Infrared small target detection method based on low-rank regularization background estimation by tensor reconstruction

Abstract

This invention discloses a low-rank regularized background estimation infrared small target detection method based on tensor reconstruction. The method mainly includes: inputting an infrared image sequence and stacking the infrared images sequentially to form an observation tensor; inputting the observation tensor into a tensor reconstruction model based on multi-dimensional expansion of the transform domain, and estimating a low-density matrix by constructing a randomized subspace to reduce computational complexity, thereby quickly and accurately calculating the rank of the observation tensor; inputting the tensor rank into a low-rank regularized tensor completion model, and updating and iterating the parameters of the low-rank regularized tensor completion model through alternating multiplier and alternating projection methods, finally calculating the target tensor, background tensor, and noise tensor to obtain the infrared small target detection result. This invention solves the problems in related technologies, such as the inability to accurately detect targets when they are occluded in single-frame detection, and the low detection efficiency in processing tensor models.

Description

Technical Field

[0001] This invention relates to a low-rank regularized background estimation infrared small target detection method based on tensor reconstruction, which belongs to the field of target detection. Background Technology

[0002] Object detection is one of the core problems in the field of computer vision. Its task is to find all targets of interest in an image and determine their category and location. Infrared small target detection, as a branch of this field, has long been widely used in military, medical, and industrial fields. However, in practical applications, infrared imaging equipment is affected by factors such as imaging distance, target movement speed, and atmospheric scattering and refraction, resulting in low signal-to-noise ratio, insufficient detail information, and low contrast between small targets and the image background, making the detection of small targets in infrared images extremely difficult.

[0003] In recent years, various infrared small target detection methods have emerged. Existing infrared small target detection methods can be divided into two main categories. One category is matrix factorization-based infrared small target detection methods: papers such as "Infrared Patch-ImageModel for Small Target Detection in a Single Image" simply use a single frame of infrared image to detect small targets. Its limitation lies in the poor real-time performance caused by singular value decomposition during iteration. Papers such as "EfficientNearest Neighbor Search for Cross-Encoder Models using Matrix Factorization" accelerate the iterative algorithm and improve real-time performance through efficient matrix factorization. However, the biggest drawback of this type of algorithm is that it cannot accurately detect small targets when they are occluded. The other category is infrared small target detection methods based on spatiotemporal tensor models: papers such as "Infrared small target detection via spatial–temporaltotal variation regularization and weighted tensor nuclear norm" stack several consecutive infrared images together, merge the spatiotemporal information of the infrared image sequence, extract the target trajectory based on the continuity and regularity of the target, and identify the target location. To improve target detection accuracy, papers such as "Small target detection in infrared videos based on spatio-temporal tensor model" add local background information to the stacked block tensor model. However, the stacking blocks lead to redundant information in these models, resulting in dimensionality explosion when approximating tensor rank, ultimately significantly reducing computational efficiency. Therefore, the impact of these problems needs to be fully considered when conducting research on infrared small target detection. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a low-rank regularized background estimation infrared small target detection method based on tensor reconstruction. This method employs a tensor reconstruction model based on multi-dimensional expansion in the transform domain, expanding the tensor in multiple dimensions and estimating a low-density matrix by constructing a randomized subspace to reduce computational complexity, thereby quickly and accurately calculating the rank of the observed tensor. Furthermore, a low-rank regularized tensor completion model is used to effectively recover the background tensor by applying regularization constraints. This method can meet the requirements for small target detection in infrared image sequences and, to a certain extent, improve detection efficiency.

[0005] To achieve the above objectives, the present invention is implemented using the following technical solution:

[0006] This invention provides a low-rank regularized background estimation infrared small target detection method based on tensor reconstruction, the method comprising the following steps:

[0007] Step S1: Input the infrared image sequence and stack the infrared images together in order to form the observation tensor D;

[0008] Step S2: Input the observation tensor D obtained in step S1 into the tensor reconstruction model based on multi-dimensional expansion of the transform domain, and calculate the tensor rank r of the infrared image sequence;

[0009] Step S3: Input the tensor rank r into the tensor completion model based on low-rank regularization, and update the parameters of the tensor completion based on low-rank regularization through the alternating multiplier method and alternating projection method. Finally, calculate the target tensor, background tensor and noise tensor to obtain the infrared small target detection result.

[0010] Furthermore, in step S1, stacking the infrared images together to form the observation tensor D specifically includes:

[0011] Step S11: Input an infrared image sequence with a sequence length of I3. When the sequence length is 1, it degenerates into an infrared image. Arrange the infrared images in chronological order and stack them sequentially to obtain the observation tensor D. I1, I2, and I3 represent the number of rows, columns, and length of the infrared image sequence, respectively.

[0012] Further, in step S2, the observation tensor D obtained in step S1 is input into the tensor reconstruction model based on multi-dimensional expansion of the transform domain to calculate the tensor rank r of the infrared image sequence, specifically:

[0013] Step S21: Expand the observation tensor D along the i-th dimension to obtain D [i] , And i,j=1,2,3;

[0014] Step S22: Solve for D [i] rank r i That is, the tensor rank r = [r1, r2, r3].

[0015] Furthermore, in step S22, D is solved. [i] The specific steps for determining the rank are as follows:

[0016] Step S221: Place D [i] Mapping to a randomized subspace Λ, and orthogonalizing the subspace Λ to obtain matrices Q and M; this process is as follows:

[0017]

[0018] Q = qr(Λ, 0)

[0019] M = Q T DD T Q

[0020] Where Ω is a Gaussian random matrix, Ω ~ N(0,1); ε is the error parameter, and 0 < ε < 1; Θ(·) denotes asymptotic, q is a positive integer; qr(·) is the QR decomposition;

[0021] Step S222: Take the first l eigenvectors (l≥2) of matrix M from step S221, and obtain the low-density matrix Z through matrix multiplication; the specific process is as follows:

[0022]

[0023]

[0024] Where svd(·) is the singular value decomposition, It is the left-hand unitary matrix of the matrix.

[0025] Step S223: Construct the covariance matrix based on the low-density matrix Z; obtain the transformation unitary matrix U. z1 and singular value matrix ∑ z1 The process is as follows:

[0026] R z =Z T Z

[0027]

[0028]

[0029] Among them, R ll Let matrix R z The value in the l-th row and l-th column; R is a matrix R z The l-th column vector is specifically R = [R 1l ,R 2l ,...,R (l-1)l ] T U z1 =[u1,u2,...,u l-1 ], u i Left-side unitary matrix The i-th column vector, i∈[1,l-1]; ∑ z1 =diag(σ1,σ2,...,σ l-1 ), σ iDenotes singular values, i∈[1,l-1]; by applying matrix R z1 Eigenvalue decomposition yields the transformation unitary matrix U. z1 ,

[0030] Step S224: Calculate the radius ρ of the Gell circle. i , ρ i =|u i H R|, i = 1, 2, ..., l-1;

[0031] Step S225: Calculate the iterative decision value de. If the value of de is less than zero or the number of iterations reaches the maximum value, then obtain the expansion matrix D. [i] The rank of l is determined by subtracting one from the iteration count; otherwise, steps S221-S225 are executed, while incrementing l by 1. The process is as follows:

[0032]

[0033]

[0034] Where t represents the number of iterations, and its maximum value is the expansion matrix D. [i] The column values, i.e. ρ t Let i be the radius of the Gell circle when i takes the value t; This is an adjustment factor, and its range is...

[0035] Furthermore, in step S3, the tensor completion model based on low-rank regularization is specifically as follows:

[0036]

[0037] stD=L+S+N

[0038] Where L, S, and N represent the background tensor, target tensor, and noise tensor, respectively. Where r i D [i] rank, γ i For non-convex regularization parameters, 0 < γ i <1, σ i It is a singular value; a i λ, η, and β are weighting parameters, and a i >0, λ>0, eta>0, β>0.

[0039] Furthermore, the parameters of tensor completion based on low-rank regularization are updated iteratively using the alternating multiplier method and the alternating projection method, specifically as follows:

[0040]

[0041]

[0042]

[0043] Where K is the number of update iterations. When the convergence condition is met, the current result is used as the final value, and the target tensor, background tensor, and noise tensor can be obtained, that is, small targets in the infrared image sequence are detected; otherwise, the update iteration continues. The specific convergence condition is as follows:

[0044]

[0045] Where o is the conditional threshold, and its value ranges from 0 < o < 1e. -3 .

[0046] The present invention has the following beneficial effects: (1) The infrared small target detection method based on tensor reconstruction and low-rank regularized background estimation provided by the present invention takes into account the problem of low detection efficiency caused by information redundancy in the tensor model. It adopts a tensor reconstruction model based on multi-dimensional expansion of the transform domain. The observed tensor is expanded in multiple dimensions through the transform domain to obtain a low-dimensional tensor. This low-dimensional tensor is an approximation of the observed tensor, which can reduce the amount of data. At the same time, the tensor reconstruction algorithm based on multi-dimensional expansion of the transform domain is used to decompose the low-dimensional tensor, which reduces the computational complexity. Therefore, the tensor rank can be calculated quickly and accurately. It replaces the weighted nuclear norm in the traditional algorithm and innovatively adopts a tensor completion model based on low-rank regularization to approximate the background tensor rank. While recovering the target tensor, the background tensor is effectively recovered. This can effectively suppress the background in the image and ensure the accuracy of infrared small target detection.

[0047] (2) This invention adopts a tensor reconstruction model based on multi-dimensional expansion of the transform domain, replacing the high-dimensional tensor with a low-dimensional tensor. First, dimensionality reduction means a reduction in the amount of data. Second, the tensor reconstruction algorithm based on multi-dimensional expansion of the transform domain decomposes the low-dimensional tensor, which also reduces the computational complexity and thus improves the processing speed. A tensor completion model based on low-rank regularization is adopted. Through iterative solution, the target tensor ensures that the complete small target is recovered in the image, while the effective recovery of the background tensor ensures that there is no background residue in the image. The recovery of the noise tensor ensures the accuracy of the small target in the detection result. While obtaining the target tensor, the background tensor is effectively recovered, which can suppress the background in the image and also ensure the detection accuracy. Attached Figure Description

[0048] Figure 1 This is a flowchart of the low-rank regularized background estimation infrared small target detection method based on tensor reconstruction described in this invention;

[0049] Figure 2 This is an infrared image sequence diagram input in an embodiment of the present invention; in the diagram, ae is a representative image in the infrared image sequence;

[0050] Figure 3 This is a diagram showing the experimental results of the present invention. Detailed Implementation

[0051] The present invention will now be further described. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0052] This invention provides a low-rank regularized background estimation infrared small target detection method based on tensor reconstruction. The detection method specifically includes:

[0053] Set the infrared image sequence length to 5;

[0054] Step S1: Input the infrared image sequence. This set of infrared images is arranged in chronological order and stacked sequentially to obtain the observation tensor D. I1 and I2 are the number of rows and columns of the infrared image sequence, respectively;

[0055] Step S2: Input the observation tensor D obtained in step S1 into the tensor reconstruction model based on multi-dimensional expansion of the transform domain, and calculate the tensor rank r of the infrared image sequence;

[0056] Specifically, step S2 includes the following steps S21-S22:

[0057] S21: Expand the observation tensor D along the i-th dimension to obtain D [i] , And i,j=1,2,3.

[0058] S22: Solve for D [i] rank r i That is, the tensor rank r = [r1, r2, r3].

[0059] Furthermore, step S221 includes the following steps S221-S225:

[0060] Step S221: Place D [i] Mapping to a randomized subspace Λ, and orthogonalizing the subspace Λ, yields matrices Q and M. The specific process is as follows:

[0061]

[0062] Q = qr(Λ, 0)

[0063] M = Q T DD T Q

[0064] Where Ω is a Gaussian random matrix, Ω ~ N(0,1). ε is the error parameter, in this implementation case ε=1e -2 Θ(·) denotes asymptotic approximation, where q is a positive integer. qr(·) is the QR decomposition.

[0065] Step S222: Take the first l eigenvectors of matrix M from step S221 (initialize l = 2), and obtain the low-density matrix Z through matrix multiplication. The specific process is as follows:

[0066]

[0067]

[0068] in It is the left-hand unitary matrix of the matrix. svd(·) is the singular value decomposition, and the specific process is as follows:

[0069] Let |φI-MM T |=0, I is the identity matrix, and the eigenvalues ​​φ are obtained. i ,i=1,2,...,ql. When φ=φ i Solve the linear equation (MM) T -φ i I) x = 0, obtain the eigenvectors but

[0070] Step S223: Construct the covariance matrix based on the low-density matrix Z. Then, the transformation unitary matrix U can be obtained. z1 and singular value matrix ∑ z1 The process is as follows:

[0071] R z =Z T Z

[0072]

[0073]

[0074] Among them, R ll Let matrix R z The value in the l-th row and l-th column; R is a matrix R z The l-th column vector is specifically R = [R 1l ,R 2l ,...,R (l-1)l ] T U z1 =[u1,u2,...,u l-1 ], u i Left-side unitary matrix The i-th column vector, i∈[1,l-1]; ∑ z1 =diag(σ1,σ2,...,σ l-1 ), σ i Denotes singular values, i∈[1,l-1]; by applying matrix R z1 Eigenvalue decomposition yields the transformation unitary matrix U. z1 ,

[0075] Step S224: Calculate the radius ρ of the Gell circle. i , ρ i =|u i H R|, i = 1, 2, ..., l-1;

[0076] Step S225: Calculate the iterative decision value de. If the value of de is less than zero or the number of iterations reaches the maximum value, then obtain the expansion matrix D. [i] rank r i Its value is the iteration count minus one. Otherwise, continue with steps S221-S225, while incrementing l by 1. The process is as follows:

[0077]

[0078]

[0079] Where t represents the number of iterations, and its maximum value is the expansion matrix D. [i] The column values, i.e. ρ t Let i be the radius of the Gell circle when i takes the value t; This is an adjustment factor, and its range is...

[0080] Step S3: Using the alternating multiplier method based on augmented Lagrange, update and iterate the parameters of the tensor completion model based on low-rank regularization, and finally calculate the target tensor, background tensor and noise tensor to realize infrared small target detection;

[0081] The tensor completion model based on low-rank regularization in step S3 is as follows:

[0082]

[0083] stD=L+S+N

[0084] Where L, S, and N represent the background tensor, target tensor, and noise tensor, respectively. Where ||·||0 is the zero norm, ||·|| F Let r be the F-norm. i D [i] rank, γi Let a be the non-convex regularization parameter. i For the weighting parameters, σ i λ is a singular value. λ, η, and β are weighting parameters. In this implementation, the value is γ. i =0.5, λ=10, η=5, β=1.

[0085] Furthermore, the parameters of tensor completion based on low-rank regularization are updated iteratively using methods such as the alternating multiplier method and the alternating projection method. Specific steps include steps S31-S38:

[0086] Step S31: Construct the augmented Lagrangian function F; To construct the augmented Lagrangian function, let X = L;

[0087]

[0088] Where μ1 and μ2 are Lagrange multipliers, and y1 and y2 are penalty factors.

[0089] Step S32: Initialize the parameters of the augmented Lagrangian function F. Let L 0 =D,S 0 =N 0 =0, Let the learning rate ρ = 1.05 and the convergence threshold o = 1e -7 .

[0090] Step S33: Fix other variables and update X k+1 :

[0091]

[0092] Where k represents the iteration number, a i These are weighted parameters.

[0093] Furthermore, solve X k+1 The specific steps include steps S331-S333:

[0094] Step S331: For Perform singular value decomposition, i.e. Where V is the right-hand unitary matrix obtained from singular value decomposition.

[0095] Step S332: Restrict the elements of the singular value matrix ∑ obtained in step S331, specifically as follows:

[0096] ∑=diag(δ1,δ2,...,δ r )

[0097]

[0098] Where, δ iLet i = 1, 2, ..., r be singular values, and r be a Rank. For ||L|| γ In σ i The gradient at that point is specifically...

[0099] Step S333: It can be calculated that

[0100] Step S34: Fix other variables and update L k+1 :

[0101]

[0102] Furthermore, by taking the L partial derivative of the augmented Lagrangian function F, we obtain:

[0103]

[0104] Then, let the derivative value Find:

[0105]

[0106] Step S35: Fix other variables and update S k+1 :

[0107]

[0108] Furthermore, by taking the S-partial derivative of the augmented Lagrange function F, we obtain:

[0109]

[0110] Then, let the derivative value Find:

[0111]

[0112] Step S36: Fix other variables and update N k+1 :

[0113]

[0114] Furthermore, by taking the N-partial derivative with respect to the augmented Lagrange function F, we obtain:

[0115]

[0116] Then, let the derivative value Find:

[0117]

[0118] Step S37: Update the Lagrange multipliers and penalty factors:

[0119]

[0120]

[0121]

[0122]

[0123] Step S38: Calculate the convergence value. The specific convergence condition is as follows:

[0124]

[0125] If the convergence condition is met, the target tensor, background tensor, and noise tensor can be obtained, thus detecting small targets in the infrared image sequence. Otherwise, continue with steps S33-S38.

[0126] To verify the effectiveness of the detection method described in this invention, the PSTNN method in infrared small target detection based on the partial sum of tensor kernel norms is used as Comparative Example 1, and the RIPT method in the reweighted infrared patch tensor model is used as Comparative Example 2. Figure 2 The infrared image sequences shown are input into Comparative Example 1, Comparative Example 2, and the Low-Rank Regularized Background Estimation Infrared Small Target Detection Method (LRBE) based on tensor reconstruction provided in the above embodiments of this application, respectively, and the detection results are output as follows: Figure 3 As shown.

[0127] The test results are shown in the table below:

[0128] Table 1 Test Results

[0129]

[0130] Among them, Figure ae is Figure 2 The algorithm for the mean score (mSCRG) is as follows: (See figure ae).

[0131]

[0132]

[0133] Among them, SCR in SCR out and represent the score before detection (SCR) and the score after detection (SCR), respectively. Where μ t μ b These are the average gray values ​​of the target and background regions, respectively; σ b The standard deviation of the background region.

[0134] The test results in Table 1 show that the method proposed in this invention is almost superior to the comparative method. (Refer to the accompanying drawings.) Figure 3 Experimental results show that the method proposed in this invention can completely preserve small targets in image sequences while effectively suppressing background.

[0135] The above are merely preferred embodiments of the present invention and do not constitute any limitation on the present invention. Any equivalent substitutions or modifications made by those skilled in the art to the technical solutions and content disclosed in the present invention without departing from the scope of the present invention shall be deemed to have remained within the scope of protection of the present invention.

Claims

1. A low-rank regularized background estimation infrared small target detection method based on tensor reconstruction, characterized in that, The method includes the following steps: Step S1: Input the infrared image sequence, stack the infrared images sequentially to form the observation tensor. ; Step S2: Convert the observation tensor obtained in step S1 into... The input is fed into a tensor reconstruction model based on multi-dimensional expansion of the transform domain to calculate the tensor rank of the infrared image sequence. Specifically: Step S21: Transfer the observation tensor Expanding along the i-th dimension, we obtain and ; Step S22: Solve rank That is, tensor rank ; Step S3: Rank the tensor The input tensor completion model based on low-rank regularization is used to update and iterate the parameters of the tensor completion model based on low-rank regularization through alternating multiplier method and alternating projection method, and finally the target tensor, background tensor and noise tensor are calculated to obtain the infrared small target detection result; in step S3, the tensor completion model based on low-rank regularization is specifically as follows: ； in, , , Let these represent the background tensor, target tensor, and noise tensor, respectively. ,in for rank, For non-convex regularization parameters, , It is a singular value; , , and For weighted parameters, , .

2. The infrared small target detection method based on tensor reconstruction with low-rank regularized background estimation as described in claim 1, characterized in that, In step S1, the infrared images are stacked together to form an observation tensor. Specifically, it includes: Step S11: Input an infrared image sequence, the sequence length is When the sequence length is 1, it degenerates into an infrared image; the infrared images are arranged in chronological order and stacked sequentially to obtain the observation tensor. ,at the same time ; These represent the number of rows, the number of columns, and the length of the infrared image sequence, respectively.

3. The infrared small target detection method based on tensor reconstruction with low-rank regularized background estimation as described in claim 1, characterized in that, In step S22, solve... The specific steps for determining the rank are as follows: Step S221: ... Mapping to randomized subspace In, for subspace Perform orthogonalization to obtain the matrix and The process is as follows: ； in, It is a Gaussian random matrix. ; Let be the error parameter, and ; Indicates asymptotic, It is a positive integer; Decompose QR; Step S222: Take the matrix from step S221 The former 1 eigenvector ( A low-density matrix is ​​obtained through matrix multiplication. The process is as follows: ； in, For singular value decomposition, It is the left-hand unitary matrix of the matrix. ; Step S223: Based on the low-density matrix Construct the covariance matrix; obtain the transformation unitary matrix. and singular value matrix The process is as follows: ； in, For matrix No. Line number The value of the column; For matrix The Column vector, specifically , , Left-side unitary matrix The i-th column vector, ; , Represents singular values, ; By analyzing the matrix Eigenvalue decomposition yields the transformation unitary matrix. , ; Step S224: Calculate the radius of the Gell circle. , , ; Step S225: Calculate the iterative decision value ,like If the value is less than zero or the number of iterations reaches its maximum value, then the expansion matrix is ​​obtained. The rank of is determined by the iteration count minus one; otherwise, continue with steps S221-S225, and simultaneously set... Increase by 1; the specific process is as follows: ； in, This represents the number of iterations, and its maximum value is the expanded matrix. The column values, i.e. ; for Values The radius of the Gaelic circle at that time; This is an adjustment factor, and its range is... .

4. The infrared small target detection method based on tensor reconstruction with low-rank regularized background estimation as described in claim 1, characterized in that, The parameters of tensor completion based on low-rank regularization are updated iteratively using the alternating multiplier method and the alternating projection method, specifically as follows: ； Where K is the number of update iterations. When the convergence condition is met, the current result is used as the final value, and the target tensor, background tensor, and noise tensor can be obtained, that is, small targets in the infrared image sequence are detected; otherwise, the update iteration continues. The specific convergence condition is as follows: ； in, This is a conditional threshold, and its value range is... .

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