ISAR imaging method based on soft threshold shrinkage weighted L1 norm minimization

Abstract

The invention relates to an ISAR (Inverse Synthetic Aperture Radar) imaging method based on soft threshold shrinkage weighted L1 norm minimization. The ISAR imaging method comprises the following steps: S1, acquiring a target wavenumber domain echo after translation compensation; s2, in combination with the target wavenumber domain echo, introducing a soft threshold shrinkage weighting coefficient, and modeling reconstruction of a two-dimensional scattering point distribution matrix as a target optimization problem; s3, introducing an auxiliary variable matrix into the target optimization problem, and constructing the target optimization problem into which the auxiliary variable matrix is introduced into an augmented Lagrange function; and S4, based on the augmented Lagrangian function, solving a two-dimensional scattering point distribution matrix, an auxiliary variable matrix and a stretched Lagrangian multiplier matrix in sequence, performing loop iteration, and obtaining a reconstructed two-dimensional ISAR image from the two-dimensional scattering point distribution matrix after iteration is completed. The method can achieve the effects of higher convergence speed and better two-dimensional reconstruction effect under the conditions of low signal-to-noise ratio and large loss rate.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar, and particularly relates to an ISAR imaging method based on soft-threshold shrinkage weighted L1 norm minimization. Background Art

[0002] Inverse Synthetic Aperture Radar (ISAR) is a key technology for all-weather, all-day, long-distance, and high-resolution imaging of non-cooperative targets. It plays an important role in space situation awareness and air target surveillance. The ISAR imaging technology mainly relies on two key processes: First, high range resolution is achieved by transmitting large time-bandwidth product signals and pulse compression technology; Second, the relative motion between the target and the radar is used to synthesize a virtual aperture, thereby obtaining high azimuth resolution.

[0003] Under the conditions of high signal-to-noise ratio and small target rotation angle, for complete echo signals, the Range-Doppler (RD) algorithm or the Polar Format Algorithm (PFA) can be used to generate high-quality ISAR images and perform subsequent motion compensation. However, the actual situation in practical applications is often more complex and is mainly affected by the following factors: 1) During the target's entry and exit from the radar station, due to the long distance from the radar, the signal-to-noise ratio of the echo signal is low. 2) There are active or passive interferences, which may cause the loss of the echo frequency band. 3) The limitation of phased array radar resource scheduling makes it impossible for ISAR to continuously observe the same target, and some frequency bands may be unavailable, which will cause the loss of the echo signal in the azimuth direction. The above factors will seriously affect the performance of classical imaging algorithms, resulting in poor focusing of the imaging results and unable to obtain ideal imaging effects.

[0004] Two-dimensional Compressed Sensing (CS) is an effective method for solving two-dimensional sparse ISAR imaging problems. Traditional two-dimensional compressed sensing optimization methods mainly include the Alternating Direction Method of Multipliers (ADMM), Iterative Shrinkage-Thresholding Algorithms (ISTA), Sparse Bayesian Learning (SBL), etc. Methods such as the Two-Dimensional Fast Iterative Shrinkage-Thresholding Algorithm (2D FISTA) and the Two-Dimensional Alternating Direction Method of Multipliers (2D ADMM) utilize the Kronecker product property and implement two-dimensional image reconstruction in matrix form.

[0005] Based on the conventional L1 norm method, algorithm performance optimization can be achieved through "weighting". For example, the Constrained L1 Regularization Alternating Direction Method of Multipliers (CRL1-ADMM) proposed in CN112946644A uses a convolution operator to perform convolution calculations on any pixel in the image, that is, weights the pixel and its surrounding 8 pixels to achieve the dilation processing of the image pixel points.

[0006] However, for existing two-dimensional reconstruction algorithms such as 2D FISTA and 2D ADMM, the convergence speed will be greatly reduced under conditions of low signal-to-noise ratio and large defect rate. The CRL1-ADMM method uses a convolution operator to achieve the dilation processing of pixel points. Under low signal-to-noise ratio conditions, the image sparsity and resolution will decline, and the imaging result will show a defocus phenomenon, resulting in poor image quality.

[0007] Existing ISAR imaging methods based on the L1 norm have defects that it is difficult to obtain a well-focused imaging result under conditions of large defect rate or low signal-to-noise ratio, and even lead to non-convergence of the algorithm and inability to image. Summary of the Invention

[0008] To solve the above problems existing in the prior art, the present invention provides an ISAR imaging method based on soft threshold shrinkage weighted L1 norm minimization. The technical problems to be solved by the present invention are achieved through the following technical solutions:

[0009] An embodiment of the present invention provides an ISAR imaging method based on soft threshold shrinkage weighted L1 norm minimization, including the steps of:

[0010] S1. Obtain the target wavenumber domain echo after translational compensation;

[0011] S2. Combine the target wavenumber domain echo, introduce a soft threshold shrinkage weighting coefficient, and model the reconstruction of the two-dimensional scattering point distribution matrix as a target optimization problem;

[0012] S3. Introduce an auxiliary variable matrix into the target optimization problem, and construct the target optimization problem introduced with the auxiliary variable matrix into an augmented Lagrangian function;

[0013] S4. Based on the augmented Lagrangian function, sequentially solve the two-dimensional scattering point distribution matrix, the auxiliary variable matrix, and the scaled Lagrange multiplier matrix, and perform iterative cycles. The reconstructed two-dimensional ISAR image is obtained from the two-dimensional scattering point distribution matrix after the iteration is completed.

[0014] In an embodiment of the present invention, the target wavenumber domain echo is:

[0015] Y = Φ1XΦ2 + N

[0016] where Y is the target wavenumber domain echo, is the distance dictionary, P < U represents sparse band observation, is the two-dimensional scattering point distribution, i.e., the ISAR image to be reconstructed, is the azimuth dictionary representing sparse aperture observation, Q < V represents sparse aperture observation, is the complex noise matrix, is the set of complex numbers, P is the number of range bins sequentially extracted from the complete range bins, U is the number of complete range bins, Q is the number of azimuth bins sequentially extracted from the complete azimuth bins, and V is the number of complete azimuth bins.

[0017] In an embodiment of the present invention, the target optimization problem is:

[0018]

[0019] where X (n+1) is the two-dimensional scattering point distribution matrix of the (n + 1)-th iteration; ||·|| F is the Frobenius norm, Y is the target wavenumber domain echo, is the distance dictionary, P < U, is the two-dimensional scattering point distribution, is the azimuth dictionary, Q < V, is the complex noise matrix, is the complex number set, P is the number of range bins sequentially extracted from the complete range bins, U is the number of complete range bins, Q is the number of azimuth bins sequentially extracted from the complete azimuth bins, V is the number of complete azimuth bins; λ is the regularization parameter, δ is a constant, X (n) is the two-dimensional scattering point distribution matrix at the n-th iteration, is the soft thresholding shrinkage weighting coefficient; for all elements of the two-dimensional scattering point distribution, it satisfies is the element at the u-th row and v-th column of the two-dimensional scattering point distribution matrix at the n-th iteration.

[0020] In an embodiment of the present invention, the objective optimization problem for introducing the auxiliary variable matrix is:

[0021]

[0022] s.t. X - Z = 0

[0023] where, X (n+1) is the two-dimensional scattering point distribution matrix at the (n + 1)-th iteration; ||·|| F is the Frobenius norm, Y is the target wavenumber domain echo, is the range dictionary, P < U, is the two-dimensional scattering point distribution, is the azimuth dictionary, Q < V, is the complex noise matrix, complex number set, P is the number of range bins sequentially extracted from the complete range bins, U is the number of complete range bins, Q is the number of azimuth bins sequentially extracted from the complete azimuth bins, V is the number of complete azimuth bins; λ is the regularization parameter, δ is a constant, X (n) is the two-dimensional scattering point distribution matrix at the n-th iteration, is the soft thresholding shrinkage weighting coefficient; is the element at the u-th row and v-th column of the two-dimensional scattering point distribution matrix at the n-th iteration; Z is the introduced auxiliary variable matrix.

[0024] In an embodiment of the present invention, the augmented Lagrangian function is:

[0025]

[0026] where, X is the two-dimensional scattering point distribution matrix, Z is the introduced auxiliary variable matrix, is the Lagrange coefficient, ρ is the penalty parameter; ||·|| Fis the Frobenius norm, Y is the echo in the target wavenumber domain, is the range dictionary, P < U, is the two-dimensional scatterer distribution, is the azimuth dictionary, Q < V, is the complex noise matrix, is the set of complex numbers, P is the number of range bins sequentially extracted from the complete range bins, U is the number of complete range bins, Q is the number of azimuth bins sequentially extracted from the complete azimuth bins, V is the number of complete azimuth bins; λ is the regularization parameter, δ is a constant, X (n) is the two-dimensional scatterer distribution matrix at the nth iteration, is the soft-thresholding shrinkage weighting coefficient; is the element in the u-th row and v-th column of the two-dimensional scatterer distribution matrix at the nth iteration.

[0027] In one embodiment of the present invention, step S4 includes:

[0028] S41. Initialize the regularization parameter λ and the penalty parameter ρ, set the initial value of the auxiliary variable matrix to 0, and set the initial value of the scaled Lagrange multiplier matrix to 0;

[0029] S42. Use the auxiliary variable matrix at the (n - 1)th iteration and the scaled Lagrange multiplier matrix at the (n - 1)th iteration to solve the optimization function of the two-dimensional scatterer distribution matrix, and obtain the two-dimensional scatterer distribution matrix at the nth iteration;

[0030] S43. Use the two-dimensional scatterer distribution matrix at the nth iteration and the scaled Lagrange multiplier matrix at the (n - 1)th iteration to perform element-by-element solution calculation on the optimization function of the auxiliary variable matrix through soft thresholding, and obtain the auxiliary variable matrix at the nth iteration;

[0031] S44. Use the two-dimensional scatterer distribution matrix at the nth iteration and the auxiliary variable matrix at the nth iteration to solve and obtain the scaled Lagrange multiplier matrix at the nth iteration;

[0032] S45. Repeat steps S42 - S44 for cyclic iteration, and obtain the reconstructed two-dimensional ISAR image from the two-dimensional scatterer distribution matrix after the iteration is completed.

[0033] In one embodiment of the present invention, the two-dimensional scatterer distribution matrix X (n) at the nth iteration is:

[0034]

[0035] where X (n) is the two-dimensional scatterer distribution matrix at the nth iteration, Z (n-1)is the auxiliary variable matrix for the (n - 1)-th iteration, is the dilated Lagrange multiplier matrix for the (n - 1)-th iteration, ρ is the penalty parameter, is the distance dictionary, is the azimuth dictionary, and Y is the echo in the target wavenumber domain.

[0036] In an embodiment of the present invention, the auxiliary variable matrix for the n-th iteration is:

[0037]

[0038] where Z (n) is the auxiliary variable matrix for the n-th iteration; X (n) is the two-dimensional scattering point distribution matrix for the n-th iteration, is the dilated Lagrange multiplier matrix for the (n - 1)-th iteration, ρ is the penalty parameter, λ is the regularization parameter, and δ is a constant, is the element at the u-th row and v-th column of the two-dimensional scattering point distribution matrix for the n-th iteration.

[0039] In an embodiment of the present invention, the dilated Lagrange multiplier matrix for the n-th iteration is:

[0040]

[0041] where, is the dilated Lagrange multiplier matrix for the n-th iteration, is the dilated Lagrange multiplier matrix for the (n - 1)-th iteration, X (n) is the two-dimensional scattering point distribution matrix for the n-th iteration, Z (n) is the auxiliary variable matrix for the n-th iteration.

[0042] Compared with the prior art, the beneficial effects of the present invention:

[0043] The ISAR imaging method based on soft-threshold shrinkage weighted L1-norm minimization of the present invention introduces a soft-threshold shrinkage weighting coefficient when reconstructing and modeling the two-dimensional scattering point distribution matrix as an objective optimization problem, and can achieve a faster convergence speed and a better two-dimensional reconstruction effect under low signal-to-noise ratio and large loss rate conditions. Brief Description of the Drawings

[0044] Figure 1 is a schematic flow chart of an ISAR imaging method based on soft-threshold shrinkage weighted L1-norm minimization provided by an embodiment of the present invention;

[0045] Figure 2 is a schematic diagram of the imaging result of the complete echo with high signal-to-noise ratio of the test data provided by an embodiment of the present invention;

[0046] Figure 3 Schematic diagram of data missing forms and proportions provided by the embodiments of the present invention;

[0047] Figures 4a - 4d Comparison diagram of imaging results of different methods under the condition of 0 dB of echo after pulse pressure provided by the embodiments of the present invention;

[0048] Figure 5 Schematic diagram of the convergence curves of SRL1 2D ADMM and 2D FISTA algorithms provided by the embodiments of the present invention. Detailed implementation manners

[0049] The present invention will be further described in detail below in conjunction with specific embodiments, but the implementation manners of the present invention are not limited thereto.

[0050] Embodiment 1

[0051] Please refer to Figure 1 , Figure 1 Schematic diagram of the process of an ISAR imaging method based on soft threshold shrinkage weighted L1 norm minimization provided by the embodiments of the present invention. The ISAR imaging method based on soft threshold shrinkage weighted L1 norm minimization includes the following steps:

[0052] S1. Obtain the wavenumber domain echo of the target after translational compensation.

[0053] Specifically, after the radar receives the original echo signal reflected by the target, the original echo signal is preprocessed in sequence, such as denoising, range error correction, and Doppler frequency shift compensation, and after range compression and translational compensation of the preprocessed signal, the wavenumber domain echo of the target is obtained.

[0054] Wavenumber domain echo of the target Can be expressed as:

[0055] Y = Φ1XΦ2 + N

[0056] Where Y is the wavenumber domain echo of the target, Is the range dictionary, P < U represents sparse band observation, Is the two-dimensional scatterer distribution, that is, the ISAR image to be reconstructed, Is the azimuth dictionary, Q < V represents sparse aperture observation, Is the complex noise matrix, Is the complex number set, P is the number of range bins sequentially extracted from the complete range, U is the number of complete range bins, Q is the number of azimuth bins sequentially extracted from the complete azimuth, and V is the number of complete azimuth bins.

[0057] S2. Combine the target wavenumber domain echo and introduce a soft-thresholding shrinkage weighting coefficient to model the reconstruction of the two-dimensional scattering point distribution matrix as an objective optimization problem.

[0058] Specifically, use the 2D ADMM method to reconstruct the two-dimensional scattering point distribution matrix. To solve the two-dimensional scattering point distribution, introduce a soft-thresholding shrinkage weighting coefficient, and model the reconstruction of the two-dimensional scattering point distribution matrix using the 2D ADMM method as an objective optimization problem:

[0059]

[0060] where, X (n+1) is the two-dimensional scattering point distribution matrix at the (n + 1)-th iteration; ||·|| F is the Frobenius norm, λ is the regularization parameter, δ is a very small constant, for example, δ takes the value 1e-6, X (n) is the two-dimensional scattering point distribution matrix at the n-th iteration, is the soft-thresholding shrinkage weighting coefficient; for all elements of the two-dimensional scattering point distribution, it satisfies is the element in the u-th row and v-th column of the two-dimensional scattering point distribution matrix at the n-th iteration.

[0061] S3. Introduce an auxiliary variable matrix into the objective optimization problem and construct the objective optimization problem with the introduced auxiliary variable matrix as an augmented Lagrangian function.

[0062] Specifically, introduce an auxiliary variable matrix Z, and the objective optimization problem with the introduced auxiliary variable matrix can be obtained:

[0063]

[0064] s.t. X - Z = 0

[0065] where, Z is the introduced auxiliary variable matrix.

[0066] The augmented Lagrangian function of the objective optimization problem with the introduced auxiliary variable matrix is:

[0067]

[0068] where, is the Lagrange coefficient, and ρ is the penalty parameter.

[0069] S4. Based on the augmented Lagrangian function, sequentially solve the two-dimensional scattering point distribution matrix, the auxiliary variable matrix, and the scaled Lagrange multiplier matrix, and perform iterative loops. Obtain the reconstructed two-dimensional ISAR image from the two-dimensional scattering point distribution matrix after the iteration is completed. Specifically, it includes the steps:

[0070] S41. Initialize the regularization parameter λ and the penalty parameter ρ. Exemplarily, λ is manually set and adjusted according to empirical values. When too much information is lost in the image reconstruction result, λ is appropriately decreased. When there are too many false points in the image reconstruction result, λ is appropriately increased. Exemplarily, λ is set to 1; ρ is set to 1. And set the initial value of the auxiliary variable matrix Z 0 to 0, and set the initial value of the scaled Lagrange multiplier matrix to 0. At the same time, set the maximum number of iterations iter.

[0071] S42. Use the auxiliary variable matrix of the (n - 1)th iteration and the scaled Lagrange multiplier matrix of the (n - 1)th iteration to solve the optimization function of the two-dimensional scattering point distribution matrix, and obtain the two-dimensional scattering point distribution matrix of the nth iteration.

[0072] Specifically, the optimization function of the two-dimensional scattering point distribution matrix is:

[0073]

[0074] where const. is a constant.

[0075] Solving the optimization function of the two-dimensional scattering point distribution matrix yields the two-dimensional scattering point distribution matrix X (n) :

[0076]

[0077] where Z (n-1) is the auxiliary variable matrix of the (n - 1)th iteration, is the scaled Lagrange multiplier matrix of the (n - 1)th iteration,

[0078] S43. Use the two-dimensional scattering point distribution matrix of the nth iteration and the scaled Lagrange multiplier matrix of the (n - 1)th iteration to perform element-by-element solution calculation on the optimization function of the auxiliary variable matrix, and obtain the auxiliary variable matrix of the nth iteration.

[0079] Specifically, the optimization function of the auxiliary variable matrix is:

[0080]

[0081] Perform element-by-element calculation on the auxiliary variable matrix Z, and the expression for element-by-element calculation is:

[0082]

[0083] where Z uvis the element in the \(u\)-th row and \(v\)-th column of the auxiliary variable matrix \(Z\), \(X\) uv is the element in the \(u\)-th row and \(v\)-th column of the two-dimensional scattering point distribution matrix \(X\), is the element in the \(u\)-th row and \(v\)-th column of the scaled Lagrange multiplier matrix , \(\|\cdot\|_1\) is the \(L_1\) norm, const. is a constant.

[0084] Solve for the element in the \(u\)-th row and \(v\)-th column of the auxiliary variable matrix in the \(n\)-th iteration through soft thresholding:

[0085]

[0086] Thus, obtain the auxiliary variable matrix \(Z\) in the \(n\)-th iteration (n) :

[0087]

[0088] where \(Z\) (n) is the auxiliary variable matrix in the \(n\)-th iteration.

[0089] S44. Use the two-dimensional scattering point distribution matrix in the \(n\)-th iteration and the auxiliary variable matrix in the \(n\)-th iteration to solve for the scaled Lagrange multiplier matrix in the \(n\)-th iteration:

[0090]

[0091] where, is the scaled Lagrange multiplier matrix in the \(n\)-th iteration, is the scaled Lagrange multiplier matrix in the \((n - 1)\)-th iteration.

[0092] S45. Repeat steps S42 - S44 for cyclic iteration until the maximum number of iterations is reached, and use the two-dimensional scattering point distribution matrix \(X\) obtained in the last iteration (n) as the reconstructed two-dimensional ISAR image.

[0093] In summary, the process of step S4 is summarized in Table 1 as follows:

[0094] Table 1

[0095]

[0096] In this embodiment, by iteratively solving the two-dimensional scattering point distribution matrix in the \(n\)-th iteration, the auxiliary variable matrix in the \(n\)-th iteration, and the scaled Lagrange multiplier matrix in the \(n\)-th iteration, matrix calculations can be realized, greatly improving the calculation efficiency.

[0097] It should be noted that the method of introducing the soft-thresholding shrinkage weighting coefficient in this embodiment can be applied not only to the 2D ADMM method, but also to L1-norm optimization algorithms such as the Iterative Shrinkage Thresholding Algorithm (ISTA), Half-Quadratic Splitting Method (HQS), Fast Iterative Shrinkage Thresholding Algorithm (FISTA), and Approximate Message Passing Algorithm (AMP), so as to improve the algorithm convergence speed and reconstruction performance.

[0098] The ISAR imaging method based on soft-thresholding shrinkage weighted L1-norm minimization of the present invention introduces a soft-thresholding shrinkage weighting coefficient when reconstructing and modeling the two-dimensional scatterer distribution matrix as an objective optimization problem, and can achieve faster convergence speed and better two-dimensional reconstruction effect under the conditions of low signal-to-noise ratio and large loss rate.

[0099] This embodiment verifies the ISAR imaging method based on soft-thresholding shrinkage weighted L1-norm minimization through simulation.

[0100] Please refer to Figure 2 and Figure 3 , Figure 2 which is a schematic diagram of the imaging result of the complete echo with high signal-to-noise ratio of the test data provided by the embodiment of the present invention, that is, the label image. Figure 3 which is a schematic diagram of the data missing form and ratio provided by the embodiment of the present invention. Among them, the missing ratio is 75%. The white represents the useful data, and the black represents the missing data.

[0101] This embodiment uses the data shown in Figure 2 as the label image, and uses the existing 2D FISTA, 2D ADMM, CRL1-ADMM and the ISAR imaging method based on soft-thresholding shrinkage weighted L1-norm minimization of the present invention (SRL1 2D ADMM) to reconstruct the data of Figure 3 . For the reconstruction results, please refer to Figures 4a - 4d , Figures 4a - 4d which is a comparison chart of the imaging results of different methods under the condition of 0 dB of the pulse-compressed echo provided by the embodiment of the present invention. Figure 4a is the 2D FISTA method. Figure 4b is the 2D ADMM. Figure 4c is the CRL1-ADMM method. Figure 4d is the SRL1 2D ADMM method. It can be seen from Figures 4a - 4d that compared with the existing algorithms 2D FISTA, 2D ADMM, and CRL1-ADMM, the image reconstructed by the SRL1 2D ADMM algorithm is closer to the original image and has a better focusing effect.

[0102] To further analyze the performance of SRL1 2D ADMM, it is compared with 2D FISTA, 2D ADMM, and CRL1-ADMM. The evaluation metrics are the normalized mean square error (NMSE), peak signal-to-noise ratio (PSNR), structural similarity (SSIM), and information entropy (Entropy). For the evaluation results, please refer to Table 2, which shows the evaluation metrics of the processing results of the SRL1 2D ADMM, 2D FISTA, 2D ADMM, and CRL1-ADMM algorithms.

[0103] Table 2

[0104] Method NMSE PSNR SSIM ENT 2D FISTA 0.6016 31.6338 0.8840 0.0953 2D ADMM 0.5845 31.8842 0.8892 0.1003 CRL1 - ADMM 0.6505 30.9546 0.8731 0.4038 SRL1 2D ADMM 0.3093 37.4112 0.9579 0.0918

[0105] As can be seen from Table 2, the normalized mean square error (NMSE) of the processing result of the SRL1 2D ADMM algorithm is smaller than that of other algorithms, indicating that the image reconstructed by the SRL1 2D ADMM algorithm is closer to the original; the peak signal-to-noise ratio (PSNR) is larger than that of other algorithms, indicating that the image quality of the processing result of the SRL1 2D ADMM algorithm is better; the structural similarity (SSIM) is closer to 1 than that of other algorithms, indicating that the image reconstructed by the SRL1 2D ADMM algorithm is closer to the original; the information entropy (Entropy) is smaller than that of other algorithms, indicating that the image focus effect of the processing result of the SRL1 2D ADMM algorithm is better. In summary, compared with the existing algorithms 2D FISTA, 2D ADMM, and CRL1-ADMM, the SRL1 2D ADMM algorithm has a better two-dimensional reconstruction effect.

[0106] Please refer to Figure 5 , Figure 5 , which is a schematic diagram of the convergence curves of the SRL1 2D ADMM and 2D FISTA algorithms provided by the embodiments of the present invention. Combining Table 2 and Figure 5 it can be seen that SRL1 2D ADMM converges faster than the original 2D ADMM, and the final NMSE is smaller.

[0107] This embodiment proposes an ISAR imaging method based on soft-threshold shrinkage weighted L1 norm minimization. Compared with existing algorithms such as 2D FISTA, 2D ADMM, and CRL1-ADMM, by increasing the soft-threshold shrinkage weighting coefficient, two-dimensional ISAR image reconstruction can be achieved under low signal-to-noise ratio and large defect rate conditions, achieving a faster convergence speed and a better two-dimensional reconstruction effect.

[0108] The above content is a further detailed description of the present invention in combination with specific preferred embodiments. It cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the concept of the present invention, several simple deductions or substitutions can be made, which should all be regarded as belonging to the protection scope of the present invention.

Claims

1. An ISAR imaging method based on soft-thresholding shrinkage weighted L1 norm minimization, characterized in that, Including the steps: S1. Obtain the target wavenumber domain echo after translational compensation; S2. Combining the target wavenumber domain echo, introducing a soft threshold shrinkage weighting coefficient, and reconstructing the two-dimensional scattering point distribution matrix into a target optimization problem; S3. Introduce an auxiliary variable matrix into the target optimization problem, and construct the target optimization problem with the introduced auxiliary variable matrix into an augmented Lagrangian function; S4. Based on the augmented Lagrangian function, solve the two-dimensional scattering point distribution matrix, the auxiliary variable matrix, and the scaled Lagrange multiplier matrix in sequence, and perform cyclic iteration. The reconstructed two-dimensional ISAR image is obtained from the two-dimensional scattering point distribution matrix after the iteration is completed.

2. The ISAR imaging method based on soft-thresholding shrinkage weighted L1-norm minimization according to claim 1, wherein The target wavenumber domain echo is: Y = Φ1XΦ2 + N where Y is the echo in the target wavenumber domain, is the range dictionary, P < U represents sparse band observations, is the two-dimensional scatterer distribution, i.e., the ISAR image to be reconstructed, is the azimuth dictionary, Q < V represents sparse aperture observations, is the complex noise matrix, is the set of complex numbers, P is the number of range profiles sequentially extracted from the complete range profile, U is the number of complete range profiles, Q is the number of azimuth profiles sequentially extracted from the complete azimuth profile, and V is the number of complete azimuth profiles.

3. The ISAR imaging method based on soft-thresholding shrinkage weighted L1-norm minimization according to claim 1, wherein The target optimization problem is: Among them, X (n+1) is the two-dimensional scattering point distribution matrix of the (n + 1)-th iteration; ‖·|| F is the Frobenius norm, Y is the echo in the target wavenumber domain, is the range dictionary, P<U, is the two-dimensional scattering point distribution, is the azimuth dictionary, Q<V, is the complex noise matrix, is the set of complex numbers, P is the number of range bins sequentially extracted from the complete range bins, U is the number of complete range bins, Q is the number of azimuth bins sequentially extracted from the complete azimuth bins, V is the number of complete azimuth bins; λ is the regularization parameter, δ is a constant, X (n) is the two-dimensional scattering point distribution matrix of the n-th iteration, is the soft-thresholding shrinkage weighting coefficient; for all elements of the two-dimensional scattering point distribution, it satisfies is the element in the u-th row and v-th column of the two-dimensional scattering point distribution matrix of the n-th iteration.

4. The ISAR imaging method based on soft-thresholding shrinkage weighted L1 norm minimization according to claim 1, characterized in that The target optimization problem with the introduced auxiliary variable matrix is: s.t. X - Z = 0 Among them, X (n+1) is the two-dimensional scattering point distribution matrix of the (n + 1)-th iteration; ||·|| F is the Frobenius norm, Y is the echo in the target wavenumber domain, is the range dictionary, P<U, is the two-dimensional scattering point distribution, is the azimuth dictionary, Q<V, is the complex noise matrix, is the set of complex numbers, P is the number of range bins sequentially extracted from the complete range bins, U is the number of complete range bins, Q is the number of azimuth bins sequentially extracted from the complete azimuth bins, V is the number of complete azimuth bins; λ is the regularization parameter, δ is a constant, X (n) is the two-dimensional scattering point distribution matrix of the n-th iteration, is the soft-thresholding shrinkage weighting coefficient; is the element in the u-th row and v-th column of the two-dimensional scattering point distribution matrix of the n-th iteration; Z is the introduced auxiliary variable matrix.

5. The ISAR imaging method based on soft threshold shrinkage weighted L1 norm minimization according to claim 1, wherein The augmented Lagrangian function is: Among them, X is a two-dimensional scattering point distribution matrix, Z is an introduced auxiliary variable matrix, is the Lagrange coefficient, ρ is the penalty parameter; ||·|| F is the Frobenius norm, Y is the target wavenumber domain echo, is the range dictionary, P<U, is the two-dimensional scattering point distribution, is the azimuth dictionary, Q<V, is the complex noise matrix, is the set of complex numbers, P is the number of range bins sequentially extracted from the complete range bins, U is the number of complete range bins, Q is the number of azimuth bins sequentially extracted from the complete azimuth bins, V is the number of complete azimuth bins; λ is the regularization parameter, δ is a constant, X (n) is the two-dimensional scattering point distribution matrix at the nth iteration, is the soft threshold shrinkage weighting coefficient; is the element in the u-th row and v-th column of the two-dimensional scattering point distribution matrix at the nth iteration.

6. The ISAR imaging method based on soft-thresholding shrinkage weighted L1 norm minimization according to claim 1, wherein Step S4 includes: S41. Initialize the regularization parameter λ and the penalty parameter ρ, set the initial value of the auxiliary variable matrix to 0, and set the initial value of the scaled Lagrange multiplier matrix to 0; S42. Using the auxiliary variable matrix of the (n - 1)th iteration and the scaled Lagrange multiplier matrix of the (n - 1)th iteration, solve the optimization function of the two-dimensional scattering point distribution matrix to obtain the two-dimensional scattering point distribution matrix of the nth iteration; S43. Using the two-dimensional scattering point distribution matrix of the nth iteration and the scaled Lagrange multiplier matrix of the (n - 1)th iteration, perform element-by-element solution calculation on the optimization function of the auxiliary variable matrix through soft threshold to obtain the auxiliary variable matrix of the nth iteration; S44. Using the two-dimensional scattering point distribution matrix of the nth iteration and the auxiliary variable matrix of the nth iteration, solve to obtain the scaled Lagrange multiplier matrix of the nth iteration; S45. Repeat steps S42 - S44 for cyclic iteration. The reconstructed two-dimensional ISAR image is obtained from the two-dimensional scattering point distribution matrix after the iteration is completed.

7. The ISAR imaging method based on soft-thresholding shrinkage weighted L1 norm minimization according to claim 6, wherein The two-dimensional scattering point distribution matrix X of the nth iteration (n) is as follows: Among them, X (n) is the two-dimensional scattering point distribution matrix for the nth iteration, Z (n-1) is the auxiliary variable matrix for the (n - 1)th iteration, is the stretched Lagrange multiplier matrix for the (n - 1)th iteration, ρ is the penalty parameter, is the distance dictionary, is the azimuth dictionary, Y is the target wavenumber domain echo, is the set of complex numbers, P is the number of range bins sequentially extracted from the complete range bins, U is the number of complete range bins, Q is the number of azimuth bins sequentially extracted from the complete azimuth bins, and V is the number of complete azimuth bins.

8. The ISAR imaging method based on soft-thresholding shrinkage weighted L1-norm minimization according to claim 6, characterized in that The auxiliary variable matrix of the nth iteration is: where, Z (n) is the auxiliary variable matrix for the n-th iteration; X (n) is the two-dimensional scattering point distribution matrix for the n-th iteration, is the dilated Lagrange multiplier matrix for the (n - 1)-th iteration, ρ is the penalty parameter, λ is the regularization parameter, and δ is a constant, is the element at the u-th row and v-th column of the two-dimensional scattering point distribution matrix for the n-th iteration.

9. The ISAR imaging method based on soft-thresholding shrinkage weighted L1 norm minimization according to claim 6, wherein, The scaled Lagrange multiplier matrix of the nth iteration is: Among them, is the scaled Lagrange multiplier matrix for the nth iteration, is the scaled Lagrange multiplier matrix for the (n - 1)th iteration, X (n) is the two-dimensional scattering point distribution matrix for the nth iteration, Z (n) is the auxiliary variable matrix for the nth iteration.

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