （15） in, is the penalty coefficient, is the Lagrange multiplier; Decompose the problem of solving equation (15) into several sub-problems, and update the variables alternately according to equations (16) to (25) until the iteration ends; Auxiliary variables The iteration formula is: （16） 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 ; Auxiliary variables The iteration formula is: （17） in, represents the identity matrix, express Hypergraph Laplacian matrix; Background tensor The iteration formula is: （18） in, , , which means that the matrices and matrix Reconstructed to size Tensor and tensors ; Target Tensor The iteration formula is: （19） in, is a soft threshold shrinkage operator, and , is the soft threshold; Noise Tensor The iteration formula is: （20） Sparse reweighted tensor The iteration formula is: （21） Lagrange multipliers The iteration formula is: （22） （23） （24） Penalty coefficient The iteration formula is: （25） in, represents the update coefficient, express The maximum value of The iteration stop condition is: when the relative error Less than the set error When, or when the target tensor When the number of non-zero elements in no longer changes, stop iterating; After the iteration stops, the target tensor is obtained .

4. The infrared small target detection method based on hypergraph according to claim 1 is characterized in that: The step 7) is specifically as follows: The target tensor that will be obtained in the end Reconstructed into infrared target detection result map, the small target detection result map sequence T is obtained to realize thermal infrared small target detection.

5. A hypergraph-based infrared small target detection device for implementing the method according to any one of claims 1 to 4, characterized in that: include: A three-dimensional space-time tensor construction module is used to construct the infrared image sequence to be detected into a three-dimensional space-time tensor; A low-rank sparse decomposition model building module is used to build a low-rank sparse tensor decomposition model corresponding to a three-dimensional space-time tensor; Laplace-based tensor nuclear norm design module, used to design Laplace-based tensor nuclear norm; A hypergraph construction module, used for constructing a sequence of image frames to be detected into a hypergraph structure; A hypergraph Laplace regularization construction module, used to construct a hypergraph Laplace regularization term corresponding to the hypergraph structure; A hypergraph-based spatiotemporal tensor decomposition model building module, which is used to build a spatiotemporal tensor decomposition model based on a hypergraph regularization term; Model optimization solution module, used to solve the spatiotemporal tensor decomposition model based on hypergraph regularization term using ADMM-based optimization algorithm; The target detection result output module is used to output the infrared weak target detection result map of each frame of infrared image in the infrared image sequence.

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