An infrared small target detection method and device based on four-dimensional kernel and moreau envelope

Abstract

The application discloses an infrared small target detection method and device based on a four-dimensional kernel and Moreau envelope. The method comprises the following steps: (1) for an infrared image sequence, each frame of image is constructed into a four-dimensional block tensor according to a given rule; (2) a four-dimensional kernel of a background tensor is extracted, and a low-rank estimation norm based on the four-dimensional kernel is defined; (3) a sparsity estimation norm based on Moreau envelope is defined, and the sparsity of a target tensor is estimated; (4) a thermal infrared small target detection model based on low-rank sparse decomposition is established; (5) an iterative optimization algorithm based on ADMM is designed, and the thermal infrared small target detection model based on low-rank sparse decomposition is solved; and (6) a target detection result matrix T is reconstructed from a target tensor output by the model, so that a target detection sequence is obtained as an infrared small target detection result, and infrared small target detection is realized. The infrared small target detection method based on the four-dimensional kernel and Moreau envelope can effectively improve the detection performance of the infrared small target.

Description

Technical Field

[0001] This invention relates to the field of image processing, and in particular to an infrared small target detection method and apparatus based on a four-dimensional kernel and Moreau envelope. Background Technology

[0002] Infrared small target detection is gaining increasing attention across various fields, such as early warning systems, low-altitude security deployments, and maritime search and rescue. Its importance lies in its ability to capture faint and small targets at long distances. Typically, targets in infrared images lose their specific shape and texture, and their size ranges from only 4 to 81 pixels. Furthermore, complex backgrounds and clutter in infrared images can easily obscure small targets, especially those with bright, sparse linear structures such as road surfaces and building edges, which negatively impact the representation of sparse targets and further affect the effectiveness of infrared small target detection. Therefore, developing efficient and practical infrared small target detection techniques remains a significant challenge.

[0003] Currently, infrared small target detection methods are mainly divided into two categories: traditional methods and deep learning-based methods. Deep learning-based methods rely heavily on data volume and computational resources to learn sample features. However, these network models may lack robustness when testing data with different distributions, especially in complex scenes for detecting weak infrared targets. Traditional methods can be further divided into single-frame and multi-frame methods. Single-frame methods can be further categorized into background filtering, local feature methods, and component analysis methods. Background filtering methods use filters to filter images to obtain targets. Inspired by the human visual system, local feature methods utilize local image features to describe targets, such as local contrast measurement and multi-directional gradients. Component analysis methods utilize low-rank sparse decomposition theory to extract sparse target information by decomposing the image matrix or image tensor. Common component analysis methods include singular value decomposition and tensor decomposition. Through the decomposition and reconstruction of low-rank background and sparse targets, target detection and background suppression are achieved. Multi-frame-based methods include spatiotemporal consistency methods and multi-frame fusion methods. Spatiotemporal consistency methods utilize the motion information and spatiotemporal consistency characteristics of targets in multi-frame image sequences for detection; common methods include optical flow and Kalman filtering. Multi-frame fusion methods fuse information from multiple frames to improve the accuracy and robustness of target detection. Typically, existing methods often suffer from unsatisfactory detection performance and timeliness in scenes with bright, sparse linear structures. Specifically, single-frame-based methods are more time-efficient than multi-frame-based methods when processing static images, but their performance may be limited for dynamic scenes or dynamic targets. Multi-frame-based methods can better utilize temporal information and have better performance in detecting dynamic targets. However, multi-frame-based methods often require more computational resources and may be limited in real-time applications. Therefore, it is necessary to conduct in-depth research on infrared small target detection methods to adapt to target detection in scenes containing bright, sparse linear structures and to possess excellent timeliness, thereby overcoming the shortcomings of existing infrared small target detection methods and achieving optimal detection results. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the present invention aims to provide an infrared small target detection method and apparatus based on a four-dimensional kernel and Moreau envelope. The method constructs a four-dimensional block tensor from a thermal infrared image frame, utilizing high-dimensional data to represent the local and global information of the infrared image sequence. For the four-dimensional background tensor, a four-dimensional kernel is extracted using fully connected tensor ring decomposition, and a low-rank background estimation norm based on the four-dimensional kernel is proposed using the Laplacian function. For sparse targets, a sparsity estimation norm based on the Moreau envelope is introduced, thereby achieving more accurate sparse target estimation. Thus, a thermal infrared small target detection model based on low-rank sparse decomposition is established. Through a designed iterative optimization solution algorithm based on ADMM, the superior performance of the infrared small target detection method based on the four-dimensional kernel and Moreau envelope is comprehensively verified in practical applications.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] This invention discloses an infrared small target detection method based on a four-dimensional kernel and Moreau envelope, characterized by comprising the following steps:

[0007] Step 1): For the infrared image sequence, using a fixed-size window and a fixed sliding step, slide across each frame of the infrared image D to obtain image patches, and construct the obtained image patches as a three-dimensional subtensor. Stack all the obtained three-dimensional subtensors sequentially in the fourth dimension to construct the infrared image D as a four-dimensional block tensor.

[0008] Step 2): Extract the background tensor using fully connected tensor ring decomposition. The four-dimensional kernel, combined with the Laplace function, defines the low-rank background estimation norm based on the four-dimensional kernel;

[0009] Step 3): Define the sparsity estimation norm based on the Moreau envelope to estimate the sparsity of the target component;

[0010] Step 4): From Step 1) to Step 3), establish a thermal infrared small target detection model based on low-rank sparse decomposition;

[0011] Step 5): Design an optimization iterative algorithm based on ADMM to solve the thermal infrared small target detection model based on low-rank sparse decomposition;

[0012] Step 6): Solve the target tensor obtained in Step 5). The target detection result matrix T is reconstructed, thus obtaining the target detection sequence T, which serves as the infrared small target detection result sequence to achieve infrared small target detection.

[0013] The present invention also discloses an infrared small target detection device based on a four-dimensional kernel and Moreau envelope for implementing the method, comprising:

[0014] The four-dimensional block tensor construction module constructs each infrared image frame of the infrared image sequence into a four-dimensional block tensor according to a given rule;

[0015] The low-rank background estimation module based on the four-dimensional kernel is decomposed by fully connected tensor ring, extracts the four-dimensional kernel, and defines the low-rank background estimation norm based on the four-dimensional kernel.

[0016] The Moreau envelope-based sparsity estimation module defines the Moreau envelope-based sparsity estimation norm and estimates the sparsity of the target component.

[0017] The thermal infrared small target detection model building module is based on a four-dimensional block tensor. It establishes a thermal infrared small target detection model based on low-rank sparse decomposition by using a low-rank background estimation norm based on a four-dimensional kernel and a sparsity estimation norm based on Moreau envelope.

[0018] The model optimization and solution module designs an optimization and solution framework based on the ADMM algorithm to solve the thermal infrared small target detection model based on low-rank sparse decomposition, obtain the target tensor, and reconstruct it into a target detection result image.

[0019] The target detection result output module is used to output the infrared small target detection result map of each frame of the infrared image sequence.

[0020] Compared with the prior art, the beneficial effects of the present invention include:

[0021] 1) Tensors can represent data in multiple dimensions, accommodating more global and local information. Unlike existing methods that construct an infrared image sequence as a four-dimensional tensor, this invention constructs an infrared image frame to be detected as a four-dimensional block tensor, which can fully express the local and global spatial information of the infrared image frame. This is beneficial for subsequent characterization and extraction of components such as low-rank background and sparse targets. Furthermore, the detection method based on single-frame images in this invention has better timeliness than existing detection methods based on sequence images.

[0022] 2) For sparse target estimation, a sparsity estimation norm based on Moreau envelope is introduced. Considering that dealing with the l0 norm is an NP-hard problem, and the l1 norm may produce solutions that are not sparsy enough because it imposes the same penalty on all features and cannot distinguish which features are truly important, the Moreau envelope can better balance sparsity and convexity and provide more accurate sparsity estimation, thus achieving more accurate sparse target estimation. In particular, when the sparsity of linear structures is strong, the sparsity estimation norm based on Moreau envelope can better suppress linear structures and improve the ability of infrared small target detection methods to separate weak infrared targets in scenes with bright linear structures.

[0023] 3) For low-rank background estimation, a four-dimensional kernel is extracted by fully connected tensor ring decomposition, and a low-rank background estimation norm based on the four-dimensional kernel is proposed by combining the Laplace function. This can better reflect the global structure information of the data, extract the low-rank structure information of the background more effectively, and achieve more accurate low-rank background estimation. Attached Figure Description

[0024] Figure 1 This is a schematic diagram illustrating the process of constructing a frame of infrared image into a four-dimensional block tensor in this invention.

[0025] Figure 2 This is a schematic diagram of the infrared small target detection device based on a four-dimensional kernel and Moreau envelope in this invention.

[0026] Figure 3 Example frame images of a thermal infrared image sequence used for experimental testing;

[0027] Figure 4 The thermal infrared small target detection results are obtained by applying the method proposed in this invention to an example frame of a thermal infrared image sequence.

[0028] Figure 5 The image shows the original image of a thermal infrared image example frame and the thermal infrared small target detection results obtained by the method of this invention, using DGRL, NRAM, METTR, NFTDGSTV, ASTTV-NTLA, 4DTR, and RCTVW. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of this invention clearer, the invention is described in detail below with reference to specific embodiments. Specific embodiments are described below to simplify the invention. However, it should be understood that the invention is not limited to the described embodiments, and various modifications are possible without departing from the basic principles; these equivalent forms also fall within the scope defined by the appended claims.

[0030] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0031] The basic steps of the infrared small target detection method based on four-dimensional kernel and Moreau envelope of the present invention in this embodiment mainly include:

[0032] Step 1: For an infrared image sequence, using a fixed-size window and a fixed sliding step, slide across each frame of infrared image D to obtain image patches, and construct each image patch as a three-dimensional subtensor. Stack all the obtained three-dimensional subtensors sequentially in the fourth dimension to construct the infrared image D as a four-dimensional block tensor.

[0033] Specifically, such as Figure 1 As shown, for infrared image D in the original infrared image sequence, I4 image blocks are obtained by sliding along a trajectory from left to right and from top to bottom on infrared image D with a fixed window size of 3ps × 3ps and a fixed sliding step size of 3ps; for each image block... i4 is the index of the image patch, representing the i4th image patch, and 1 ≤ i4 ≤ i4; the resulting image patch The image is uniformly divided into 3×3 sub-image blocks. These 9 sub-image blocks are stacked sequentially along the third dimension to construct a three-dimensional subtensor. i4 is the index of the three-dimensional subtensor, and 1 ≤ i4 ≤ I4; the resulting I4 three-dimensional subtensors are stacked sequentially in the fourth dimension to construct a four-dimensional block tensor from the original infrared image D. The dimensions are I1×I2×I3×I4, where I1=I2=ps, ​​I3=9;

[0034] In the specific implementation example, ps is set to 25, and the constructed five-dimensional spacetime block tensor The dimensions are 25×25×9×16.

[0035] Step 2: Extract the background tensor using fully connected tensor ring decomposition. The four-dimensional kernel, combined with the Laplace function, defines the low-rank background estimation norm based on the four-dimensional kernel;

[0036] Specifically, for the four-dimensional background tensor Using fully connected tensor ring decomposition, for Tensor decomposition is performed, and the expression is:

[0037]

[0038] Where Φ(·) denotes the fully connected tensor ring decomposition operator. This represents the set consisting of the extracted four-dimensional kernels, including Both represent the kernel tensor obtained by decomposing a fully connected tensor ring, and are called a four-dimensional kernel;

[0039] Based on a four-dimensional kernel Using the Laplace function, a low-rank sparse norm based on a four-dimensional kernel is defined. The expression is:

[0040]

[0041] Where, β k Indicates the weighting coefficient. The Laplace-based tensor nuclear norm of the k-th four-dimensional kernel is expressed as:

[0042]

[0043] in, Represents the k-th four-dimensional kernel The result obtained after Fast Fourier Transform The t-th frontal slice, ι represents the Laplace coefficient; the t-th frontal slice The singular values ​​are arranged from largest to smallest. express The s-th largest singular value;

[0044] In a specific embodiment, r 1,2 =…=r 1,4 =r 2,3 =…=r 3,4 =3,R 1,2 =…=R 1,4 =R 2,3 =…=R 3,4 =7, ι=0.0001.

[0045] Step 3: Define the sparsity estimation norm based on Moreau envelope to estimate the sparsity of the target component;

[0046] Specifically, for the three-dimensional target subtensor 1≤i4≤I4, Moreau envelope-based l0 norm The definition is as follows:

[0047]

[0048] in, express The element with position index (i1, i2, i3) in the middle is defined as ζ(x) as

[0049]

[0050] From formula (4) to formula (5), for the target tensor Define the l0 norm based on the Moreau envelope for

[0051]

[0052] Where 1≤i4≤I4;

[0053] In the specific embodiment, γ is set to 0.006.

[0054] Step 4: From Step 1) to Step 3), establish a thermal infrared small target detection model based on low-rank sparse decomposition;

[0055] Specifically, from step 1) to step 3), a thermal infrared small target detection model based on low-rank sparse decomposition is established, as shown in formula (7):

[0056]

[0057] in, Let these represent the four-dimensional background tensor, the four-dimensional target tensor, and the four-dimensional noise tensor, respectively. λ1 and λ2 represent the square of the Frobenius norm of the noise tensor, and the coordination parameters.

[0058] Solving model (7) is an iterative optimization process. By introducing a sparsity reweighting strategy, the sparsity estimation is accelerated. The reweighted tensor in each iteration process... The target tensor obtained from the previous iteration Determined; in the (i+1)th iteration, the four-dimensional reweighted weight tensor of the target. Where ε0 represents a positive constant, (·) -1 The operation of calculating the reciprocal of an element is represented by |·|, and the operation of calculating the absolute value is represented by |·|. Thus, the final thermal infrared small target detection model based on low-rank sparse decomposition is established, as shown in formula (8):

[0059]

[0060] Where ⊙ represents the Hadamarda.

[0061] Step 5: Design an optimization iterative algorithm based on ADMM to solve the thermal infrared small target detection model based on low-rank sparse decomposition;

[0062] Specifically, the ADMM algorithm is used to solve the thermal infrared small target detection model (8) based on low-rank sparse decomposition in step 4). To ensure that each variable to be solved in (8) is solvable, the following is introduced: Auxiliary variables k = 1, 2, 3, 4, resulting in formula (9) as shown below:

[0063]

[0064] The corresponding augmented Lagrangian function is

[0065]

[0066] in, Let be the Lagrange multiplier and μ be the penalty coefficient; each variable is solved through alternating iterations, and the subproblems corresponding to each variable are as follows:

[0067] 1) The iterative formula is

[0068]

[0069] Where i represents the iteration number. Indicates tensor Expanding along pattern -k into a matrix, UnFold(·) represents the tensor expansion operator. This indicates that after removing the k-th four-dimensional kernel, a fully connected tensor ring decomposition is performed. Represent tensors respectively The matrix obtained by expanding along pattern -k is (·). T This represents the matrix transpose operator, where I represents the identity matrix. The operator for the pseudo-inverse of a matrix;

[0070] Depend on get as follows

[0071]

[0072] Where GenFold(·) represents the matrix Shrinks along pattern -k into a four-dimensional tensor

[0073] 2) The iterative formula is

[0074]

[0075] in, express The singular value tensor, and Tensor The orthogonal tensor obtained after singular value decomposition This represents the singular value contraction operator based on the Laplace function. σ represents Singular values ​​in;

[0076] 3) The iterative formula is

[0077]

[0078] in, This represents the result obtained in the (i+1)th iteration. And there are Let i represent a unit tensor, and 1 ≤ i4 ≤ I4;

[0079] 4) The iterative formula is

[0080]

[0081] in, This represents the result obtained in the (i+1)th iteration.

[0082] 5) The iterative formula is

[0083]

[0084] in, This represents the result obtained in the (i+1)th iteration.

[0085] 6) Lagrange multipliers The iterative formula is

[0086]

[0087]

[0088]

[0089] in, They represent the results obtained in the (i+1)th iteration.

[0090] 8) The iterative formula for the penalty coefficient μ is:

[0091]

[0092] Where, μ (i+1) μ represents the value obtained in the (i+1)th iteration, γ represents the iteration update coefficient, and μ max This represents the maximum value of μ;

[0093] The iteration stopping condition is:

[0094] This completes the iterative solution of the thermal infrared small target detection model (8) based on low-rank sparse decomposition in step 4), and yields the four-dimensional target tensor.

[0095] Specifically, in the embodiments... λ L =25, μ max =100, γ=1.5, μ (0) =0.0005,

[0096] Step 6: Solve the target tensor obtained in Step 5 The target detection result matrix T is reconstructed, thus obtaining the target detection sequence T, which serves as the infrared small target detection result sequence, achieving infrared small target detection.

[0097] Specifically, the target tensor obtained in step 5... The target detection image T is reconstructed to have the same size as the infrared image D in the input original infrared image sequence, with a size of n1×n2. The target detection result sequence T is composed of the target detection images corresponding to each infrared image, which serves as the infrared small target detection result of the original infrared thermal infrared image sequence, realizing infrared small target detection based on four-dimensional kernel and Moreau envelope.

[0098] Corresponding to the aforementioned embodiment of an infrared small target detection method based on a four-dimensional kernel and Moreau envelope, the present invention also provides an embodiment of an infrared small target detection device based on a four-dimensional kernel and Moreau envelope.

[0099] Figure 2 This is a block diagram illustrating an infrared small target detection device based on a four-dimensional kernel and Moreau envelope according to an exemplary embodiment, such as... Figure 2 As shown, the device includes:

[0100] The four-dimensional block tensor construction module constructs each infrared image frame of the infrared image sequence into a four-dimensional block tensor according to a given rule;

[0101] The low-rank background estimation module based on the four-dimensional kernel is decomposed by fully connected tensor ring, extracts the four-dimensional kernel, and defines the low-rank background estimation norm based on the four-dimensional kernel.

[0102] The Moreau envelope-based sparsity estimation module defines the Moreau envelope-based sparsity estimation norm and estimates the sparsity of the target component.

[0103] The thermal infrared small target detection model building module is based on a four-dimensional block tensor. It establishes a thermal infrared small target detection model based on low-rank sparse decomposition by using a low-rank background estimation norm based on a four-dimensional kernel and a sparsity estimation norm based on Moreau envelope.

[0104] The model optimization and solution module designs an optimization and solution framework based on the ADMM algorithm to solve the thermal infrared small target detection model based on low-rank sparse decomposition, obtain the target tensor, and reconstruct it into a target detection result image.

[0105] The target detection result output module is used to output the infrared small target detection result map of each frame of the infrared image sequence.

[0106] Regarding the apparatus in the above embodiments, the specific manner in which each module performs its operation has been described in detail in the embodiments related to the method, and will not be elaborated upon here.

[0107] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to the description of the method embodiments. The device embodiments described above are merely illustrative; the various modules in the device represent a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules may be combined or integrated into another unit. Furthermore, the connections between the displayed or discussed modules may be communication connections through some interfaces, which may be electrical or other forms. Some or all of the modules can be selected to achieve the purpose of this application according to actual needs. Those skilled in the art can understand and implement this without creative effort. The following uses a publicly available real thermal infrared image sequence as an example to illustrate specific implementation methods to demonstrate the technical effects of the present invention; specific steps in the embodiments will not be repeated.

[0108] Example

[0109] The accompanying drawings illustrating the embodiments of the present invention will make the objectives, technical solutions, and advantages of the present invention clearer. It should be noted that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention. All equivalent substitutions and improvements made within the framework of the methods and principles provided by the present invention should be included within the protection scope of the present invention.

[0110] In this embodiment, the effectiveness of the thermal infrared small target detection algorithm will be verified using a publicly available infrared image sequence. The publicly available infrared image sequence is described as follows: It contains 50 image frames, each 25×25 pixels. The sequence has a forest-ground background, with locally bright sparse linear structures, strong clutter and noise, and a small aircraft moving in the air, exhibiting high contrast with the surrounding background. Figure 3 The image shown is an example frame of an infrared image sequence. Figure 4 The images shown are example frames of an infrared image sequence, processed by the infrared small target detection method based on a four-dimensional kernel and Moreau envelope, as described in this invention. The intuitive detection results demonstrate that this method effectively suppresses complex backgrounds, noise, and clutter in the image, while significantly enhancing small targets. To more accurately and objectively evaluate the effectiveness of the infrared small target detection method based on a four-dimensional kernel and Moreau envelope, a qualitative analysis compares and evaluates the target detection results of this method on example frames in an infrared image sequence. Quantitatively, the detection performance of the algorithm is evaluated using the 3D-ROC evaluation index system, first proposed by Chein-I Chang, which includes three main categories of indicators:

[0111] 1) Target detection capability: AUC (D,τ) AUC TD ;

[0112] 2) Background suppression capability: AUC (F,τ) AUC BS AUC SNPR ;

[0113] 3) Overall detector capabilities: AUC (D,F) AUC TDBS AUC ODP ;

[0114] To more objectively verify the effectiveness of the method of this invention, seven thermal infrared small target detection methods were selected for comparison with the method of this invention. The comparison methods include DGRL, NRAM, METTR, NFTDGSTV, ASTTV-NTLA, 4DTR, and RCTVW. Table 1 shows the 3D-ROC evaluation system index of the small target detection results of this thermal infrared image sequence using the comparison methods and the method of this invention. The bold and underlined values ​​represent the best and second-best performance, respectively.

[0115] DGRL originates from Zhou, Fei, et al. "Robust infrared small target detection via joint sparse constraint of l 1 / 2-metric and dual-graph regularization." Remote Sensing 12.12(2020):1963.

[0116] NRAM originates from Zhang, Landan, et al. "Infrared small target detection via non-convex rank approximation minimization joint l 2,1 norm." Remote Sensing 10.11(2018):1821.

[0117] METTR originates from Cao, Zhaoyang, et al. "Infrared dim target detection via mode-k1k2 extension tensor tubal rank under complex ocean environment." ISPRS Journal of Photogrammetry and Remote Sensing 181(2021):167-190.

[0118] NFTDGSTV originates from Liu, Ting, et al. "Infrared small target detection via nonconvex tensor tucker decomposition with factor prior." IEEE Transactions on Geoscience and Remote Sensing(2023).

[0119] ASTTV-NTLA originates from Liu, Ting, et al. "Nonconvex tensor low-rank approximation for infrared small target detection." IEEE Transactions on Geoscience and Remote Sensing 60(2021):1-18.

[0120] 4DTR originates from Wu, Fengyi, et al. "Infrared small target detection using spatio-temporal 4d tensor train and ring unfolding." IEEE Transactions onGeoscience and Remote Sensing (2023).

[0121] RCTVW originates from Liu, Ting, et al. "Representative coefficient total variation for efficient infrared small target detection." IEEE Transactions onGeoscience and Remote Sensing (2023).

[0122] Figure 5 The image shows the original infrared image of the example frame and the detection results of thermal infrared small targets detected by the method of this invention, including DGRL, NRAM, METTR, NFTDGSTV, ASTTV-NTLA, 4DTR, and RCTVW. Figure 5 The target detection results images show that METTR, NRAM, and DGRL are more sensitive to noise clutter and bright structures, resulting in more false alarms in the detection images. NFTDGSTV, ASTTV-NTLA, 4DTR, and RCTVW have insufficient background suppression capabilities. Conversely, the infrared small target detection method based on a four-dimensional kernel and Moreau envelope proposed in this invention can enhance the saliency of small targets and suppress background, clutter, and noise components. According to the index results based on the 3D-ROC evaluation system shown in Table 1, the method proposed in this invention achieves the best and second-best performance in target detection capability, background suppression capability, and overall capability, followed by DGRL. In contrast, although METTR has excellent target detection capability, its background suppression capability is the weakest, resulting in the weakest overall capability. In summary, based on the above qualitative and quantitative analyses, the infrared small target detection method based on a four-dimensional kernel and Moreau envelope proposed in this invention has superior target detection capability, background suppression capability, and overall effectiveness.

[0123] Table 1. Quantitative indicators of the detection results of thermal infrared image example sequences using DGRL, NRAM, METTR, NFTDGSTV, ASTTV-NTLA, 4DTR, RCTVW, and the method of this invention.

[0124] This invention 1.0000 0.9960 5.6381e-6 1.9960 1.0000 1.7665e5 0.9960 1.9960 DGRL 1.0000 0.9960 7.5269e-5 1.9960 0.9999 1.3233e4 0.9959 1.9959 NRAM 1.0000 0.9960 4.9348e-4 1.9960 0.9995 2.0183e3 0.9955 1.9955 METTR 1.0000 0.9960 1.5077e-1 1.9960 0.8492 6.6060 0.8452 1.8452 NFTDGSTV 0.9998 0.9524 3.7601e-3 1.9522 0.9961 2.5329e2 0.9486 1.9485 ASTTV-NTLA 1.0000 1.0000 5.6207e-2 2.0000 0.9438 1.7791e1 0.9438 1.9438 4DTR 1.0000 0.9952 6.2585e-2 1.9952 0.9374 1.5902e1 0.9326 1.9326 RCTVW 0.9800 0.9800 1.1669e-5 1.9600 0.9800 8.3980e4 0.9800 1.9600

[0125] The accompanying drawings illustrating the embodiments of the present invention will make the objectives, technical solutions, and advantages of the present invention clearer. It should be noted that the specific embodiments described herein are merely illustrative and not intended to limit the scope of the invention. All equivalent substitutions and improvements made within the framework of the methods and principles provided by the present invention should be included within the protection scope of the present invention.

Claims

1. A method for detecting small infrared targets based on a four-dimensional kernel and Moreau envelope, characterized in that, Includes the following steps: Step 1): For an infrared image sequence, using a fixed-size window and a fixed sliding step, in each frame of the infrared image... The image patch is obtained by sliding upwards, and the obtained image patch is constructed into a three-dimensional subtensor. All the obtained three-dimensional subtensors are stacked sequentially in the fourth dimension to realize the infrared image... Constructed as a four-dimensional block tensor ; Step 1) Specifically involves: for the infrared images in the original infrared image sequence... Using a fixed window size of 3ps × 3ps and a fixed sliding step size of 3ps, in infrared images The trajectory is obtained by sliding from left to right and from top to bottom. Image patches; for image patches , The index of this image patch indicates the number of... There are image patches, and there are The resulting image patch Evenly divided into Nine sub-image blocks are stacked sequentially along the third dimension to construct a three-dimensional subtensor. , The index of this three-dimensional subtensor, and has ; will be obtained The three-dimensional subtensors are stacked sequentially in the fourth dimension to realize the processing of the original infrared image. Constructed as a four-dimensional block tensor , The size is ,in, , ; Step 2): Extract the background tensor using fully connected tensor ring decomposition. The four-dimensional kernel, combined with the Laplace function, defines the low-rank background estimation norm based on the four-dimensional kernel; Step 2) specifically refers to: For the four-dimensional background tensor Using fully connected tensor ring decomposition, for Tensor decomposition is performed, and the expression is: （1） in, This represents the operator for decomposing a fully connected tensor ring. This represents the set consisting of the extracted four-dimensional kernels, including , Both represent the kernel tensor obtained by decomposing a fully connected tensor ring, and are called a four-dimensional kernel; Based on a four-dimensional kernel Using the Laplace function, a low-rank sparse norm based on a four-dimensional kernel is defined. The expression is: （2） in, Indicates the weighting coefficient. Indicates the first The Laplace-based tensor kernel norm of a four-dimensional kernel is expressed as: （3） in, Indicates the first A four-dimensional kernel The result obtained after Fast Fourier Transform The A frontal slice, Represents the Laplace coefficient; [The text abruptly ends here, likely due to an incomplete sentence or a formatting error Zhang frontal slice The singular values ​​are arranged from largest to smallest. express The Large singular values; Step 3): Define the sparsity estimation norm based on the Moreau envelope to estimate the sparsity of the target component; Step 3) specifically refers to: For the three-dimensional target subtensor , , Moreau envelope-based norm The definition is as follows: （4） in, express The position index is elements, Represents the Moreau envelope coefficient. Defined as （5） From formulas (4) and (5), for the target tensor Define Moreau envelope-based norm for （6） in, ; Step 4): From Step 1) to Step 3), establish a thermal infrared small target detection model based on low-rank sparse decomposition; Step 5): Design an optimization iterative algorithm based on ADMM to solve the thermal infrared small target detection model based on low-rank sparse decomposition; Step 6): Solve the target tensor obtained in Step 5). Reconstructed into a matrix of object detection results Thus, the target detection sequence T is obtained, which serves as the infrared small target detection result sequence, thereby realizing infrared small target detection.

2. The infrared small target detection method based on four-dimensional kernel and Moreau envelope according to claim 1, characterized in that, Step 4) specifically refers to: From step 1) to step 3), a thermal infrared small target detection model based on low-rank sparse decomposition is established, as shown in formula (7): （7） in, Let these represent the four-dimensional background tensor, the four-dimensional target tensor, and the four-dimensional noise tensor, respectively. The square of the Frobenius norm of the noise tensor. and Indicates coordination parameters; Solving model (7) is an iterative optimization process. By introducing a sparsity reweighting strategy, the sparsity estimation is accelerated. The reweighted tensor in each iteration process... The target tensor obtained from the previous iteration Confirmed; the first In each iteration, the target's four-dimensional reweighted weight tensor ,in, Represents positive numbers. This represents the operation of calculating the reciprocal of an element. This indicates the operation of calculating the absolute value; thus, the final thermal infrared small target detection model based on low-rank sparse decomposition is established, as shown in formula (8): （8） in, It represents the Hadamardi (or Hadama) stack.

3. The infrared small target detection method based on four-dimensional kernel and Moreau envelope according to claim 1, characterized in that, Step 5) specifically refers to: The ADMM algorithm is used to solve the thermal infrared small target detection model (8) based on low-rank sparse decomposition in step 4). To ensure that each variable to be solved in (8) is solvable, the following is introduced: Auxiliary variables , Formula (9) is obtained as follows: （9） The corresponding augmented Lagrangian function is （10） in, For Lagrange multipliers, The penalty coefficient is used; each variable is solved through alternating iterations, and the subproblems corresponding to each variable are as follows: 1) The iterative formula is （11） in, Indicates the number of iterations. Indicates tensor Along the pattern - Expand into a matrix, This represents the tensor expansion operator. Indicates removing the first After a four-dimensional kernel, a fully connected tensor ring decomposition is performed. , , , Represent tensors respectively , , , Along the pattern - The expanded matrix This represents the matrix transpose operator. Represents the identity matrix. The operator for the pseudo-inverse of a matrix; Depend on ,get as follows （12） in, Indicates the matrix Along the pattern - Shrink into a four-dimensional tensor ; 2) The iterative formula is （13） in, , express The singular value tensor, and Tensor The orthogonal tensor obtained after singular value decomposition This represents the singular value contraction operator based on the Laplace function. , , express Singular values ​​in; 3) The iterative formula is （14） in, Indicates the first Round iterations obtained And there are , , Represents a unit tensor, and has ; 4) The iterative formula is （15） in, Indicates the first Round iterations obtained ; 5) The iterative formula is （16） in, Indicates the first Round iterations obtained ; 6) Lagrange multipliers The iterative formula is （17） （18） （19） in, They represent the first Round iterations obtained ; 7) Penalty coefficient The iterative formula is （20） in, Indicates the first Round iterations obtained , Indicates the iterative update coefficients. express The maximum value; The iteration stopping condition is: 1) ;2) ; This completes the iterative solution of the thermal infrared small target detection model (8) based on low-rank sparse decomposition in step 4), and yields the four-dimensional target tensor. .

4. The infrared small target detection method based on four-dimensional kernel and Moreau envelope according to claim 1, characterized in that, Step 6) specifically refers to: The target tensor obtained in step 5) Reconstructed to resemble the infrared images in the input original infrared image sequence. Size-consistent target detection images The size is The target detection result sequence T is composed of the target detection image corresponding to each infrared image, which serves as the infrared small target detection result of the original infrared thermal infrared image sequence, realizing infrared small target detection based on four-dimensional kernel and Moreau envelope.

5. An infrared small target detection device based on a four-dimensional kernel and Moreau envelope, implementing the method of claim 1, characterized in that, include: The four-dimensional block tensor construction module constructs each infrared image frame of the infrared image sequence into a four-dimensional block tensor according to a given rule; The low-rank background estimation module based on the four-dimensional kernel extracts the four-dimensional kernel of the background tensor by decomposing the fully connected tensor ring and combining it with the Laplace function to define the low-rank background estimation norm based on the four-dimensional kernel. The Moreau envelope-based sparsity estimation module defines the Moreau envelope-based sparsity estimation norm and estimates the sparsity of the target component. The thermal infrared small target detection model building module is based on a four-dimensional block tensor. It establishes a thermal infrared small target detection model based on low-rank sparse decomposition by using a low-rank background estimation norm based on a four-dimensional kernel and a sparsity estimation norm based on Moreau envelope. The model optimization and solution module designs an optimization and solution framework based on the ADMM algorithm to solve the thermal infrared small target detection model based on low-rank sparse decomposition, obtain the target tensor, and reconstruct it into a target detection result image. The target detection result output module is used to output the infrared small target detection result map of each frame of the infrared image sequence.

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