Infrared small target detection method based on compound eye structure feature weight operator

Abstract

The invention relates to an infrared small target detection method based on a compound eye structure feature weight operator. According to the method, firstly, on the basis that the same target has different pixel coordinates and response characteristics in different apertures of an infrared compound eye camera, a compound eye structure weight operator is designed for enhancing a sparse target; then, constructing an effective imaging area structure tensor of the infrared compound eye image, and avoiding complex singular value decomposition by using a representative coefficient regularization method; according to the invention, the speed and precision of infrared small target detection in the infrared compound eye image sequence can be effectively improved, and background interference can be effectively suppressed.

Description

Technical Field

[0001] The present invention relates to an infrared small target detection method based on a compound eye structure feature weight operator, and in particular to an infrared compound eye image small target detection method based on low-rank sparse decomposition. Background Art

[0002] With the diversification of imaging system application scenarios and target detection requirements, the currently widely used traditional single-aperture infrared imaging system relies on a single main lens for imaging. Since its perception mechanism is based on a single perspective to obtain two-dimensional image information of the target, it lacks multi-directional perception of the target and understanding of the target's behavior. In areas such as rapid detection of moving targets in complex backgrounds and large fields of view, there are still many technical bottlenecks. Infrared compound eye cameras have the ability to simultaneously image the same target with multiple apertures. The same target has different pixel coordinates and response characteristics in different apertures of the infrared compound eye camera. The structural characteristics of the compound eye can be used to achieve rapid detection of small targets. Existing infrared small target detection methods are mostly based on single-aperture image feature design. They do not utilize the multi-aperture spatial relationship of the compound eye camera and do not fully utilize the application advantages of the infrared compound eye camera in infrared small target detection. Therefore, there is an urgent need to conduct research on algorithms for rapid detection of small targets in infrared compound eye images.

[0003] A literature review shows that low-rank sparse decomposition methods for small target detection in single-aperture infrared images have achieved promising results, but no low-rank sparse decomposition methods suitable for small target detection in infrared compound eye images have been found. In their review paper, "Research Progress on Infrared Small Target Detection Algorithms Based on Low-Rank Sparse Decomposition," Luo Haijun et al. compared the performance of different algorithms in different scenarios, but did not specifically review small target detection in infrared compound eye images. In their paper "Infrared Patch-Image Model for Small Target Detection in a Single Image," Gao et al. systematically introduced low-rank sparsity theory into infrared small target detection and proposed the IPI method, which has inspired numerous subsequent improved algorithms. In their paper "A Method for Detecting Small Infrared Targets on Sea Surfaces" (China Invention Application Publication No.: CN105931264A), Fang Houzhang et al. decomposed the original single-aperture infrared image matrix into overlapping sub-blocks from left to right and top to bottom, then expanded the sub-blocks into column vectors. The column vectors were then combined to form a new image matrix, which was then decomposed into a sparse small target component, a low-rank background image component, and a noise component. In "Infrared Small Target Detection Algorithm Based on Low-Rank and Reweighted Sparse Representation" by Yang Yadong et al. and "Infrared Small Target Detection Based on Low-Rank Weighted Sparse Decomposition" by Zhang Guiyu et al., both start from the image structure of single-aperture infrared images and design local prior weights. The former designs a fusion weight of local prior weights and self-enhanced sparse weights to constrain the sparse matrix, while the latter calculates the weight of geometric structure information and extracts background prior information. In "A Method and Apparatus for Infrared Small Target Detection Based on Posterior Information" (China Invention Application Publication No.: CN118172564A), Chen Shuhan et al. use the temporary target tensor obtained in the current iteration to extract morphological posterior information as the saliency weight information for the next iteration of the model based on low-rank sparse tensor decomposition to construct an infrared small target detection model based on the tensor nuclear norm of Framelet and Log and posterior information. In their paper "A Method and Apparatus for Infrared Small Target Detection Based on Four-Dimensional Spatiotemporal Tensor" (China Invention Application Publication No. CN117475161A), Chen Shuhan et al. transformed the infrared small target detection task into a low-rank sparse decomposition problem based on a four-dimensional spatiotemporal tensor. They established an optimization framework based on the theory of low-rank sparse tensor decomposition and utilized a reweighting strategy to accelerate convergence. In their paper "A Method for Small Target Detection Based on Infrared Video Images" (China Invention Patent Authorization Announcement No. CN111160181B), Liang Junli et al. constructed an infrared video image target detection model based on a sparse target representation term and a noise-resistant interference term.

[0004] The above research shows that existing infrared small target detection methods use the characteristics of single-aperture infrared sequence images to detect small targets by constructing different forms of tensors or calculating background target weights using prior and posteriori information. For small target detection tasks based on infrared compound eye image sequences, these methods do not effectively utilize the structural characteristics of the compound eye, making it difficult to achieve ideal detection results in terms of quickly detecting small targets in infrared compound eye images and effectively suppressing background clutter. Therefore, it is urgent to develop an infrared small target detection method that is suitable for compound eye image sequences and can fully utilize the structural characteristics of the compound eye. Summary of the Invention

[0005] The purpose of the present invention is to provide an infrared small target detection method based on a compound eye structure feature weight operator, which mainly solves the problem that the existing low-rank sparse decomposition infrared small target detection method based on single aperture image features does not effectively utilize the multi-aperture spatial relationship of the compound eye camera. This method can effectively improve the speed and accuracy of infrared small target detection in infrared compound eye image sequences, effectively suppress background interference, and give full play to the advantages of the compound eye structure in infrared small target detection applications.

[0006] The idea of the method of the present invention is: first, based on the fact that the same target has different pixel coordinates and response characteristics in different apertures of the infrared compound eye camera, a compound eye structure weight operator is designed to enhance sparse targets; then, the structure tensor of the effective imaging area of the infrared compound eye image is constructed and the representative coefficient regularization method is used to avoid complex singular value decomposition.

[0007] The technical solutions of the present invention are as follows:

[0008] A method for detecting small infrared targets based on a compound eye structure feature weight operator, characterized in that it comprises the following steps:

[0009] Step 1) obtaining a sequence of clear infrared compound eye images, wherein a single frame of the compound eye image contains multiple ommatidium imaging areas, and the number of ommatidium imaging areas is consistent with the number of apertures of the compound eye camera;

[0010] Step 2) extracting the imaging area of each ommatidium, calculating the normalized gradient standard deviation for each ommatidium image, and using the ommatidium with the smallest normalized gradient standard deviation as a reference, calculating the compound eye structure weight operator based on the pixel overlap range between it and the imaging area of each ommatidium;

[0011] Step 3) Reconstruct the single-frame image of the entire ommatidium imaging area into an M×N matrix. The F-frame continuous image sequence tensor is expanded along the time dimension. Anisotropic total variation regularization is applied to the representative coefficient matrix. Combined with the reweighted l1 minimization scheme of the compound eye structure weight operator, the weights are adaptively assigned to the targets.

[0012] Step 4) using the augmented Lagrange multiplier method to solve the convex optimization problem of minimizing the combination of the nuclear norm and the l1 norm, and using the alternating direction multiplier method for iterative solution to separate the low-rank background tensor and the sparse target tensor;

[0013] Step 5) restore the expanded sparse target tensor to the size of the input image sequence;

[0014] Step 6) Extract small targets using the adaptive threshold method to obtain target pixel coordinates.

[0015] Calculating the compound eye structure weight operator in step 2) includes the following steps:

[0016] Step 2.1) Extract each ommatidium image area, and record the i-th ommatidium image as

[0017] Step 2.2) Use the Laplace operator to calculate the four-directional gradient

[0018]

[0019] Where (x, y) is the pixel coordinate of the ommatidium image, d1 and d2 are the step sizes of gradient calculation in the x and y directions respectively;

[0020] Step 2.3) Normalize the gradient value to obtain

[0021] Step 2.4) Calculate the normalized gradient value Standard deviation

[0022] Step 2.5) Normalize the gradient standard deviation The smallest ommatidium is used as the reference benchmark. The compound eye structure weight operator is calculated based on the pixel overlap range between it and the imaging area of each ommatidium. The pixel displacement range d between the reference ommatidium and the remaining ommatidia is calculated. i , use the benchmark to calculate the weight operator w of all ommatidia within the range of l p :

[0023]

[0024] Among them, l represents the error tolerance range of the estimation result, Indicates the multiplication operation of the corresponding area according to the displacement result, is an operator, which represents that the ommatidium images together constitute the whole compound eye image according to the compound eye structure.

[0025] In step 3), the single-frame images of all ommatidium imaging areas are reconstructed into a matrix of size M×N, and the F-frame continuous image sequence tensor is expanded into D along the time dimension, that is, for a matrix of rank r Its decomposition formula is D=UV T , the orthogonal matrix is Its representative coefficient matrix can be obtained by U=DV. Anisotropic total variation regularization is applied to the representative coefficient matrix U. Combined with the reweighted l1 minimization scheme of the compound eye structure weight operator, weights are adaptively assigned to the target matrix T to construct the target detection model:

[0026]

[0027] stD=UV T +T,V T V=I

[0028] in, is a two-dimensional difference operator, ⊙ is the Hadamard product, w = w rep ⊙w t , w rep is the eye weight operator w p The value of λ and α is the reciprocal of 1,2 represents a positive trade-off parameter, ε is a minimum value. In order to avoid the denominator being 0 in the calculation, ‖.‖1 represents the l1 norm.

[0029] Separating the low-rank background tensor and the sparse target tensor in step 4) comprises the following steps:

[0030] Step 4.1) Use the augmented Lagrange multiplier method to solve the convex optimization problem of minimizing the combination of the nuclear norm and the l1 norm, introducing auxiliary variables G1 and G2:

[0031]

[0032] Where β1, β2, β3 are Lagrange multipliers, μ is the penalty parameter, ‖.‖ F represents the Frobenius norm;

[0033] Step 4.2) Use the alternating direction multiplier method to iteratively solve the problem. The specific steps are as follows:

[0034] Step 4.2.1) Fix the formula (5) and remove G i For other variables except G1 and G2, we can iteratively solve them as follows:

[0035]

[0036] Use the soft threshold function Soft to solve:

[0037]

[0038] Step 4.2.2) Fix all variables except V in formula (9) and iteratively solve for V using the following formula:

[0039]

[0040] V = AC T

[0041] Step 4.2.3) Fix all variables except U in formula (9) and iteratively solve for U using the following formula:

[0042]

[0043] Taking the derivative of the above formula, we can get:

[0044]

[0045] Where: express The transpose operator of As a differential filter Convolution, where O i is a correlation difference filter. By Fourier transforming both sides of the equation and applying the convolution theorem, the closed-form solution of U can be easily derived as:

[0046] in and |.| 2 represent Fourier transform and element-by-element square operation respectively, and ten(1) represents a tensor whose elements are all 1;

[0047] Step 4.2.4) Fix all variables except T in formula (9) and iteratively solve for T using the following formula:

[0048]

[0049] Step 4.2.5) Use the following formula to iteratively solve for w:

[0050] w=w rep ⊙w t (15)

[0051]

[0052] Step 4.2.6) Use the following formula to iteratively solve the Lagrange multipliers β1, β2, β3 and the penalty parameter μ:

[0053]

[0054] β3=β3+μ(D-UV T -T) (18)

[0055] μ=min(ρμ,μ max ) (19)

[0056] The iteration termination condition is:

[0057]

[0058] ||T k+1 ||1=||T k ||1 (21).

[0059] In step (6), the threshold th is calculated using the mean mμ, standard deviation σ and hyperparameter k, and the small target is extracted by the adaptive threshold method to obtain the target pixel coordinates:

[0060] th=mμ+kσ (22).

[0061] Based on the above technical solution, the beneficial effects of the present invention are: this method utilizes the multi-angle imaging characteristics of the compound eye camera to detect small targets in the infrared compound eye image with higher precision, quickly completes the detection task with higher computational efficiency, improves the speed and accuracy of infrared small target detection in the infrared compound eye image sequence, effectively suppresses background interference, and gives full play to the advantages of the compound eye structure in the application of infrared small target detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 This is a flow chart of the small target detection method based on low-rank sparse decomposition of the compound eye structure of the present invention.

[0063] Figure 2 The left side of the figure shows three frames of infrared compound eye images, and red, yellow and blue circular frames are used to mark the ommatidium image areas in a single frame of compound eye images. The right side of the figure shows the image sequence of the compound eye at a time scale of N. t The ommatidium images retained in the image sequence, the scale of a single ommatidium image is N w ×N h , a total of N n ommatidium images.

[0064] Figure 3 The following are the detection results of the present invention and the comparison with the small target detection results of the IPI method. In the figure, (a) and (d) are compound eye images containing infrared small targets in two different scenes, (b) and (e) are the detection results of the classic infrared small target detection method (IPI) based on low-rank sparse decomposition, and (c) and (f) are the detection results of the present invention. The red rectangle in the figure is the target, and the green oval box is the background interference. The figure shows that the detection results of IPI have obvious false alarms and missed detections. DETAILED DESCRIPTION

[0065] The present invention discloses a method for detecting small infrared targets based on a compound eye structure feature weight operator. The method comprises the following steps:

[0066] Step 1) obtaining a sequence of clear infrared compound eye images, wherein a single frame of the compound eye image contains multiple ommatidium imaging areas, and the number of ommatidium imaging areas is consistent with the number of apertures of the compound eye camera;

[0067] Step 2) extracting the imaging area of each ommatidium, calculating the normalized gradient standard deviation for each ommatidium image, and using the ommatidium with the smallest normalized gradient standard deviation as a reference, calculating the compound eye structure weight operator based on the pixel overlap range between it and the imaging area of each ommatidium;

[0068] Step 3) Reconstruct the single-frame image of the entire ommatidium imaging area into an M×N matrix. The F-frame continuous image sequence tensor is expanded along the time dimension. Anisotropic total variation regularization is applied to the representative coefficient matrix. Combined with the reweighted l1 minimization scheme of the compound eye structure weight operator, the weights are adaptively assigned to the targets.

[0069] Step 4) using the augmented Lagrange multiplier method to solve the convex optimization problem of minimizing the combination of the nuclear norm and the l1 norm, and using the alternating direction multiplier method for iterative solution to separate the low-rank background tensor and the sparse target tensor;

[0070] Step 5) restore the expanded sparse target tensor to the size of the input image sequence;

[0071] Step 6) Extract small targets using the adaptive threshold method to obtain target pixel coordinates.

[0072] Calculating the compound eye structure weight operator in step 2) includes the following steps:

[0073] Step 2.1) Extract each ommatidium image area, and record the i-th ommatidium image as

[0074] Step 2.2) Use the Laplace operator to calculate the four-directional gradient

[0075]

[0076] Where (x, y) is the pixel coordinate of the ommatidium image, d1 and d2 are the step sizes of gradient calculation in the x and y directions respectively;

[0077] Step 2.3) Normalize the gradient value to obtain

[0078] Step 2.4) Calculate the normalized gradient value Standard deviation

[0079] Step 2.5) Normalize the gradient standard deviation The smallest ommatidium is used as the reference benchmark. The compound eye structure weight operator is calculated based on the pixel overlap range between it and the imaging area of each ommatidium. The pixel displacement range d between the reference ommatidium and the remaining ommatidia is calculated. i , use the benchmark to calculate the weight operator w of all ommatidia within the range of l p :

[0080]

[0081] Among them, l represents the error tolerance range of the estimation result, Indicates the multiplication operation of the corresponding area according to the displacement result, is an operator, which represents that the ommatidium images together constitute the whole compound eye image according to the compound eye structure.

[0082] In step 3), the single-frame images of all ommatidium imaging areas are reconstructed into a matrix of size M×N, and the F-frame continuous image sequence tensor is expanded into D along the time dimension, that is, for a matrix of rank r Its decomposition formula is D=UV T , the orthogonal matrix is Its representative coefficient matrix can be obtained by U=DV. Anisotropic total variation regularization is applied to the representative coefficient matrix U. Combined with the reweighted l1 minimization scheme of the compound eye structure weight operator, weights are adaptively assigned to the target matrix T to construct the target detection model:

[0083]

[0084] stD=UV T +T,V T V=I

[0085] in, is a two-dimensional difference operator, ⊙ is the Hadamard product, w = w rep ⊙w t , w rep is the eye weight operator w p The value of λ and α is the reciprocal of 1,2 represents a positive trade-off parameter, ε is a minimum value. In order to avoid the denominator being 0 in the calculation, ‖.‖1 represents the l1 norm.

[0086] Separating the low-rank background tensor and the sparse target tensor in step 4) comprises the following steps:

[0087] Step 4.1) Use the augmented Lagrange multiplier method to solve the convex optimization problem of minimizing the combination of the nuclear norm and the l1 norm, introducing auxiliary variables G1 and G2:

[0088]

[0089] Where β1, β2, β3 are Lagrange multipliers, μ is the penalty parameter, ‖.‖ F represents the Frobenius norm;

[0090] Step 4.2) Use the alternating direction multiplier method to iteratively solve the problem. The specific steps are as follows:

[0091] Step 4.2.1) Fix the formula (5) and remove G i For other variables except G1 and G2, we can iteratively solve them as follows:

[0092]

[0093] Use the soft threshold function Soft to solve:

[0094]

[0095] Step 4.2.2) Fix all variables except V in formula (9) and iteratively solve for V using the following formula:

[0096]

[0097] V = AC T

[0098] Step 4.2.3) Fix all variables except U in formula (9) and iteratively solve for U using the following formula:

[0099]

[0100] Taking the derivative of the above formula, we can get:

[0101]

[0102] Where: express The transpose operator of As a differential filter Convolution, where O i is a correlation difference filter. By Fourier transforming both sides of the equation and applying the convolution theorem, the closed-form solution of U can be easily derived as:

[0103] in and |.| 2 represent Fourier transform and element-by-element square operation respectively, and ten(1) represents a tensor whose elements are all 1;

[0104] Step 4.2.4) Fix all variables except T in formula (9) and iteratively solve for T using the following formula:

[0105]

[0106] Step 4.2.5) Use the following formula to iteratively solve for w:

[0107] w=w rep ⊙w t (15)

[0108]

[0109] Step 4.2.6) Use the following formula to iteratively solve the Lagrange multipliers β1, β2, β3 and the penalty parameter μ:

[0110]

[0111] β3=β3+μ(D-UV T -T) (18)

[0112] μ=min(ρμ,μ max ) (19)

[0113] The iteration termination condition is:

[0114]

[0115] ‖T k+1 ‖1=||T k ||1 (21).

[0116] In step (6), the threshold th is calculated using the mean mμ, standard deviation σ and hyperparameter k, and the small target is extracted by the adaptive threshold method to obtain the target pixel coordinates:

[0117] th=mμ+kσ (22).

[0118] The method of the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0119] Figure 1 The flowchart of the small target detection method based on low-rank sparse decomposition of compound eye structure of the present invention is shown. Referring to the flowchart, the specific embodiment of the present invention can be divided into the following six steps:

[0120] Step 1) Obtain a clear infrared compound eye image sequence, such as Figure 2 In a single-frame compound eye image, there are 19 ommatidium imaging areas, and the number of ommatidium imaging areas is consistent with the number of compound eye camera apertures.

[0121] Step 2) Extract the imaging area of each ommatidium, calculate the normalized gradient standard deviation for each ommatidium image, and use the ommatidium with the smallest normalized gradient standard deviation as the reference benchmark. Calculate the compound eye structure weight operator based on the pixel overlap range between it and the imaging area of each ommatidium. The specific steps are as follows:

[0122] Step 2.1) Extract each ommatidium image area, and record the i-th ommatidium image as

[0123] Step 2.2) Use the Laplace operator to calculate the four-directional gradient

[0124]

[0125] Where (x, y) is the pixel coordinate of the ommatidium image, d1 and d2 are the step sizes of gradient calculation in the x and y directions respectively;

[0126] Step 2.3) Normalize the gradient value to obtain

[0127] Step 2.4) Calculate the normalized gradient value Standard deviation

[0128] Step 2.5) Normalize the gradient standard deviation The smallest ommatidium is used as the reference benchmark. The compound eye structure weight operator is calculated based on the pixel overlap range between it and the imaging area of each ommatidium. The pixel displacement range d between the reference ommatidium and the remaining ommatidia is calculated. i , use the benchmark to calculate the weight operator w of all ommatidia in the range of l = 3 p :

[0129]

[0130] Among them, l represents the error tolerance range of the estimation result, Indicates the multiplication operation of the corresponding area according to the displacement result, is an operator, which represents that the ommatidium images together constitute the whole compound eye image according to the compound eye structure.

[0131] Step 3) Reconstruct the single-frame image of all ommatidium imaging areas into a matrix of size M×N, and expand the F-frame continuous image sequence tensor along the time dimension to D, that is, for a matrix of rank r Its decomposition formula is D=UV T , the orthogonal matrix is Its representative coefficient matrix can be obtained by U=DV. Anisotropic total variation regularization is applied to the representative coefficient matrix U. Combined with the reweighted l1 minimization scheme of the compound eye structure weight operator, weights are adaptively assigned to the target matrix T to construct the target detection model:

[0132]

[0133] stD=UV T +T,V T V=I

[0134] in, is a two-dimensional difference operator, ⊙ is the Hadamard product, w = w rep ⊙w t , w rep is the eye weight operator w p The value of λ and α is the reciprocal of 1,2 represents a positive trade-off parameter, ε is a minimum value. In order to avoid the denominator being 0 in the calculation, ‖.‖1 represents the l1 norm. During the detection process, F=10 and r=6 are set.

[0135] Step 4) The augmented Lagrange multiplier method is used to solve the convex optimization problem of minimizing the combination of the nuclear norm and the l1 norm. The alternating direction multiplier method is used for iterative solution to separate the low-rank background tensor and the sparse target tensor. The specific steps are as follows:

[0136] Step 4.1) Use the augmented Lagrange multiplier method to solve the convex optimization problem of minimizing the combination of the nuclear norm and the l1 norm, introducing auxiliary variables G1 and G2:

[0137]

[0138] Where: β1, β2, β3 are Lagrange multipliers, μ is the penalty parameter, ‖.‖ F represents the Frobenius norm, initially set to β i =1,μ=0.01,α=0.1;

[0139] Step 4.2) Use the alternating direction multiplier method to iteratively solve the problem. The specific steps are as follows:

[0140] Step 4.2.1) Fix the formula (5) and remove G i For other variables except G1 and G2, we can iteratively solve them as follows:

[0141]

[0142] Use the soft threshold function Soft to solve:

[0143]

[0144] Step 4.2.2) Fix all variables except V in formula (9) and iteratively solve for V using the following formula:

[0145]

[0146] V = AC T

[0147] Step 4.2.3) Fix all variables except U in formula (9) and iteratively solve for U using the following formula:

[0148]

[0149] Taking the derivative of the above formula, we can get:

[0150]

[0151] Where, express The transpose operator of As a differential filter Convolution, where O i is a correlation difference filter. By Fourier transforming both sides of the equation and applying the convolution theorem, the closed-form solution of U can be easily derived as:

[0152] in and |.| 2 represent Fourier transform and element-by-element square operation respectively, and

[0153] ten(1) represents a tensor whose elements are all 1;

[0154] Step 4.2.4) Fix all variables except T in formula (9) and iteratively solve for T using the following formula:

[0155]

[0156] Step 4.2.5) Use the following formula to iteratively solve for w:

[0157] w=w rep ⊙w t (15)

[0158]

[0159] Step 4.2.6) Use the following formula to iteratively solve the Lagrange multipliers β1, β2, β3 and the penalty parameter μ:

[0160]

[0161] β3=β3+μ(D-UV T -T) (18)

[0162] μ=min(ρμ,μ max ) (19)

[0163] The iteration termination condition is:

[0164]

[0165] ||T k+1 ||1=||T k ||1 (21) The iteration terminates if any of the conditions are met.

[0166] Step 5) restore the expanded sparse target tensor to the size of the input image sequence.

[0167] Step 6) Use the mean mμ, standard deviation σ and hyperparameter k to calculate the threshold th, extract small targets through the adaptive threshold method, and obtain the target pixel coordinates:

[0168] th=mμ+kσ (22)

[0169] Figure 3 It is a comparison of the detection result effect diagram of the embodiment of the method of the present invention and the small target detection result of the IPI method. In the figure, (a) and (d) are compound eye images containing infrared small targets in two different scenes, (b) and (e) are detection result diagrams of the classic infrared small target detection method (IPI) based on low-rank sparse decomposition, and (c) and (f) are detection result diagrams of the present invention. The red rectangular box in the figure is the target, and the green oval box is background interference. The figure shows that the detection result of IPI has obvious false alarms and missed detections. It can be seen that the method of the present invention can improve the speed and accuracy of infrared small target detection in infrared compound eye image sequences, effectively suppress background interference, and give full play to the advantages of the compound eye structure in infrared small target detection applications.

Claims

1. A method for detecting small infrared targets based on a compound eye structure feature weight operator, characterized by: It contains the following steps: Step 1) obtaining a sequence of clear infrared compound eye images, wherein a single frame of the compound eye image contains multiple ommatidium imaging areas, and the number of ommatidium imaging areas is consistent with the number of apertures of the compound eye camera; Step 2) extracting the imaging area of each ommatidium, calculating the normalized gradient standard deviation for each ommatidium image, and using the ommatidium with the smallest normalized gradient standard deviation as a reference, calculating the compound eye structure weight operator based on the pixel overlap range between it and the imaging area of each ommatidium; Step 3) Reconstruct the single-frame image of the entire ommatidium imaging area into an M×N matrix. The F-frame continuous image sequence tensor is expanded along the time dimension. Anisotropic total variation regularization is applied to the representative coefficient matrix. Combined with the reweighted l1 minimization scheme of the compound eye structure weight operator, the weights are adaptively assigned to the targets. Step 4) using the augmented Lagrange multiplier method to solve the convex optimization problem of minimizing the combination of the nuclear norm and the l1 norm, and using the alternating direction multiplier method for iterative solution to separate the low-rank background tensor and the sparse target tensor; Step 5) restore the expanded sparse target tensor to the size of the input image sequence; Step 6) Extract small targets using the adaptive threshold method to obtain target pixel coordinates.

2. The infrared small target detection method based on compound eye structure feature weight operator according to claim 1 is characterized by: Calculating the compound eye structure weight operator in step 2) includes the following steps: Step 2.1) Extract each ommatidium image area, and record the i-th ommatidium image as Step 2.2) Use the Laplace operator to calculate the four-directional gradient Where (x, y) is the pixel coordinate of the ommatidium image, d1 and d2 are the step sizes of gradient calculation in the x and y directions respectively; Step 2.3) Normalize the gradient value to obtain Step 2.4) Calculate the normalized gradient value Standard deviation Step 2.5) Normalize the gradient standard deviation The smallest ommatidium is used as the reference benchmark. The compound eye structure weight operator is calculated based on the pixel overlap range between it and the imaging area of each ommatidium. The pixel displacement range d between the reference ommatidium and the remaining ommatidia is calculated. i , use the benchmark to calculate the weight operator w of all ommatidia within the range of l p : Among them, l represents the error tolerance range of the estimation result, Indicates the multiplication operation of the corresponding area according to the displacement result, is an operator, which represents that the ommatidium images together constitute the whole compound eye image according to the compound eye structure.

3. The infrared small target detection method based on compound eye structure feature statistical weight operator according to claim 1 is characterized by: In the step 3), the single-frame images of all ommatidium imaging areas are reconstructed into a matrix of size M×N, and the F-frame continuous image sequence tensor is expanded into D along the time dimension, that is, for a matrix of rank r Its decomposition formula is D=UV T , the orthogonal matrix is Its representative coefficient matrix can be obtained by U=DV. Anisotropic total variation regularization is applied to the representative coefficient matrix U. Combined with the reweighted l1 minimization scheme of the compound eye structure weight operator, weights are adaptively assigned to the target matrix T to construct the target detection model: in, is a two-dimensional difference operator, ⊙ is the Hadamard product, w = w rep ⊙w t , w rep is the eye weight operator w p The value of λ and α is the reciprocal of 1,2 represents a positive trade-off parameter, ε is a minimum value. In order to avoid the denominator being 0 in the calculation, ‖.‖1 represents the l1 norm.

4. The infrared small target detection method based on compound eye structure feature statistical weight operator according to claim 1 is characterized by: Separating the low-rank background tensor and the sparse target tensor in step 4) comprises the following steps: Step 4.1) Use the augmented Lagrange multiplier method to solve the convex optimization problem of minimizing the combination of the nuclear norm and the l1 norm, introducing auxiliary variables G1 and G2: Where β1, β2, β3 are Lagrange multipliers, μ is the penalty parameter, ‖.‖ F represents the Frobenius norm; Step 4.2) Use the alternating direction multiplier method to iteratively solve the problem. The specific steps are as follows: Step 4.2.1) Fix the formula (5) and remove G i For other variables except G1 and G2, we can iteratively solve them as follows: Use the soft threshold function Soft to solve: Step 4.2.2) Fix all variables except V in formula (9) and iteratively solve for V using the following formula: Step 4.2.3) Fix all variables except U in formula (9) and iteratively solve for U using the following formula: Taking the derivative of the above formula, we can get: Where: express The transpose operator of As a differential filter Convolution, where O i is a correlation difference filter. By Fourier transforming both sides of the equation and applying the convolution theorem, the closed-form solution of U can be easily derived as: in and |.| 2 represent Fourier transform and element-by-element square operation respectively, and ten(1) represents a tensor whose elements are all 1; Step 4.2.4) Fix all variables except T in formula (9) and iteratively solve for T using the following formula: Step 4.2.5) Use the following formula to iteratively solve for w: w=w rep ⊙in t (15) Step 4.2.6) Use the following formula to iteratively solve the Lagrange multipliers β1, β2, β3 and the penalty parameter μ: β3=β3+μ(D-UV T -T) (18)μ=min(ρμ,μ max ) (19) The iteration termination condition is: ||T k+1 ||1=||T k ||1 (21)。 5. The infrared small target detection method based on compound eye structure feature statistical weight operator according to claim 1 is characterized by: In step (6), the threshold th is calculated using the mean mμ, standard deviation σ and hyperparameter k, and the small target is extracted by the adaptive threshold method to obtain the target pixel coordinates: th=mμ+kσ (22).

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