Infrared small target detection method based on non-convex tensor tuck decomposition

Abstract

The invention discloses an infrared small target detection method based on non-convex tensor tuck decomposition, and the method employs a non-convex rank approaching norm to restrain a potential factor of low-rank tuck decomposition, thereby avoiding the arrangement of a rank in advance according to experience, and improving the robustness of an algorithm in different scenes. Meanwhile, in order to use more structural information, an alternating direction multiplier method (sGSADMM) based on symmetric Gaussian-Seidel is designed to solve the provided model. Through organic combination of non-convex tensor tuck decomposition based on factor prior and a symmetric Gaussian-Seidel alternating direction multiplier method, the technology provided by the invention can accurately detect a small target in different scenes.

Description

Technical Field

[0001] The invention relates to the technical field of image data processing, in particular to an infrared small target detection method based on non-convex tensor Tucker decomposition. Background Art

[0002] In recent years, low-rank sparse decomposition methods have been rapidly developed in the field of infrared small target detection. However, due to the long imaging distance of infrared targets, there is often a lack of effective shape and texture information. Therefore, studying infrared small target detection in complex scenes is a challenging task.

[0003] In order to better detect small targets in complex scenes, researchers have proposed many methods. Existing infrared small target detection methods can be divided into three categories: filtering-based methods, methods based on human visual contrast mechanism, and methods based on low-rank sparse decomposition. The filtering-based method has a simple structural design and is suitable for simple and uniform scenes. The detection performance decreases in complex scenes. The method based on human visual attention mechanism is suitable for scenes with large contrast differences between the target and the background. When the contrast difference between the target and the background is small, the detection performance decreases. Infrared small target detection methods based on low-rank sparse decomposition have developed rapidly in the field of infrared small target detection due to their high detection performance. In particular, methods based on low-rank Tucker decomposition have achieved good detection performance in complex scenes. The existing mathematical definition based on low-rank Tucker decomposition is expressed as follows: in, and Represent the factor matrix and the kernel tensor respectively. In recent years, the low-rank Tucker decomposition method has achieved good detection performance in infrared small target detection. However, the existing low-rank Tucker decomposition method requires the rank to be pre-defined based on experience, and inaccurate pre-defined rank may lead to problems such as missed detection or false alarm. Moreover, the size of the rank is different in different scenes, which is not applicable to practical scenes. At the same time, the existing methods based on low-rank Tucker decomposition usually use the alternating direction multiplier method to solve the model, which fails to make full use of the structural information and cannot obtain the optimal detection performance. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide an infrared small target detection method based on non-convex tensor Tucker decomposition to accurately detect small targets in different scenes in view of the shortcomings of the existing technology.

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is: an infrared small target detection method based on non-convex tensor Tucker decomposition, comprising the following steps: S1. Obtain an infrared image sequence, and stack N adjacent frames of the infrared image sequence into an image tensor ; S2, use the following formula to transform the image tensor Decompose into target tensor and the background tensor : ;in, and denote the factor matrix and the kernel tensor respectively, , and represents the positive regularization parameter, , N represents the dimension of the input tensor, represents the product with the first factor matrix, represents the product with the Nth factor matrix; S3. Update the variables in the above formula until the convergence condition is met to obtain the final target tensor; wherein the convergence condition is: ; is the set threshold.

[0006] In step S3, the specific implementation process of updating each variable includes: in one update cycle, updating each variable in the following order: , , , , , , , .

[0007] Update variables The specific implementation process includes: Fix other variables and update using the following formula : ; in, represents the regularization parameter, represents the Lagrange multiplier, is the variable updated in the k+1th iteration, Variables updated for the kth iteration.

[0008] Update variables The specific implementation process includes: Fix other variables and update using the following formula : ; ; , is the identity matrix, is the matrix form of the background, is the matrix form of the kernel tensor, is the Lagrange multiplier, represents the factor matrix.

[0009] Update variables The specific implementation process includes: Fix other variables and update using the following formula : ; represents the Lagrange multiplier; but, ; .

[0010] Update variables The specific implementation process includes: Fix other variables and update using the following formula : ; but, ; Represents an operation where the columns of a tensor or matrix are superimposed into a single column vector.

[0011] Update variables The specific implementation process includes: Fix other variables and update using the following formula : ; but, ; in, Represents the threshold segmentation function: .

[0012] Update completed Then, update using the following formula , , and : ; ;in, , , represents the regularization parameter.

[0013] Compared with the prior art, the present invention has the following beneficial effects: the present invention uses a non-convex rank approximation norm to constrain the potential factors of the low-rank Tucker decomposition, avoids setting the rank in advance based on experience, and improves the robustness of the method in different scenarios. At the same time, in order to use more structural information, a symmetric Gauss-Seidel alternating direction multiplier method (sGSADMM) is designed to calculate the proposed model, organically combining the non-convex tensor Tucker decomposition based on factor prior and the symmetric Gauss-Seidel alternating direction multiplier method, the method proposed by the present invention can accurately detect small targets in different scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 This is a flow chart of a method according to an embodiment of the present invention; Figure 2 Comparison between the ADMM method and the sGSADMM method, (a) ADMM, (b) sGSADMM; Figure 3 The detection results of the embodiment of the present invention are visualized. DETAILED DESCRIPTION

[0015] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution 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 described embodiments are 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 creative work are within the scope of protection of the present invention.

[0016] The infrared small target detection method based on non-convex tensor Tucker decomposition based on factor prior proposed in the embodiment of the present invention consists of two parts, including non-convex tensor Tucker decomposition based on factor prior and symmetric Gauss-Seidel alternating direction multiplier method. By organically combining non-convex tensor Tucker decomposition based on factor prior and symmetric Gauss-Seidel alternating direction multiplier method, the technology proposed in the embodiment of the present invention can accurately detect small targets in different scenarios. The overall flow chart is as follows Figure 1 As shown in the figure, the adjacent 5 frames of the input infrared image sequence O are stacked into an image tensor , and then take the input image tensor Decompose into target tensor and background tensor The mathematical expression is as follows: (1) For the entire image, the target tensor is sparse, and a sparse constraint is added to the target tensor. Since the infrared image has a long imaging distance, there are a large number of similar areas in the images of adjacent frames, so the background tensor has a low rank. Existing methods usually use low-rank Tucker decomposition to constrain the background tensor, which can obtain better detection performance. However, the existing low-rank Tucker decomposition method needs to set the rank in advance based on experience in different scenes, and the size of the rank in different scenes is different, which is not suitable for application in actual engineering. In order to improve the detection performance and robustness of the existing low-rank Tucker decomposition method, an infrared small target detection method based on non-convex tensor Tucker decomposition with factor prior is proposed. In this method, a non-convex rank approximation norm is used to constrain the latent factors of the low-rank Tucker decomposition, which avoids setting the rank in advance based on experience and improves the robustness of the algorithm in different scenes. The non-convex rank approximation norm proposed in the present invention is referred to as The norm is defined as follows: .

[0017] Based on this, the definition of the new factor-based non-convex tensor Tucker decomposition NFTD is as follows: .

[0018] In summary, in order to solve the rank selection problem of the existing low-rank Tucker decomposition method, the embodiment of the present invention proposes an infrared small target detection method based on factor prior non-convex tensor Tucker decomposition, and the model is expressed as follows:

[0019] To solve the above equation, existing methods usually use the alternating iterative multiplier method, but cannot make full use of structural information. In the embodiment of the present invention, in order to use more structural information, a symmetric Gauss-Seidel alternating direction multiplier method (sGSADMM) is designed to solve the proposed model. Figure 2 A comparison of the alternating direction method of multipliers (ADMM) and the symmetric Gauss-Seidel alternating direction method of multipliers (sGSADMM) is shown. Figure 2 As can be seen from (a) of , ADMM updates all variables sequentially within a cycle and treats each variable equally. Figure 2 As shown in (b), it can be seen that sGSADMM updates all variables in each iteration, and then repeatedly updates some variables to form a symmetric iterative structure. Compared with ADMM, sGSADMM can make full use of the non-smooth structural information in the above model, so higher detection accuracy can be achieved. By organically combining the non-convex tensor Tucker decomposition based on factor prior and the symmetric Gauss-Seidel alternating direction multiplier method, the technology proposed in the present invention can accurately detect small targets in different scenarios.

[0020] Considering that the existing low-rank Tucker decomposition method needs to set the rank in advance based on experience, and the size of the rank is different in different scenarios, in order to improve the detection performance of the existing low-rank Tucker decomposition method and the robustness in different scenarios, a definition of non-convex tensor Tucker decomposition NFTD based on factor prior is proposed as follows: (2) Based on formula (2), the infrared small target detection method based on factor prior non-convex tensor Tucker decomposition proposed in the present invention is expressed as follows: (3) in, and represents the positive regularization parameter, Represents singular values.

[0021] Next, we need to solve equation (3). By introducing auxiliary variables Formula (3) is constructed as follows: (4) Then, the augmented Lagrangian function is expressed as follows: (5) The embodiment of the present invention adopts the symmetric Gauss-Seidel alternating direction multiplier method to solve equation (5). Figure 2 A comparison of the alternating direction method of multipliers (ADMM) and the symmetric Gauss-Seidel alternating direction method of multipliers (sGSADMM) is shown. Figure 2 As can be seen from (a) in Figure 2, ADMM updates all variables sequentially within a cycle and treats each variable equally. Figure 2 As shown in (b), we can see that sGSADMM updates all variables in each iteration, and then repeatedly updates some variables to form a symmetric iterative structure. Compared with ADMM, sGSADMM can make full use of the non-smooth structural information in equation (5), so it can achieve higher detection accuracy. Next, we use sGSADMM to decompose equation (5) into several sub-problems, and then iterate and update each variable alternately.

[0022] The specific update steps are as follows: 1) Fix other variables and update : (6) The closed-form solution of formula (6) is expressed as follows: (7) 2) Fix other variables and update : (8) According to Lemma 1 in X. Tian, ​​K. Xie, and H. Zhang, “A low-rank tensor decomposition model with factors prior and total variation for impulsive noise removal,” IEEE Transactions on Image Processing, 2022., formula (8) is rewritten as follows: (9) Then, The solution of is as follows: (10) in, .

[0023] 3) Fix other variables and update : (11) The solution of formula (11) is expressed as follows: (12) in, .

[0024] 4) Fix other variables and update : (13) In order to solve equation (13), the method in Lemma 1 is used to expand the core tensor into the n-th module , formula (13) is rewritten as follows: (14) Using Kronecker product and The properties of , combined with the optimality condition, update The representation is as follows: (15) in, Represents an operation that adds the columns of a tensor or matrix into a single column vector.

[0025] 5) Fix other variables and update : (16) According to the soft threshold algorithm, the solution of equation (16) is as follows: (17) Fix other variables, update : (18) 7) Fix other variables and update : (19) The NFTD-sGSADMM method of an embodiment of the present invention is described as follows: Input: infrared image sequence, , ,L,H, , , , , , , ; Output: Background image , target image ; Step 1. Update according to formula (7) ; Step 2. Update according to formula (10) ; Step 3. Update according to formula (12) ; Step 4. Update according to formula (15) ; Step 5. Update according to formula (17) ; Step 6. Update according to formula (12) ; Step 7. Update according to formula (10) ; Step8. Update according to formula (7) ; Step9. Update according to formula (18), , , ; Step 10. Update according to formula (19) : Step 11. Check whether the convergence condition is met .

[0026] In order to verify the detection performance of the method proposed in the embodiment of the present invention, it is compared with 8 different detection algorithms on 3 sequences. Figure 3 The detection results of different algorithms are shown. Figure 3 It can be seen that the Top-hat method has more background clutter residues in the three different scenes. This is because the Top-hat method has a simple structure design, low computational complexity, and is suitable for simple and uniform scenes. Compared with the Top-hat method, the NRAM method has less background clutter residues in different scenes, but in sequence 1 and sequence 3, the NRAM method over-shrinks the target and the target energy is low. Figure 3 It can be seen that although the ECASTT method can greatly improve the contrast between the target and the background, there is still a small amount of background clutter in the detection results. Figure 3 It can be seen that the MSLSTIPT and ASTTV-NTLA methods can retain the target well, but their detection results are usually gray, which means that they cannot suppress the background well. In contrast, the IMNN-LWEC, SRSTT and 4D-TT methods can suppress background clutter well, but the IMNN-LWEC method usually over-shrinks the target and the target intensity is weak. This shows that its target detection ability needs to be further improved. Figure 3 It can be seen that the NFTD-sGSADMM method proposed in the embodiment of the present invention can effectively suppress background clutter while enhancing the target, and there is almost no residual clutter in the detection result, which shows that the detection performance and background suppression ability of the NFTD-sGSADMM method in different scenarios are higher than those of other comparison methods.

[0027] The AUC index was further used to evaluate the performance of each comparison method, as shown in Table 1. Bold indicates the best result, and underlined indicates the second best result. As shown in Table 1, in sequences 1-3, the NFTD-sGSADMM method proposed in the embodiment of the present invention has This shows that the above three methods have strong detection capabilities. However, the ASTTV-NTLA and Top-hat methods The value is high, which means that it performs poorly in suppressing background clutter. This also leads to the poor performance of ASTTV-NTLA and Top-hat methods. and As can be seen from Table 1, the IMNN-LWEC, SRSTT, 4D-TT and NFTD-sGSADMM methods proposed in the embodiment of the present invention have The lowest, which shows that they can suppress background clutter well. However, the The value is not high, which also leads to The values ​​are low, which indicates that their detection capabilities need to be improved. As can be seen from Table 1, the NFTD-sGSADMM method proposed in the embodiment of the present invention has high and This shows that the method proposed in the embodiment of the present invention can accurately detect the target and suppress background clutter well.

[0028] Table 1 Detection performance evaluation of different methods on sequence 1-sequence 3

[0029] Although the preferred embodiments of the present application have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present application.

[0030] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is also intended to include these modifications and variations.

Claims

1. A method for infrared small target detection based on non-convex tensor Tucker decomposition, characterized in that: The following steps are involved: S1. Obtain an infrared image sequence, and stack N adjacent frames of the infrared image sequence into an image tensor ; S2, use the following formula to transform the image tensor Decompose into target tensor and the background tensor : ;in, and denote the factor matrix and the kernel tensor respectively, , and represents the positive regularization parameter, , N represents the dimension of the input tensor, represents the product with the first factor matrix, represents the product with the Nth factor matrix; S3. Update the variables in the above formula until the convergence condition is met to obtain the final target tensor; wherein the convergence condition is: ; is the set threshold.

2. The infrared small target detection method based on non-convex tensor Tucker decomposition according to claim 1 is characterized in that: In step S3, the specific implementation process of updating each variable includes: in one update cycle, updating each variable in the following order: , , , , , , , .

3. The infrared small target detection method based on non-convex tensor Tucker decomposition according to claim 1 or 2 is characterized in that: Update variables The specific implementation process includes: Fix other variables and update using the following formula : ； in, represents the regularization parameter, represents the Lagrange multiplier, is the variable updated in the k+1th iteration, Variables updated for the kth iteration.

4. The infrared small target detection method based on non-convex tensor Tucker decomposition according to claim 1 or 2 is characterized in that: Update variables The specific implementation process includes: Fix other variables and update using the following formula : ； ； , is the identity matrix, is the matrix form of the background, is the matrix form of the kernel tensor, is the Lagrange multiplier, represents the factor matrix.

5. The infrared small target detection method based on non-convex tensor Tucker decomposition according to claim 1 or 2, characterized in that: Update variables The specific implementation process includes: Fix other variables and update using the following formula : ; represents the Lagrange multiplier; but, ； 。 6. The infrared small target detection method based on non-convex tensor Tucker decomposition according to claim 1 or 2 is characterized in that: Update variables The specific implementation process includes: Fix other variables and update using the following formula : ； but, ； Represents an operation where the columns of a tensor or matrix are superimposed into a single column vector.

7. The infrared small target detection method based on non-convex tensor Tucker decomposition according to claim 1 or 2 is characterized in that: Update variables The specific implementation process includes: Fix other variables and update using the following formula : ； but, ； in, Represents the threshold segmentation function: .

8. The infrared small target detection method based on non-convex tensor Tucker decomposition according to claim 2 is characterized in that: In each update cycle, the update is completed Then, update using the following formula , , and : ； ； in, , , represents the regularization parameter.

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