A weak and small target detection method in strong light halo background based on smooth sparse decomposition

Abstract

The application discloses a weak and small target detection method based on smooth sparse decomposition in a strong halo background. The method regards the weak and small target detection in the strong halo background as a decomposition process of smooth components and sparse components of a matrix. In an optimization framework of smooth sparse decomposition, the application uses a spline base to fit the halo, uses a total variation constraint of a smooth coefficient matrix to constrain the smoothness of the background, simultaneously uses an l0 norm to constrain the sparsity of the target, and introduces a space-time prior weight to enhance the saliency of the target. When solving, the application uses an alternating multiplier method to realize the fast separation of the target and the background.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of image processing and target detection, and particularly relates to a weak and small target detection method based on smooth sparse decomposition in a strong halo background. BACKGROUND

[0002] Weak and small target detection plays an important role in many applications such as military reconnaissance, space monitoring and city monitoring, and different application scenarios have different image backgrounds. At present, there are a large number of weak and small target detection methods for improving the robustness of strong noise, clutter and complex background, but there are still few studies on weak and small target detection in a strong halo background. In many applications, a strong halo background will appear and cause great interference to the detection process. For example, in the field of quantum communication, the strong halo background generated by sunlight will interfere with the detection of beacon light and cause the failure to establish a communication link; in the field of astronomical navigation, the strong halo caused by solar scattering will make the star sensor unable to complete the star map recognition task. Therefore, the study of the weak and small target detection method in a strong halo background is of great significance to the above fields.

[0003] The weak and small target image in a strong background has the following characteristics: the image background is a quite bright halo, and the background has different degrees of non-uniformity and noise; the number of pixels of the target is less than 7x7, the target is easily submerged in the halo background, and the contrast and signal-to-clutter ratio are extremely low. These image characteristics make it extremely difficult to detect weak and small targets in a strong background.

[0004] At present, weak and small target detection is divided into three categories: (1) the background modeling method is based on the assumption of background consistency, and a filter is used to predict the background of the image, and then the predicted background is subtracted from the original image to obtain the target. Since the strong halo destroys the background consistency, this method cannot accurately model the halo background; (2) the local contrast method uses the characteristic that the target region has high contrast, and enhances the saliency of the target by calculating the local contrast map to realize target detection. Because the local contrast of the target in a strong background is extremely low, the calculated local contrast map cannot highlight the target; (3) the low-rank sparse decomposition method regards the background as a low-rank component and the target as a sparse component, and then separates the target and the background through optimization. However, the low-rank sparse decomposition method is not sensitive to the weak undulations in the image, resulting in an inaccurate separation of the strong halo background and the extremely weak target.

[0005] The existing weak and small target detection methods have certain deficiencies in a strong background, and therefore, a weak and small target detection method specifically for a strong halo background is needed. SUMMARY

[0006] The present application aims at the deficiency of the existing weak small target detection algorithm in the detection performance under strong halo background, and provides a weak small target detection method under strong halo background based on smooth sparse decomposition. The method regards the halo background as a smooth component from a new perspective of the image background, and fits the background by using a spline basis. An optimization solving problem is established by constraining the total variation of the fitting coefficient matrix and the l0 norm of the target with a significance weight, so that the accurate separation of the target and the background is realized.

[0007] The technical scheme adopted by the present application is as follows: a weak small target detection method under strong halo background based on smooth sparse decomposition, comprising the following four steps:

[0008] Step one: according to the size of the original image, the spline basis function S is calculated in the horizontal direction and the vertical direction respectively H ,S V The calculation process is as follows:

[0009]

[0010] The meanings of the symbols in formula (1) are as follows:

[0011] S i,x : the value of the i-th row and x-th column of the spline basis matrix;

[0012] u i : the i-th node;

[0013] Step two: the background is represented by using the spline basis function, and an optimization problem is constructed by the total variation of the coefficient matrix and the l0 norm of the target matrix, and the optimization problem is as follows:

[0014]

[0015] The meanings of the symbols in formula (2) are as follows:

[0016] O: the original image matrix;

[0017] B: the background matrix;

[0018] T: the target matrix;

[0019] N: the noise matrix;

[0020] Theta: the coefficient matrix;

[0021] Lambda: the sparse coefficient;

[0022] Beta: the noise coefficient;

[0023] D1: the gradient operator in the x direction;

[0024] D2: the gradient operator in the y direction;

[0025] Z1: total variation value in x direction;

[0026] Z2: total variation value in y direction;

[0027] ||·||0: norm of matrix l0, i.e. number of non-zero elements in the matrix;

[0028] ||·||0: norm of matrix l0, i.e. number of non-zero elements in the matrix; 2,1 : norm of matrix l 2,1 , i.e. l1 norm of l2 norm of matrix row vectors;

[0029] Step three: calculate saliency map using noise components of consecutive frames and introduce it as a weight of the target into the optimization problem constructed in step two, the calculation process of saliency weight is as follows:

[0030] Step 3a: do mean filtering on the noise extracted from the previous k frames and the noise of the current frame The calculation formula is as follows:

[0031]

[0032] The meanings of symbols in formula (3) are as follows:

[0033] Noise matrix of the current t frame and the mth iteration;

[0034] N t-k : noise matrix of the previous t-k frames;

[0035] f: mean filtering operator;

[0036] Noise tensor obtained after mean filtering;

[0037] Step 3b: do three-dimensional dilation operation on The calculation formula is as follows:

[0038]

[0039] The meanings of symbols in formula (4) are as follows:

[0040] Tensor obtained after three-dimensional dilation;

[0041] d: three-dimensional dilation operator;

[0042] Step 3c: difference between the last frame of and the last frame of to obtain D, and do the following calculation to obtain saliency weight:

[0043] ​​

[0044] The meaning of each symbol in equation (5) is as follows:

[0045] D: the difference between the last frame of the last frame of

[0046] ε(·): step function, i.e.

[0047] W m : the saliency weight under the mth iteration;

[0048] Step 3d: introduce the obtained weight into the optimization problem in step two, and the optimization problem is as follows:

[0049]

[0050] The meaning of each symbol in equation (6) is as follows:

[0051] W: saliency weight;

[0052] matrix dot product operation;

[0053] Step four: use the alternating multiplier method to solve the target matrix and the background matrix. The calculation process is as follows:

[0054] Step 4a: initialize the augmented Lagrange equation of the optimization problem, and the specific formula is as follows:

[0055]

[0056] The meaning of each symbol in equation (7) is as follows:

[0057] Y i ,i = 1, 2, 3, 4: Lagrange multiplier;

[0058] η: non-negative penalty factor;

[0059] ||·|| F : Frobenius norm;

[0060] <·>: inner product operation;

[0061] Step 4b: parameter initialization: Θ 0 = 0, B 0 = 0, T 0 = 0, N 0 = 0, Z 0 = 0, μ 0 = 10 -6 , β = 100λ, m = 0, iterMax = 200;

[0062] Step 4c: Fix B, T, N, Z, update Θ m The resulting subproblem is as follows:

[0063]

[0064] The solution to equation (8) is as follows:

[0065]

[0066] Step 4d: Fix T, N, Z, Θ, update B m The resulting subproblem is as follows:

[0067]

[0068] The solution to equation (10) is as follows:

[0069]

[0070] Step 4e: Fix B, N, Z, Θ, update T m The calculation formula is as follows:

[0071]

[0072] Equation (12) is an l0 optimization problem, which is solved using the following Gaussian function:

[0073]

[0074] Step 4f: Fix B, T, Z, Θ, update N m The calculation formula is as follows:

[0075]

[0076] Equation (14) is an l 2,1 optimization problem, the solution formula is as follows:

[0077]

[0078] Step 4e: Fix B, T, N, Θ, update Z m The calculation formula is as follows:

[0079]

[0080] Equation (16) is an l2 optimization problem, the solution formula is as follows:

[0081]

[0082] Step 4f: update Y m ,μ m , the calculation formula is as follows:

[0083]

[0084] Step 4g: iteration number m = m + 1;

[0085] Step 4h: judge whether m is greater than iterMax, if yes, stop iteration, and go to step 4i; if not, stop iteration when the following condition is met, and go to step 4i: if the iteration stop condition is not met, and the iteration number does not reach the maximum value, go to step 4c;

[0086]

[0087] Step 4i: find the optimal solution, and output the background matrix B and the target matrix T.

[0088] The advantages and beneficial effects of the present application compared with the prior art are:

[0089] 1. The present application models and realizes the small target detection task under the halo background from a new angle, and proposes a smooth sparse decomposition optimization model. For the strong halo of the background, spline basis is used to fit the halo, solving the problem that the existing method has poor reconstruction effect on the background; for the low saliency of the target, the saliency map is calculated by using the noise of the continuous frame, and is introduced into the optimization model as the target weight, avoiding the problem that the target cannot be detected due to insufficient target saliency.

[0090] 2. The present application, the model minimizes the total variation of the background smoothness coefficient and the l0 norm of the target, BRIEF DESCRIPTION OF DRAWINGS

[0091] Figure 1 is a specific flow chart of the weak small target detection method under strong halo background based on smooth sparse decomposition of the present application;

[0092] Figure 2 is the first frame in the experimental test sequence of the present application;

[0093] Figure 3 is the comparison of the present application and the existing weak small target detection algorithm after detecting the experimental test sequence, (a) MPCM, (b) FKRW, (c) PSTNN, (d) ASTTV-NTLA, (e) SRSTT, (f) HOC, (g) the present application; DETAILED DESCRIPTION

[0094] The specific flow chart of the weak small target detection method under strong halo background based on smooth sparse decomposition of the present application is as follows Figure 1The application is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0095] 1) Experimental conditions: The computer used in the experiment is Intel(R) Core(TM) i5-10400 CPU, the memory is 16.0 GB, and the programming platform is MATLAB R2021a. The image resolution of the test sequence used in the experiment is 253x247, and the target signal-to-noise ratio is -0.0095 dB, see Figure 2 .

[0096] 2) Experimental content:

[0097] The method proposed in the application is compared with existing weak and small target detection algorithms, wherein the commonly used image enhancement algorithms mainly include:

[0098] (1) MPCM: proposed by Wei, Yantao, Xinge You, and Hong Li, published in "Multiscale patch-based contrast measure for small infrared target detection." Pattern Recognition 58 (2016): 216-226;

[0099] (2) FKRW: proposed by Qin, Yao, et al, published in "Infrared small target detection based on facet kernel and random walker." IEEE Transactions on Geoscience and Remote Sensing 57.9 (2019): 7104-7118;

[0100] (3) PSTNN: proposed by Zhang, Landan, and Zhenming Peng, published in "Infrared small target detection based on partial sum of the tensor nuclear norm." Remote Sensing 11.4 (2019): 382;

[0101] (4) ASTTV-NTLA: proposed by Liu, Ting, et al. in "Nonconvex tensor low-rank approximation for infrared small target detection." IEEE Transactions on Geoscience and Remote Sensing 60 (2021): 1-18;

[0102] (5) SRSTT: proposed by Li, Jie, et al. in "Sparse Regularization-Based Spatial-Temporal Twist Tensor Model for Infrared Small Target Detection." IEEE Transactions on Geoscience and Remote Sensing (2023);

[0103] (6) HOC: proposed by Niu, Wenlong, et al. in "Moving point target detection based on higher order statistics in very low SNR." IEEE Geoscience and Remote Sensing Letters 15.2 (2017): 217-221.

[0104] Figure 3 The target detection results of seven methods on the experimental sequence 1 are given, and the lower right corner is the enlarged image of the target area. The experimental results show that: except for the present application, other methods do not detect the target; the present application detects the target while suppressing the background halo and noise to the greatest extent, proving that the method is suitable for weak small target detection in strong halo background.

[0105] In this experiment, the signal-to-clutter ratio gain SCRG and the background suppression factor BSF are used as evaluation indexes, which reflect the target detection performance and background suppression performance of the algorithm respectively. Table 1 gives the SCRG and BSF of the existing weak small target detection method and the present application, and NaN in the table represents that the detection algorithm does not detect the target, and Inf represents that the background area of the target accessory is completely suppressed or the target is not detected. The experimental results show that: the present application has the largest SCRG and BSF on the experimental test sequence, which shows that the target detection and background suppression performance of the present application is better than that of the existing weak small target detection method.

[0106] Table 1

[0107]

[0108] The present application provides a weak and small target detection method in strong halo background based on smooth sparse decomposition. The present application regards the weak and small target detection in strong halo background as a decomposition process of smooth component and sparse component of matrix. In the optimization framework of smooth sparse decomposition, the present application uses spline base to fit the halo, uses total variation constraint of smooth coefficient matrix to constrain the smoothness of background, simultaneously uses l0 norm to constrain the sparsity of target and introduces space-time prior weight to enhance the saliency of target. The present application fills the vacancy of weak and small target detection algorithm research in strong halo scene, and realizes the fast separation of weak and small target and strong halo background.

[0109] The part of the present application not described in detail is the known technology in the technical field. The above description is only the specific examples of the present application, and is not used to limit the present application. Any modification, equivalent replacement, improvement, etc. made in the spirit and principle of the present application should be included in the protection scope of the present application.

Claims

1. A method for detecting weak targets against a strong halo background based on smooth sparse decomposition, characterized in that, The detection of weak targets is achieved through the following four steps: Step 1: Calculate the spline basis functions in the horizontal and vertical directions based on the original image size. ; Step 2: Represent the background using spline basis functions, and construct the optimization problem using the total variation of the coefficient matrix and the l0 norm of the objective matrix; Step 3: Calculate the saliency map using the noise components of consecutive frames, and introduce it as the weight of the objective into the optimization problem constructed in Step 2; Step 4: Solve for the target matrix and background matrix using the alternating multiplier method; The optimization problem described in step two is as follows: The optimization problem is constructed using the total variation of the coefficient matrix and the l0 norm of the objective matrix, as shown in the following formula: ， (2) The symbols in formula (2) have the following meanings: : Original image matrix; Background matrix; : Target matrix; Noise matrix; : Coefficient matrix; : Sparsity coefficient; Noise figure; : Gradient operator for direction; : Gradient operator for direction; : Total variation value of direction; : Total variation value of direction; :matrix The norm of a matrix is ​​the number of non-zero elements in the matrix. :matrix The norm of the matrix row vectors norm Norm; The calculation process for the significance weight in step three is as follows: Step 3a: For the front Noise extracted from the frame and noise in the current frame Perform mean filtering to obtain The calculation formula is as follows: ， (3) The symbols in formula (3) have the following meanings: :current Frame, number The noise matrix of the next iteration; :forward The noise matrix of the frame; Mean filtering operator; : The noise tensor obtained after mean filtering; Step 3b: For Perform a three-dimensional dilation calculation to obtain The calculation formula is as follows: ， (4) The symbols in formula (4) have the following meanings: The tensor obtained after three-dimensional dilation; : Three-dimensional dilation operator; Step 3c: The last frame and The last frame is obtained by differential extraction The significance weights are calculated as follows: ， (5) The symbols in formula (5) have the following meanings: : The last frame and The difference result of the last frame, i.e. ; Step function, i.e. ; : No. Significance weights in the next iteration; Step 3d: Introduce the obtained weights into the optimization problem in Step 2. The optimization problem is as follows: ， (6) The symbols in formula (6) have the following meanings: Significance weight; Dot multiplication of matrices.

2. The method for detecting weak targets against a strong halo background based on smooth sparse decomposition according to claim 1, characterized in that: The calculation process for the spline basis described in step one is as follows: ， (1) The symbols in formula (1) have the following meanings: : The first spline basis matrix Okay, number The value of the column; : No. Each node.

3. The method for detecting weak targets against a strong halo background based on smooth sparse decomposition according to claim 1, characterized in that: The calculation process based on the alternating multiplier method in step four is as follows: Step 4a: Initialize the augmented Lagrange equation for the optimization problem, the specific formula is as follows: ，(7) The symbols in formula (7) have the following meanings: Lagrange multipliers; : Non-negative penalty factor; :Frobenius norm; Inner product operation; Step 4b: Parameter initialization: ； Step 4c: Fix ,renew The resulting subproblems are as follows: ， (8) The solution to formula (8) is as follows: ， (9) Step 4d: Fix ,renew The resulting subproblems are as follows: ， (10) The solution to formula (10) is as follows: ， (11) Step 4e: Fix ,renew The calculation formula is as follows: ， (12) Formula (12) is a The optimization problem is solved using the following Gaussian function: ， (13) Step 4f: Fix ,renew The calculation formula is as follows: ， (14) Formula (14) is a The optimization problem can be solved using the following formula: ， (15) Step 4e: Fix ,renew The calculation formula is as follows: ， (16) Formula (16) is a The optimization problem can be solved using the following formula: ， (17) Step 4f: Update The calculation formula is as follows: ， (17) Step 4g: Number of iterations ; Step 4h: Judgment Is it greater than If yes, then stop the iteration and go to step 4i; if no, then stop the iteration and go to step 4i when the following conditions are met: if the iteration stopping condition is not met and the number of iterations has not reached the maximum value, then go to step 4c. ， (18) Step 4i: Find the optimal solution and output the background matrix. and target matrix .

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