A method and system for infrared small target detection based on frame tensor nuclear norm

Abstract

The present invention discloses a method and system for detecting infrared small targets based on the framework tensor nuclear norm, which obtains a tensor composed of several consecutive frames of images and inputs it into a pre-built infrared small target detection model based on the framework tensor nuclear norm; divides the model into sub-problems including background part, target part and noise part, optimizes and solves these sub-problems respectively, and obtains the current optimal solution of each sub-problem; judges whether the current optimal solution of the target part converges or whether the maximum number of iterations is reached, and if so, outputs the current optimal solution of the target part; if not, updates the model with the current optimal solution of each sub-problem and re-optimizes and solves it. Advantages: By transforming the image into the frame domain, the multi-rank approximation of the tensor is more effectively achieved, and the background details are better characterized. At the same time, the noise in the background is well handled by the morphological regularization term, so that the accuracy and robustness of infrared small target detection are improved.

Description

Technical Field

[0001] The present invention relates to a method and system for detecting small infrared targets based on a frame tensor nuclear norm, and belongs to the technical field of image processing. Background Art

[0002] In daily life, vision is an important channel for people to perceive the outside world. In recent years, with the continuous development of imaging and storage technologies, videos and images have also become important carriers of information recording and an important part of people's understanding and perception of the world. Therefore, it is particularly important to obtain information from images efficiently and quickly. However, to process such a huge amount of image and video information, manpower alone is not enough. Therefore, many researchers have studied image processing technology in order to be able to process and obtain information from images in batches through computers, thereby saving manpower and material resources and reducing costs. The main process of image processing technology is as follows: first, images or videos are acquired through acquisition equipment, then these images or videos are digitized as input, and then computer programs and algorithms are designed according to the desired results to process the parts of the image of interest, and finally, the information people need is output.

[0003] In real life, two imaging technologies are commonly used: visible light imaging and infrared imaging. Although visible light imaging offers high image resolution and a richness of target detail, it is susceptible to external influences due to its inherent linear propagation and limited penetrating power. Furthermore, in environments subject to erratic changes, the high resolution and high detail of visible light imaging can negatively impact detection results. Therefore, visible light imaging is not widely used in real life. Infrared light, on the other hand, is invisible and has strong penetrating power. It primarily forms images by receiving infrared thermal radiation from objects. Therefore, infrared imaging is less susceptible to interference from environmental fluctuations and offers advantages such as high concealment, long operating range, strong anti-interference capabilities, and long operating time. Consequently, infrared imaging technology has found widespread application in both military and civilian fields. In the military field, infrared imaging technology can be used in early warning, missile tracking, precision guidance, etc.; in the medical field, infrared imaging technology can help doctors identify the type and location of lesions, detect symptoms in advance, and assist doctors in making diagnoses; in transportation, infrared imaging technology can have a certain auxiliary effect on unmanned driving technology and reduce risks; in the agricultural field, infrared technology can monitor crop growth and has far-reaching significance for the realization of agricultural modernization; in the industrial field, infrared imaging can be used for industrial nondestructive testing to find problems without damaging machinery.

[0004] Although infrared imaging technology has great advantages, its special imaging method poses challenges to infrared small target detection technology: (1) The infrared imaging distance is long, resulting in blurred imaging and low image resolution, and the target occupies a very small proportion of the entire image. (2) There are many unavoidable noises and clutters in the imaging system and the background, which will affect the final detection results. (3) The blur and low resolution caused by long-distance imaging will lead to the lack of effective shape and texture features of the target. In addition, for small targets in complex backgrounds, there is a lot of background clutter, and the signal-to-clutter ratio of the image is very low, and the target is almost submerged in the background clutter. These problems have posed great challenges to infrared small target detection technology. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to overcome the defects of the prior art and provide an infrared small target detection method and system based on the frame tensor nuclear norm, which has higher accuracy and robustness.

[0006] To solve the above technical problems, the present invention provides an infrared small target detection method based on the frame tensor nuclear norm, comprising:

[0007] Obtain a tensor composed of several consecutive frames of images and input it into a pre-built infrared small target detection model based on the frame tensor nuclear norm;

[0008] The infrared small target detection model based on the frame tensor nuclear norm is divided into sub-problems including background part, target part and noise part. These sub-problems are optimized and solved respectively to obtain the current optimal solution of each sub-problem.

[0009] Determine whether the current optimal solution of the target part has converged or whether the maximum number of iterations has been reached.

[0010] If so, output the current optimal solution of the target part.

[0011] If not, the current optimal solution of each sub-problem is used to update the infrared small target detection model based on the framework tensor nuclear norm, and the optimization is re-performed to obtain the current optimal solution of each new sub-problem, and the convergence and number of iterations are judged again.

[0012] Furthermore, the infrared small target detection model based on the frame tensor nuclear norm is:

[0013]

[0014] stG N +G B +G T =G D

[0015] In the above formula, is the noise regularization term, α||G B || F-TNN is the framework tensor nuclear norm term, βW(G T ) is the morphological regularization term, G B For the background part, G T is the target part, G N is the random Gaussian noise in the image, G D is a tensor, m is the number of input images, n1×n2 is the size of each image, R represents a set of real numbers, α is the coefficient of the rank minimization term, β is the penalty coefficient of the morphological regularization term, W is the frame transformation matrix, stG N +G B +G T =G D Indicates constraints.

[0016] Furthermore, the infrared small target detection model based on the frame tensor nuclear norm is divided into sub-problems including background part, target part, and noise part, and these sub-problems are optimized and solved respectively to obtain the current optimal solution of each sub-problem. The process includes:

[0017] Introducing auxiliary variables The background part after frame transformation is recorded as The objective function is obtained as:

[0018]

[0019] stG N +G B +G T =G D ,

[0020] Combining the objective function with the constraints, the augmented Lagrangian form of the above equation is:

[0021]

[0022] Among them, G Z and S are Lagrange multipliers, ρ and a are penalty factors, Represents ||G B || F-TNN The expansion, Represents auxiliary variables The frontal slice of ||·|| * is the nuclear norm, w=(n-1)l+1, l represents the number of levels of the framework transformation, n represents the number of filters, and n3 represents the original tensor G B The third dimension of

[0023] The ADMM algorithm is used to divide the objective function into the following sub-problems:

[0024]

[0025] Solving these subproblems yields the following results:

[0026]

[0027] In the formula, the symbol with superscript n+1 represents the current result after the optimization solution, the symbol with superscript n represents the result after the previous optimization solution, SVT is the singular value threshold algorithm, 2α / ρ is the shrinkage threshold, γ is the update factor, and Fold3 means folding the matrix into a tensor according to mode 3.

[0028] Furthermore, the process of determining whether the current optimal solution of the target part has converged includes:

[0029] Through the expression Determine whether the current optimal solution of the target part converges. If the calculated result is greater than or equal to 0.01, it is considered to be converged, otherwise it is not converged.

[0030] An infrared small target detection system based on frame tensor nuclear norm, comprising:

[0031] The acquisition module is used to obtain the tensors composed of several consecutive frames of images and input them into the pre-built infrared small target detection model based on the nuclear norm of the frame tensor;

[0032] The partitioning module is used to divide the infrared small target detection model based on the frame tensor nuclear norm into sub-problems including background part, target part and noise part, and optimize and solve these sub-problems respectively to obtain the current optimal solution of each sub-problem;

[0033] The judgment module is used to judge whether the current optimal solution of the target part has converged or whether the maximum number of iterations has been reached.

[0034] If so, output the current optimal solution of the target part.

[0035] If not, the current optimal solution of each sub-problem is used to update the infrared small target detection model based on the framework tensor nuclear norm, and the optimization is re-performed to obtain the current optimal solution of each new sub-problem, and the convergence and number of iterations are judged again.

[0036] Furthermore, the acquisition module includes a model acquisition module,

[0037] It is used to obtain the infrared small target detection model based on the framework tensor nuclear norm. The model is expressed as:

[0038]

[0039] stG N +G B +G T =G D

[0040] In the above formula, is the noise regularization term, α||G B || F-TNN is the framework tensor nuclear norm term, βW(G T ) is the morphological regularization term, G B For the background part, G T is the target part, G N is the random Gaussian noise in the image, G D is a tensor, m is the number of input images, n1×n2 is the size of each image, R represents a set of real numbers, α is the coefficient of the rank minimization term, β is the penalty coefficient of the morphological regularization term, W is the frame transformation matrix, stG N +G B +G T =G D Indicates constraints.

[0041] Furthermore, the division module includes:

[0042] Transformation module, used to introduce auxiliary variables The background part after frame transformation is recorded as The objective function is obtained as:

[0043]

[0044] stG N +G B +G T =G D ,

[0045] The combination module is used to combine the objective function with the constraints, and the augmented Lagrangian form of the above equation is obtained as follows:

[0046]

[0047] Among them, G Z and S are Lagrange multipliers, ρ and a are penalty factors, Represents ||G B || F-TNN The expansion, Represents auxiliary variables The frontal slice of ||·|| *is the nuclear norm, w=(n-1)l+1, l represents the number of levels of the framework transformation, n represents the number of filters, and n3 represents the original tensor G B The third dimension of

[0048] The ADMM processing module is used to divide the objective function into the following sub-problems using the ADMM algorithm:

[0049]

[0050] The solution module is used to solve these sub-problems, and the results are:

[0051]

[0052] In the formula, the symbol with superscript n+1 represents the current result after the optimization solution, the symbol with superscript n represents the result after the previous optimization solution, SVT is the singular value threshold algorithm, 2α / ρ is the shrinkage threshold, γ is the update factor, and Fold3 means folding the matrix into a tensor according to mode 3.

[0053] Furthermore, the judgment module converges to the judgment module.

[0054] Used to pass expressions Determine whether the current optimal solution of the target part converges. If the calculated result is greater than or equal to 0.01, it is considered converged, otherwise it is not converged.

[0055] The beneficial effects achieved by the present invention are:

[0056] The present invention makes full use of the prior knowledge of the image, regards the infrared small target detection problem as a rank minimization problem of a low-rank tensor, and uses the frame-based tensor nuclear norm to approximate the rank minimization problem of the background. Its technical effects include: First, to address the problem of less feature information in infrared images, we use continuous images to form a tensor as input to fully utilize the spatial and temporal features in the image; second, to address the rank minimization approximation problem, we use the frame tensor nuclear norm (F-TNN), which can more effectively approximate the multi-rank minimization problem of the tensor, and the basis functions in the frame transformation are redundant, which can restore the background more carefully and detect small targets more accurately; third, in order to better utilize the prior knowledge of the image, we add a morphological regularization term to the model, fully utilize the local difference information between the target and its surrounding background, and greatly improve the model's ability to suppress noise. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 Flow chart of the method of the present invention.

[0058] Figure 2This is a ROC comparison diagram of the method of the present invention in the real picture 1;

[0059] Figure 3 This is a ROC comparison diagram of the method of the present invention in real picture 2;

[0060] Figure 4 This is the ROC comparison diagram of the method of the present invention in real picture 3;

[0061] Figure 5 This is a ROC comparison diagram of the method of the present invention in real picture 4;

[0062] Figure 6 This is a ROC comparison diagram of the method of the present invention in real picture 5;

[0063] Figure 7 This is a comparison chart of the BSF values of the method of the present invention under 5 real pictures;

[0064] Figure 8 This is a comparison chart of the SCRG values of the method of the present invention under 5 real pictures. DETAILED DESCRIPTION

[0065] In order to make the purpose, features, and advantages of the present invention more obvious and easy to understand, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described below are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0066] like Figure 1 As shown in the figure, a small infrared target detection method based on the framework tensor nuclear norm is implemented to detect small infrared targets in complex backgrounds. The specific steps are as follows:

[0067] Step 1: Build an infrared small target detection model based on the frame tensor nuclear norm

[0068] We form three consecutive frames of images into a tensor G D As input, where n1×n2 is the size of each image, and we denote the background part as G B , the target part is recorded as G T , we assume that the noise in the image is random Gaussian noise, denoted by G N , α is the coefficient of the rank minimization term, and β is the penalty coefficient of the morphological regularization term. Here, we can get the following objective function:

[0069]

[0070] stG N +G B +G T =G D

[0071] In the above formula, is the noise regularization term, α||G B || F-TNN is the framelet-Tensor Nuclear Norm (F-TNN), βW(G T ) is the morphological regularization term, G B For the background part, G T is the target part, G N is the random Gaussian noise in the image, G D is a tensor, m is the number of input images, n1×n2 is the size of each image, R represents a set of real numbers, α is the coefficient of the rank minimization term, β is the penalty coefficient of the morphological regularization term, W is the frame transformation matrix, stG N +G B +G T =G D Indicates constraints.

[0072] Step 2: Construct the framework transformation matrix and morphological operator, and initialize the relevant parameters

[0073] Similar to wavelet transform, frame transform also has single-layer frame transform and multi-layer frame transform. Considering the high real-time requirements of infrared small target detection, we choose to use single-layer frame transform here. We use a linear segmented frame to construct the corresponding transformation matrix W, where W consists of two high-pass filters and one low-pass filter.

[0074] In order to make full use of the local difference information between the target and the surrounding background, we construct a ring morphological structure operator to perform morphological operations on the target in the following work.

[0075] After multiple tests, we choose α to be 1.1 and β to be 0.8.

[0076] Step 3: Solve the model using the ADMM method:

[0077] (1) Since the model is convex, it can be solved using the ADMM method. We first combine the objective function with the constraints to obtain the augmented Lagrangian form of the above equation:

[0078]

[0079] (2) Among them, G Z and S are Lagrange multipliers, ρ and a are penalty factors. According to the definition of F-TNN, for a tensor of order n3 Its F-TNN can be expanded as in, is a tensor The tensor after the frame transformation, w = (n-1)l + 1, l represents the number of levels of the frame transformation, n represents the number of filters, and n3 represents The third dimension size of . That is ||G B || F-TNN The expansion, Represents auxiliary variables The frontal slice of ||·|| * is the nuclear norm, n3 represents the original tensor G B The third dimension of

[0080] (3) Using the ADMM algorithm to optimize the function, the above equation is divided into the following sub-problems:

[0081]

[0082] (4) ADMM solution results:

[0083] ① Pair problem G N(n+1) :

[0084] We can derive G from the above formula N(n+1) The optimal solution:

[0085]

[0086] ② Pair problem G T(n+1) :

[0087] We can derive G from the above formula T(n+1) The optimal solution:

[0088]

[0089] Since the morphological regularization term is concave, we find the sub-gradient of this part and denote the sub-gradient of the dilated image as The sub-gradient of the eroded image is recorded as

[0090]

[0091]

[0092] RE and E m RE are stored inguided (j) and E mguided (j) Pixel values in the coverage area.

[0093] In the model, we first dilate the image and then erode it. We define the dilated image as It can be defined as follows:

[0094]

[0095] According to the above formula, we can calculate G T(n+1)

[0096] ③ Pair problem G B(n+1) :

[0097] According to the definition of the framework tensor nuclear norm, it can be concluded that for any tensor Its frame transformation can be written as WX (3) , where W is the frame transformation matrix, X (3) is a tensor The mode 3 expansion of its frame tensor nuclear norm can be written as

[0098]

[0099] in, Represents a tensor block diagonal matrix, and fold3(*) means folding the matrix in the brackets back into the tensor according to mode 3.

[0100] In order to G B(n+1) To solve, we first introduce an auxiliary variable The background of the frame after frame transformation is recorded as Then the objective function can be written as:

[0101]

[0102]

[0103] Correspondingly, its augmented Lagrangian form can be written as:

[0104]

[0105] Where S is the Lagrange multiplier and ρ is the penalty factor.

[0106] The above function can be decomposed into the following sub-problems:

[0107]

[0108] Derivatives of the above two equations can be obtained and GB(n+1) The optimal solution:

[0109]

[0110]

[0111] In the formula, the symbol with superscript n+1 represents the current result after optimization, and the symbol with superscript n represents the result after the previous optimization. SVT (Singular Value Thresholding) is a singular value threshold algorithm. 2α / ρ in the formula is the shrinkage threshold. 2α / ρ In (·), let “·” = U×S×V, where U, S, and V are decomposed by “·” through SVD, and SVT 2α / ρ (·) can be described by the formula as follows:

[0112] SVT 2α / ρ (·)=U×diag(max{diag -1 (S) (i) -2α / ρ,0})×V, 0≤i≤n.

[0113] Where diag(·) means converting the vector into a diagonal matrix, diag -1 It means taking the diagonal elements of the diagonal matrix, γ is the update factor, and Fold3 means folding the matrix into a tensor in mode 3.

[0114] Step 4: Determine whether the current result meets the conditions (convergence) or has reached the maximum number of iterations, if the conditions are met, the target detection result G is output T If the condition is not met, return to step 3 to continue the iterative operation.

[0115] To demonstrate the superior performance of the present invention, experiments were conducted on five real infrared images. Six recent infrared small target detection methods were selected for comparison: the weighted local difference measure (WLDM), the directional saliency-based method (DSBM), the infrared patch image model (IPM), the spatio-temporal saliency approach (STSA), the multiscale patch-based contrast measure (MPCM), and the new top-hat transform (NTHT). Three evaluation metrics were used to evaluate the experimental results: background suppression factor (BSF), signal-to-clutter ratio gain (SCRG), and receiver operating characteristic curve (ROC). The horizontal axis of the ROC represents the false alarm rate, and the vertical axis represents the detection rate. The larger the BSF, the stronger the suppression effect on the background. The larger the SCRG, the stronger the enhancement effect on the target. The larger the area between the ROC and the coordinate axis, the better the detection effect on small targets. Figure 2-Figure 8 The experimental results show that compared with other methods, the proposed method has the largest BSF and the largest SCRG, and the area between the ROC and the coordinate axis of this method is always the largest, which shows that compared with the other six methods, this method can better suppress the background and enhance the target, and has better infrared small target detection performance.

[0116] In summary, the present invention proposes an infrared small target detection method based on the frame nuclear norm, which more effectively achieves the low-rank approximation of the tensor by transforming the image to the frame domain, and better characterizes the background details. At the same time, it uses the morphological regularization term to well handle the noise in the background, thereby improving the accuracy and robustness of infrared small target detection.

[0117] Correspondingly, the present invention also provides an infrared small target detection system based on the frame tensor nuclear norm, comprising:

[0118] The acquisition module is used to obtain the tensors composed of several consecutive frames of images and input them into the pre-built infrared small target detection model based on the nuclear norm of the frame tensor;

[0119] The partitioning module is used to divide the infrared small target detection model based on the frame tensor nuclear norm into sub-problems including background part, target part and noise part, and optimize and solve these sub-problems respectively to obtain the current optimal solution of each sub-problem;

[0120] The judgment module is used to judge whether the current optimal solution of the target part has converged or whether the maximum number of iterations has been reached.

[0121] If so, output the current optimal solution of the target part.

[0122] If not, the current optimal solution of each sub-problem is used to update the infrared small target detection model based on the framework tensor nuclear norm, and the optimization is re-performed to obtain the current optimal solution of each new sub-problem, and the convergence and number of iterations are judged again.

[0123] The acquisition module includes a model acquisition module,

[0124] It is used to obtain the infrared small target detection model based on the framework tensor nuclear norm. The model is expressed as:

[0125]

[0126] stG N +G B +G T =G D

[0127] In the above formula, is the noise regularization term, α||G B || F-TNN is the framework tensor nuclear norm term, βW(G T ) is the morphological regularization term, G B For the background part, G T is the target part, G N is the random Gaussian noise in the image, G D is a tensor, m is the number of input images, n1×n2 is the size of each image, R represents a set of real numbers, α is the coefficient of the rank minimization term, β is the penalty coefficient of the morphological regularization term, W is the frame transformation matrix, stG N +G B +G T =G D Indicates constraints.

[0128] The division module includes:

[0129] Transformation module, used to introduce auxiliary variables The background part after frame transformation is recorded as The objective function is obtained as:

[0130]

[0131] stG N +G B +G T =G D ,

[0132] The combination module is used to combine the objective function with the constraints, and the augmented Lagrangian form of the above equation is obtained as follows:

[0133]

[0134] Among them, G Z and S are Lagrange multipliers, ρ and a are penalty factors, Represents ||G B || F-TNN The expansion, Represents auxiliary variables The frontal slice of ||·|| * is the nuclear norm, w=(n-1)l+1, l represents the number of levels of the framework transformation, n represents the number of filters, and n3 represents the original tensor G B The third dimension of

[0135] The ADMM processing module is used to divide the objective function into the following sub-problems using the ADMM algorithm:

[0136]

[0137] The solution module is used to solve these sub-problems, and the results are:

[0138]

[0139] In the formula, the symbol with superscript n+1 represents the current result after the optimization solution, the symbol with superscript n represents the result after the previous optimization solution, SVT is the singular value threshold algorithm, 2α / ρ is the shrinkage threshold, γ is the update factor, and Fold3 means folding the matrix into a tensor according to mode 3.

[0140] The judgment module converges to the judgment module,

[0141] Used to pass expressions Determine whether the current optimal solution of the target part converges. If the calculated result is greater than or equal to 0.01, it is considered converged, otherwise it is not converged.

[0142] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0143] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the steps in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0144] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0145] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0146] As described above, the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that the technical solutions described in the above embodiments can still be modified, or some of the technical features thereof can be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for detecting small infrared targets based on the framework tensor nuclear norm, characterized in that: include: Obtain a tensor composed of several consecutive frames of images and input it into a pre-built infrared small target detection model based on the frame tensor nuclear norm; The infrared small target detection model based on the frame tensor nuclear norm is divided into sub-problems including background part, target part and noise part. These sub-problems are optimized and solved respectively to obtain the current optimal solution of each sub-problem. Determine whether the current optimal solution of the target part has converged or whether the maximum number of iterations has been reached. If so, output the current optimal solution of the target part. If not, the current optimal solution of each sub-problem is used to update the infrared small target detection model based on the framework tensor nuclear norm, and the optimization is re-performed to obtain the current optimal solution of each new sub-problem, and the convergence and number of iterations are judged again; The infrared small target detection model based on the frame tensor nuclear norm is: s.t.G N +G B +G T =G D In the above formula, is the noise regularization term, α||G B || F-TNN is the framework tensor nuclear norm term, βW(G T ) is the morphological regularization term, G B For the background part, G T is the target part, G N is the random Gaussian noise in the image, G D is a tensor, m is the number of input images, n1×n2 is the size of each image, R represents a set of real numbers, α is the coefficient of the rank minimization term, β is the penalty coefficient of the morphological regularization term, W is the frame transformation matrix, stG N +G B +G T =G D Indicates constraints.

2. The infrared small target detection method based on the frame tensor nuclear norm according to claim 1 is characterized in that: The infrared small target detection model based on the frame tensor nuclear norm is divided into sub-problems including background part, target part, and noise part, and these sub-problems are optimized and solved respectively to obtain the current optimal solution of each sub-problem. The process includes: Introducing auxiliary variables The background part after frame transformation is recorded as The objective function is obtained as: Combining the objective function with the constraints, the augmented Lagrangian form of the above equation is: Among them, G Z and is the Lagrange multiplier, ρ and a are penalty factors, Represents ||G B || F-TNN The expansion, Represents auxiliary variables The frontal slice of ||·|| * is the nuclear norm, w=(n-1)l+1, l represents the number of levels of the framework transformation, n represents the number of filters, and n3 represents the original tensor G B The third dimension of The ADMM algorithm is used to divide the objective function into the following sub-problems: Solving these subproblems yields the following results: In the formula, the symbol with superscript n+1 represents the current result after the optimization solution, the symbol with superscript n represents the result after the previous optimization solution, SVT is the singular value threshold algorithm, 2α / ρ is the shrinkage threshold, γ is the update factor, and Fold3 means folding the matrix into a tensor according to mode 3.

3. The infrared small target detection method based on the frame tensor nuclear norm according to claim 2 is characterized in that: The process of determining whether the current optimal solution of the target part has converged includes: Through the expression Determine whether the current optimal solution of the target part converges. If the calculated result is greater than or equal to 0.01, it is considered to be converged, otherwise it is not converged.

4. An infrared small target detection system based on the frame tensor nuclear norm, characterized in that: include: The acquisition module is used to obtain the tensors composed of several consecutive frames of images and input them into the pre-built infrared small target detection model based on the nuclear norm of the frame tensor; The partitioning module is used to divide the infrared small target detection model based on the frame tensor nuclear norm into sub-problems including background part, target part and noise part, and optimize and solve these sub-problems respectively to obtain the current optimal solution of each sub-problem; The judgment module is used to judge whether the current optimal solution of the target part has converged or whether the maximum number of iterations has been reached. If so, output the current optimal solution of the target part. If not, the current optimal solution of each sub-problem is used to update the infrared small target detection model based on the framework tensor nuclear norm, and the optimization is re-performed to obtain the current optimal solution of each new sub-problem, and the convergence and number of iterations are judged again; The acquisition module includes a model acquisition module, It is used to obtain the infrared small target detection model based on the framework tensor nuclear norm. The model is expressed as: s.t.G N +G B +G T =G D In the above formula, is the noise regularization term, α||G B || F-TNN is the framework tensor nuclear norm term, βW(G T ) is the morphological regularization term, G B For the background part, G T is the target part, G N is the random Gaussian noise in the image, G D is a tensor, m is the number of input images, n1×n2 is the size of each image, R represents a set of real numbers, α is the coefficient of the rank minimization term, β is the penalty coefficient of the morphological regularization term, W is the frame transformation matrix, stG N +G B +G T =G D Indicates constraints.

5. The infrared small target detection system based on the frame tensor nuclear norm according to claim 4 is characterized in that: The partitioning module includes: Transformation module, used to introduce auxiliary variables The background part after frame transformation is recorded as The objective function is obtained as: Combining the objective function with the constraints, the augmented Lagrangian form of the above equation is: Among them, G Z and is the Lagrange multiplier, ρ and a are penalty factors, Represents ||G B || F-TNN The expansion, Represents auxiliary variables The frontal slice of ||·|| * is the nuclear norm, w=(n-1)l+1, l represents the number of levels of the framework transformation, n represents the number of filters, and n3 represents the original tensor G B The third dimension of The ADMM algorithm is used to divide the objective function into the following sub-problems: Solving these subproblems yields the following results: In the formula, the symbol with superscript n+1 represents the current result after the optimization solution, the symbol with superscript n represents the result after the previous optimization solution, SVT is the singular value threshold algorithm, 2α / ρ is the shrinkage threshold, γ is the update factor, and Fold3 means folding the matrix into a tensor according to mode 3.

6. The infrared small target detection system based on the frame tensor nuclear norm according to claim 5, characterized in that: The judgment module converges to the judgment module, Used to pass expressions Determine whether the current optimal solution of the target part converges. If the calculated result is greater than or equal to 0.01, it is considered converged, otherwise it is not converged.

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