Radar sparse contour preserving super-resolution imaging method
By constructing a radar azimuth echo signal model and combining weighted l1 norm and contour maintenance constraints, the problem is decomposed by using the Bregman method to solve the problem of poor contour details in the radar super-resolution method, and high azimuth resolution and contour details are achieved protection to obtain higher quality imaging effects.
Patent Information
- Application Number
- CN202411346803.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-09-26
- Publication Date
- 2024-12-20
AI Technical Summary
The existing radar super-resolution method fails to effectively maintain contour details in scenarios with large edge variations, and the angle resolution is insufficient.
Construct the radar azimuth echo signal model, use weighted l1 norm and contour to maintain the constraint terms, and combine the Bregman method to decompose the problem into subproblems, and achieve the sparseness of the goal through sparse iterative covariance estimation and total variance norm optimization cost function. Sexual reconstruction and contour detail protection.
The high orientation resolution and contour detail are achieved to achieve higher quality imaging effects, which exceeds the limitations of existing methods in resolution and detail protection.
Smart Images
Figure CN119168868A_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of radar imaging, and in particular relates to a radar sparse contour preserving super-resolution imaging method. Background Art
[0002] Radar sensors have been widely used in the civilian field due to their all-day and all-weather imaging capabilities, such as terrain mapping, autonomous landing, and regional reconnaissance. By transmitting linear frequency modulation (LFM) signals and performing matched filtering in the range direction, high resolution in the range direction can be easily achieved. However, since the antenna aperture is limited by the physical size of the airborne platform, the azimuth resolution is very poor. In order to improve the imaging resolution of radar, the literature "Petre Stoica, Prabhu Babu, and Jian Li, 'New method of sparse parameter estimation in separable models and its use for spectral analysis of irregularly sampled data, 'IEEE Transactions on Signal Processing, vol.59, no.1, pp.35-47, 2011" proposed a sparse iterative covariance estimation (SPICE) method. This method makes full use of the sparsity of target distribution in the scene and obtains a higher angular resolution. However, for scenes with large edge changes, this method fails to maintain more contour details. The paper "Qiping Zhang, YinZhang, Yongchao Zhang, Yulin Huang, and Jianyu Yang, 'Airborne radar super-resolution imaging based on fast total variation method, 'Remote Sensing, vol.13, no.4, 2021" proposes a total variation regularization method for radar angle super-resolution imaging. This method uses the total variation norm as a penalty term to maintain the edge details of the target and is applied to high-quality imaging. However, this method fails to provide better angular resolution. Summary of the invention
[0003] In order to solve the above technical problems, the present invention proposes a radar sparse contour preserving super-resolution imaging method to solve the problem that the existing super-resolution methods have poor edge contour detail preservation.
[0004] The technical solution adopted by the present invention is: a radar sparse contour preserving super-resolution imaging method, the specific steps are as follows:
[0005] Step 1: Construct a radar azimuth echo signal model;
[0006] The azimuth convolution model expression of airborne radar is as follows:
[0007]
[0008] in, represents the echo vector, N represents the number of sampling points in the azimuth of the echo signal, represents a complex set, [] T Represents a transpose operation. represents the target scattering vector, K represents the number of sampling points in the target azimuth, Represents a convolution operation. represents additive white Gaussian noise (AWGN). represents the antenna pattern vector, and L represents the number of sampling points of the antenna pattern.
[0009] Rewrite equation (1) into matrix-vector multiplication form, the expression is as follows:
[0010] y=As+n (2)
[0011] in, represents the steering matrix, and its specific expression is as follows:
[0012]
[0013] Among them, N, K, and L satisfy the relationship N=K+L-1.
[0014] Step 2: Based on step 1, construct the cost function, derive the weighted square root minimum absolute value convergence and selection operator formula in the sparse scene, and use the weighted l1 norm to ensure the sparsity of the reconstructed target;
[0015] According to the sparse covariance criterion, the optimization cost function expression of the sparse iterative covariance estimation algorithm is as follows:
[0016]
[0017] in,
[0018]
[0019] in, represents the estimate of the target scattering vector s, ||·|| F represents the Frobenius norm, R -1 / 2 Represents R -1 The Hermitian positive definite root mean square of Hrepresents the conjugate transpose, and I represents the N×N identity matrix. i represents the i-th column of the matrix G, P represents the set matrix of target scattering power and noise standard deviation, diag(·) represents the diagonal matrix converted from the vector, represents the noise variance, i=1,2,…,N.
[0020] Then the equivalent expression of minimizing equation (5) is as follows:
[0021]
[0022] Where p represents the set vector of target scattered power and noise standard deviation, p = [p1, p2, ..., p N+K ] T , and P = diag(p), the specific expression of W is as follows:
[0023]
[0024] Assume that the variance of the noise term is consistent, that is, According to the derivation, the optimization problem (6) is equivalent to a weighted mean square LASSO problem, which is expressed as follows:
[0025]
[0026] Among them, the weighted matrix D satisfies the following conditional expression:
[0027]
[0028] Among them, a K represents the Kth column vector of the steering matrix A.
[0029] Formula (8) is the optimization problem The Lagrangian form of
[0030] Among them, ε represents a small positive number set according to the actual situation, D′ represents the mapping matrix of D, and There is a bidirectional mapping relationship.
[0031] Then the original sparse iterative covariance estimation method is equivalent to solving the weighted LASSO problem J1 of equation (10), which is expressed as follows:
[0032]
[0033] Step 3: Based on step 2, the contour preservation constraint term and the weighted l1 norm constraint are combined into a joint constraint to construct a new cost function;
[0034] The anisotropic total variation norm is used to describe the azimuthal gradient information of the target, and the expression is as follows:
[0035]
[0036] Among them, ||·|| TV represents the total variation norm, represents the azimuthal derivative, and its matrix form is as follows:
[0037]
[0038] By adding the azimuthal gradient information to equation (10), the new cost function J2 can be expressed as follows:
[0039]
[0040] Among them, μ represents the introduced contour preservation regularization parameter; is the error norm term; ||Ds||1 is the weighted sparse constraint; is a contour preserving constraint.
[0041] Step 4: Based on step 3, the original problem is divided into three sub-problems using the Bregman method and the sub-problems are solved separately, and the imaging results are output to achieve azimuth super-resolution imaging;
[0042] Introducing intermediate variables d1 and d2 to solve equation (13), equation (13) becomes a constraint problem, expressed as follows:
[0043]
[0044] Then equation (14) can be rewritten as follows:
[0045]
[0046] Among them, γ1 and γ2 represent the introduced Lagrange multiplier coefficients.
[0047] Then, the Bregman method is introduced and equation (15) is rewritten to obtain the following expression:
[0048]
[0049] Where k represents the number of iterations, Represents the introduced intermediate variables.
[0050] Then separate the variables and split equation (16) into three sub-problems and solve them separately, as follows:
[0051] (1) The first question;
[0052]
[0053] The solution expression is as follows:
[0054]
[0055] (2) The second question;
[0056]
[0057] The solution expression is as follows:
[0058]
[0059] Wherein, shrink represents the shrinkage function, and x and η are set as the independent variables of the function. The specific expression is as follows:
[0060]
[0061] (3) The third problem is given by equations (17) and (18);
[0062]
[0063] Initialize each parameter in the iteration process to k=0,s (k) =y, Substituting the above variable initialization values into the iteration process, the expression is as follows:
[0064]
[0065] Finally, after K iterations or when the iteration termination condition ||s is met k+1 -s k ||2<δ, the target scattering can be obtained, and azimuth super-resolution imaging can be achieved while ensuring the target azimuth profile.
[0066] Wherein, δ represents a small positive number set according to the actual situation.
[0067] The beneficial effects of the present invention are as follows: the method of the present invention first constructs a radar azimuth echo signal model, then derives the weighted square root minimum absolute value convergence and selection operator formula in a sparse scene, uses the weighted l1 norm to ensure the sparsity of the reconstructed target, and then combines the contour preservation constraint with the weighted l1 norm constraint as a joint constraint, and finally uses the Bregman method to divide the original problem into three sub-problems for solving them separately, obtains a fast iterative estimate of target scattering, and realizes radar fast super-resolution imaging. The method of the present invention obtains high azimuth resolution through the weighted l1 norm constraint in the sparse super-resolution method, uses the contour preservation constraint to maintain the imaging edge details, obtains a higher quality imaging effect, can obtain azimuth super-resolution, and can better maintain contour details, and has more contour details and higher resolution than the existing super-resolution method. BRIEF DESCRIPTION OF THE DRAWINGS
[0068] Figure 1 The present invention provides a flow chart of a radar sparse contour preserving super-resolution imaging method.
[0069] Figure 2 Schematic diagram of the original scene of the radar in the embodiment of the present invention.
[0070] Figure 3 This is a diagram of the real beam imaging result when SNR=25dB in an embodiment of the present invention.
[0071] Figure 4 Graph showing the imaging result of the total variation method in an embodiment of the present invention.
[0072] Figure 5 This is an imaging result diagram of the split sparse iterative covariance estimation method in an embodiment of the present invention.
[0073] Figure 6 Graph showing the imaging result of the method of the present invention in an embodiment of the present invention. DETAILED DESCRIPTION
[0074] The present invention is mainly verified by simulation experiment, and all steps and conclusions are verified to be correct on Matlab 2018. The method of the present invention is further described below in conjunction with the accompanying drawings and embodiments.
[0075] like Figure 1 As shown, a flow chart of a radar sparse contour preserving super-resolution imaging method of the present invention, the specific steps are as follows:
[0076] Step 1: Construct a radar azimuth echo signal model;
[0077] In this embodiment, the original scene of the radar is as follows: Figure 2 shown. Figure 2 A typical sparse scene is shown as 11 ships parked around the coastline. In the example of surface target radar signal, the scanning range The initialization azimuth scanning speed is 100° / s, the beam width is 3°, the PRF is 1000Hz, and the carrier frequency is f c is 10GHz, the signal pulse width T is 1μs, the frequency modulation bandwidth B is 45MHz, and the sampling frequency f s It is 90MHz.
[0078] The azimuth convolution model expression of airborne radar is as follows:
[0079]
[0080] in, represents the echo vector, N represents the number of sampling points in the azimuth of the echo signal, represents a complex set, [] T Represents a transpose operation. represents the target scattering vector, K represents the number of sampling points in the target azimuth, Represents a convolution operation. represents additive white Gaussian noise (AWGN). represents the antenna pattern vector, and L represents the number of sampling points of the antenna pattern.
[0081] Rewrite equation (1) into matrix-vector multiplication form, the expression is as follows:
[0082] y=As+n (2)
[0083] in, represents the steering matrix, and its specific expression is as follows:
[0084]
[0085] Among them, N, K, and L satisfy the relationship N=K+L-1.
[0086] Step 2: Based on step 1, construct the cost function, derive the weighted square root minimum absolute value convergence and selection operator formula in the sparse scene, and use the weighted l1 norm to ensure the sparsity of the reconstructed target;
[0087] According to the sparse covariance criterion, the optimization cost function expression of the sparse iterative covariance estimation algorithm is as follows:
[0088]
[0089] in,
[0090]
[0091] in, represents the estimate of the target scattering vector s, ||·|| F represents the Frobenius norm, R -1 / 2 Represents R -1 The Hermitian positive definite root mean square of H represents the conjugate transpose, and I represents the N×N identity matrix. i represents the i-th column of the matrix G, P represents the set matrix of target scattering power and noise standard deviation, diag(·) represents the diagonal matrix converted from the vector, represents the noise variance, i=1,2,…,N.
[0092] Then the equivalent expression of minimizing equation (5) is as follows:
[0093]
[0094] Where p represents the set vector of target scattered power and noise standard deviation, p = [p1, p2, ..., p N+K ] T , and P = diag(p), the specific expression of W is as follows:
[0095]
[0096] Assume that the variance of the noise term is consistent, that is, According to the derivation, the optimization problem (6) is equivalent to a weighted mean square LASSO problem, which is expressed as follows:
[0097]
[0098] Among them, the weighted matrix D satisfies the following conditional expression:
[0099]
[0100] Among them, a K represents the Kth column vector of the steering matrix A.
[0101] Formula (8) is the optimization problem The Lagrangian form of
[0102] Among them, ε represents a small positive number set according to the actual situation, D′ represents the mapping matrix of D, and There is a bidirectional mapping relationship.
[0103] Then the original sparse iterative covariance estimation method is equivalent to solving the weighted LASSO problem J1 of equation (10), which is expressed as follows:
[0104]
[0105] Step 3: Based on step 2, the contour preservation constraint term and the weighted l1 norm constraint are combined into a joint constraint to construct a new cost function;
[0106] In order to consider the azimuthal edge information of the target, the anisotropic total variation norm is used to describe the azimuthal gradient information of the target. The expression is as follows:
[0107]
[0108] Among them, ||·|| TV represents the total variation norm, represents the azimuthal derivative, and its matrix form is as follows:
[0109]
[0110] By adding the azimuth gradient information to equation (10) to maintain the contour of the reconstructed target, the new cost function J2 can be expressed as follows:
[0111]
[0112] Where μ represents the introduced contour preservation regularization parameter, which is used to balance the resolution constraint and the edge constraint. In formula (13), is the error norm term, used to ensure fidelity; ||Ds||1 is the weighted sparse constraint, used to ensure sparsity; It is a contour preserving constraint, which is used to ensure the edge details of the image orientation.
[0113] Step 4: Based on step 3, the original problem (Equation (13)) is divided into three sub-problems using the Bregman method and solved separately, and the imaging results are output to achieve azimuth super-resolution imaging;
[0114] In order to solve equation (13), the intermediate variables d1 and d2 are introduced, and equation (13) becomes a constraint problem, which is expressed as follows:
[0115]
[0116] Then formula (14) can be rewritten as follows:
[0117]
[0118] Among them, γ1 and γ2 represent the introduced Lagrange multiplier coefficients.
[0119] Then, the Bregman method is introduced and equation (15) is rewritten to obtain the following expression:
[0120]
[0121] Where k represents the number of iterations, Represents the introduced intermediate variables.
[0122] Then separate the variables and split equation (16) into three sub-problems and solve them separately, as follows:
[0123] (1) The first question;
[0124]
[0125] The solution expression is as follows:
[0126]
[0127] (2) The second question;
[0128]
[0129] The solution expression is as follows:
[0130]
[0131] Wherein, shrink represents the shrinkage function, and x and η are set as the independent variables of the function. The specific expression is as follows:
[0132]
[0133] (3) The third problem is given by equations (17) and (18);
[0134]
[0135] Initialize each parameter in the iteration process to k=0,s (k) =y, Substituting the above variable initialization values into the iteration process, the expression is as follows:
[0136]
[0137] Finally, after K iterations or when the iteration termination condition ||s is met k+1 -s k ||2<δ, the target scattering can be obtained, and azimuth super-resolution imaging can be achieved while ensuring the target azimuth profile.
[0138] Wherein, δ represents a small positive number set according to the actual situation, and is set to 10 in this embodiment. -3 . .
[0139] In this embodiment, Figure 3 This is the result of real beam imaging under SNR = 25dB. From the simulation results, it can be seen that Figure 3 In the real beam result, the adjacent targets in the center of the scene are blurred due to the wide main lobe in azimuth, making them difficult to distinguish, and the coastline outline is blurred. Figure 4 is the imaging result diagram of the total variation method, Figure 4 The reconstruction results of the total variation method are shown. Figure 5 is the imaging result of the split sparse iterative covariance estimation method, Figure 5 The reconstruction results of the split sparse iterative covariance estimation method are shown. This method can reconstruct the target well, but cannot restore the contour details in the azimuth direction well. Figure 6 It is the result of reconstruction by the method of the present invention. Compared with the existing method, the method of the present invention can obtain higher resolution and sidelobe suppression ratio, and can also protect the azimuth profile details.
[0140] In summary, the method of the present invention obtains high azimuthal resolution through the weighted l1 norm constraint in the sparse super-resolution method, and uses the contour preserving constraint to maintain the imaging edge details, thereby obtaining a higher quality imaging effect. It can not only obtain azimuthal super-resolution, but also better maintain contour details. It has more contour details and higher resolution than the existing super-resolution methods.
[0141] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.
Claims
1. A radar sparse contour preserving super-resolution imaging method, the specific steps are as follows: Step 1: Construct a radar azimuth echo signal model; The azimuth convolution model expression of airborne radar is as follows: in, represents the echo vector, N represents the number of sampling points in the azimuth of the echo signal, represents a complex set, [] T Represents a transpose operation; represents the target scattering vector, K represents the number of sampling points in the target azimuth, Represents the convolution operation; represents additive white Gaussian noise (AWGN); represents the antenna pattern vector, and L represents the number of sampling points of the antenna pattern; Rewrite equation (1) into matrix-vector multiplication form, the expression is as follows: y=As+n (2) in, represents the steering matrix, and its specific expression is as follows: Wherein, N, K, L satisfy the relationship N=K+L-1; Step 2: Based on step 1, construct the cost function, derive the weighted square root minimum absolute value convergence and selection operator formula in the sparse scene, and use the weighted l1 norm to ensure the sparsity of the reconstructed target; According to the sparse covariance criterion, the optimization cost function expression of the sparse iterative covariance estimation algorithm is as follows: in, in, represents the estimate of the target scattering vector s, ||·|| F represents the Frobenius norm, R -1 / 2 Represents R -1 The Hermitian positive definite root mean square of H represents conjugate transpose, I represents the N×N identity matrix; g i represents the i-th column of the matrix G, P represents the set matrix of target scattering power and noise standard deviation, diag(·) represents the diagonal matrix converted from the vector, represents the noise variance, i=1,2,…,N; Then the equivalent expression of minimizing equation (5) is as follows: Where p represents the set vector of target scattered power and noise standard deviation, p = [p1, p2, ..., p N+K ] T , and P = diag(p), the specific expression of W is as follows: Assume that the variance of the noise term is consistent, that is, According to the derivation, the optimization problem (6) is equivalent to a weighted mean square LASSO problem, which is expressed as follows: Among them, the weighted matrix D satisfies the following conditional expression: Among them, a K represents the Kth column vector of the steering matrix A; Formula (8) is the optimization problem The Lagrangian form of Among them, ε represents a small positive number set according to the actual situation, D′ represents the mapping matrix of D, and There is a bidirectional mapping relationship; Then the original sparse iterative covariance estimation method is equivalent to solving the weighted LASSO problem J1 of equation (10), which is expressed as follows: Step 3: Based on step 2, the contour preservation constraint term and the weighted l1 norm constraint are combined into a joint constraint to construct a new cost function; The anisotropic total variation norm is used to describe the azimuthal gradient information of the target, and the expression is as follows: ||s|| TV =||▽s||1 (11) Among them, ||·|| TV represents the total variation norm, ▽ represents the azimuthal derivative, and its matrix form is as follows: By adding the azimuthal gradient information to equation (10), the new cost function J2 can be expressed as follows: Among them, μ represents the introduced contour preservation regularization parameter; is the error norm term; ||Ds||1 is the weighted sparse constraint; μ||▽s||1 is the contour preservation constraint; Step 4: Based on step 3, the original problem is divided into three sub-problems using the Bregman method and the sub-problems are solved separately, and the imaging results are output to achieve azimuth super-resolution imaging; Introducing intermediate variables d1 and d2 to solve equation (13), equation (13) becomes a constraint problem, expressed as follows: Then equation (14) can be rewritten as follows: Among them, γ1 and γ2 represent the introduced Lagrange multiplier coefficients; Then, the Bregman method is introduced and equation (15) is rewritten to obtain the following expression: Where k represents the number of iterations, Indicates the introduced intermediate variables; Then separate the variables and split equation (16) into three sub-problems and solve them separately, as follows: (1) The first question; The solution expression is as follows: (2) The second question; The solution expression is as follows: Wherein, shrink represents the shrinkage function, and x and η are set as the independent variables of the function. The specific expression is as follows: (3) The third problem is given by equations (17) and (18); Initialize each parameter in the iteration process to k=0,s (k) =y, Substituting the above variable initialization values into the iteration process, the expression is as follows: Finally, after K iterations or when the iteration termination condition ||s is met k+1 -s k ||2<δ, the target scattering can be obtained, and azimuth super-resolution imaging can be achieved while ensuring the target azimuth profile; Wherein, δ represents a small positive number set according to the actual situation.