A scanning radar anti-jamming super-resolution imaging method based on joint sparse constraint

Abstract

A super-resolution imaging method for scanning radar based on joint sparsity constraints is presented, belonging to the field of radar imaging. Improving the azimuth imaging resolution of scanning radar in jammed environments is a major challenge for real-aperture radar imaging. To address this, this invention combines the sparsity of interference in the range-time and azimuth-time domains with the sparsity of the target in the range-frequency and azimuth-time domains as joint constraints. On the one hand, the prior constraint of the sparsity of interference in the range-time and azimuth-time domains effectively separates interference from the echo signal, thereby suppressing interference. On the other hand, the constraint of the sparsity of target scattering in the range-frequency and azimuth-time domains effectively improves the azimuth resolution. Compared to traditional methods, the proposed method effectively solves the problem of super-resolution performance loss in jammed environments. Simulation and experimental results show that the method of this invention can effectively suppress interference while also improving azimuth resolution.

Description

Technical Field

[0001] This invention belongs to the field of radar imaging, and is particularly suitable for super-resolution imaging of forward-looking scanning radar. Specifically, it relates to a super-resolution imaging method for anti-jamming scanning radar based on joint sparse constraints. Background Technology

[0002] High-resolution imaging of the forward-looking area by forward-looking radar (FLAR) has urgent application needs in fields such as terrain avoidance, intelligent driving, and ship navigation. Real-aperture radar (PARa) has a limited antenna aperture, resulting in low azimuth resolution. To improve azimuth resolution, Tianzhi Sun et al. proposed a super-resolution imaging method for FLAR based on the Likes method. This method constrains the target's solution space using a maximum likelihood approach and then solves it using gradient descent, thus improving the azimuth resolution in FLAR imaging. However, this method lacks anti-jamming capability, leading to severe degradation of super-resolution performance in jammed environments. Deqing Mao et al. proposed an anti-jamming super-resolution imaging method for FLAR based on a non-uniform sampling model. When strong pulse interference is detected, the contaminated pulse is discarded, and then super-resolution reconstruction is performed using the non-uniform sampling model to reconstruct the target scattering from the uncontaminated signal. However, as the number of discarded pulses increases, the error of this model increases sharply, leading to a severe deterioration in super-resolution performance. Weixin Li et al. proposed a super-resolution imaging method for scanning radar based on variational Bayesian methods. By modeling interference as outliers in the azimuth direction and using the Student's t-distribution as the prior distribution of outlier noise, interference is eliminated in the azimuth direction. This method relies on the prior model, and when the model mismatch occurs, the imaging effect deteriorates. Although the above methods can improve imaging resolution or suppress interference, they cannot achieve both interference suppression and improved imaging resolution simultaneously. Summary of the Invention

[0003] To address the aforementioned technical problems, this invention provides a scanning radar anti-jamming super-resolution imaging method based on joint sparsity constraints. Compared to the limitations of traditional azimuth super-resolution methods that only process a single range cell, this invention extends it to the entire range cell range, improving super-resolution performance by fully utilizing the sparsity constraints of target scattering across the entire range cell. Furthermore, to effectively suppress the disruption of convolution relationships by interference and reduce interference-induced deconvolution errors, this invention fully utilizes the sparse prior characteristics of interference in the range-frequency domain and azimuth-time domain, employing a regularization method to constrain interference and achieve precise interference suppression. This invention effectively removes interference from echoes through joint sparsity constraints across the time and frequency domains, while simultaneously achieving efficient reconstruction of target scattering based on interference-free echoes, enabling stable and accurate reconstruction of target scattering even under interference environments. The specific details of this invention are as follows:

[0004] A scanning radar anti-jamming super-resolution imaging method based on joint sparse constraints includes the following steps:

[0005] Step 1: Based on the echo signal of the forward-looking area of ​​the scanning radar under interference environment, establish an echo convolution model, which is specifically represented by adding random interference signal to the convolution relationship between the target scattering vector and the antenna pattern;

[0006] Step 2: Construct a sparse regularized reconstruction model, specifically by using the least squares method to solve for the target scattering coefficients and introducing a model based on... Sparsity regularization constraints of norms;

[0007] Step 3: Transform the sparse regularized reconstruction model into a joint sparse constraint reconstruction model that solves for the target scattering coefficient and the interference signal;

[0008] Step 4: Solve the joint sparse constraint reconstruction model using the fast iterative soft thresholding method and the alternating direction multiplier method.

[0009] Furthermore, the sparse regularized reconstruction model is represented as follows:

[0010] ;

[0011] in, This represents the solved target scattering coefficient. This represents the echo signal across the entire range of cells. Represents the target scattering coefficient across the entire range cell. Represented as a convolution matrix written from the antenna pattern function, It is a regularization parameter. Representation matrix Norm, Representation matrix Norm.

[0012] Furthermore, the joint sparse constraint reconstruction model is expressed as follows:

[0013] ;

[0014] in, This represents the interference signal in the range-time domain versus the azimuth-time domain. For the normalized inverse Fourier transform matrix, For interference regularization parameters; To interfere with the sparse constraint term, This is a sparse constraint term for target scattering.

[0015] Furthermore, step four is specifically solved jointly in the following manner:

[0016] Solving the joint sparse constraint reconstruction model can be viewed as a two-layer minimum absolute value contraction and operator selection problem:

[0017] ;

[0018] The first layer is to solve for the interference signal. The first problem is to solve using a fast iterative soft thresholding method; the second layer involves solving for the target scattering coefficient. The problem is solved using the alternating direction multiplier method; the specific solution process is as follows:

[0019] Solving for interference signals Then, the original problem is transformed into:

[0020] ;

[0021] Among them, the fidelity term function It is a convex function and differentiable; regularization term function It is a convex function but not differentiable; for Differentiating, we get:

[0022] ;

[0023] in The fidelity function represents the pair of terms. The derivative, after derivation and solution, yields:

[0024] ;

[0025] in For the optimal result of interference, It is a soft threshold function. Step size, superscript Indicates the first The next iteration is performed to obtain the iterative results of the iterative soft thresholding algorithm. Here, the Nesterov acceleration algorithm can be introduced to accelerate the iteration of the soft threshold method.

[0026] Solve for the target scattering coefficient Then, the original problem is transformed into:

[0027] ;

[0028] Introducing auxiliary variables and dual variables Constructing the augmented Lagrange function :

[0029] ;

[0030] in These are the Lagrange multiplier parameters, for The subproblems are constructed and solved alternately. After the solutions converge, the final target scattering coefficient and interference signal are obtained.

[0031] Furthermore, regarding The subproblems are constructed and solved alternately as follows:

[0032] Solve subproblem 1: ;

[0033] right Differentiating gives ;

[0034] Solving for the given information ;in It is the identity matrix;

[0035] Solve subproblem 2: ;

[0036] Transforming the original problem into a set of separable problems yields... ; , This represents the number of sampling points in the distance direction.

[0037] set up ;

[0038] right Solving for the partial derivative yields the following results. ;

[0039] By moving direction ;

[0040] Solving for the given information ;

[0041] Solve subproblem 3: .

[0042] The innovation of this invention lies in addressing the low super-resolution imaging accuracy of forward-looking scanning radar under interference environments. The proposed anti-jamming super-resolution imaging method for scanning radar based on joint sparsity constraints achieves accurate reconstruction of the target scattering coefficients by jointly constraining the interference and target scattering coefficients. On one hand, the prior constraints on the sparsity of interference in the range-time and azimuth-time domains effectively separate interference from the echo signal, thereby suppressing interference. On the other hand, the sparsity constraints on target scattering in the range-frequency and azimuth-time domains effectively improve azimuth resolution. Finally, the anti-jamming super-resolution framework based on full-range-cell processing proposed in this invention avoids pulse-by-pulse interference suppression and range-by-range-cell super-resolution processing. Related methods remain within the scope of protection of this invention. Attached Figure Description

[0043] Figure 1A flowchart of the method provided for this invention.

[0044] Figure 2 This is a schematic diagram of a simulation scenario for a point target.

[0045] Figure 3 This is a schematic diagram of the simulated imaging results under a 10% random interference pulse environment.

[0046] Figure 4 This is a schematic diagram of the simulated imaging results under a 5% continuous interference pulse environment. Detailed Implementation

[0047] This invention uses simulation experiments to demonstrate the effectiveness of the proposed method. All steps and conclusions of this invention are verified on the Matlab 2019b simulation platform. The specific implementation steps are as follows: Figure 1 As shown in the accompanying drawings. To enable those skilled in the art to understand the invention, the invention will be further described below with reference to the accompanying drawings.

[0048] A scanning radar anti-jamming super-resolution imaging method based on joint sparse constraints includes the following steps:

[0049] Step 1: Establish a forward-looking scanning radar echo convolution model under interference conditions.

[0050] The echo model of the forward-looking area of ​​a scanning radar can be represented as the convolution relationship between the target scattering vector and the antenna pattern:

[0051]

[0052] in This represents the echo signal at a certain distance unit. This represents the number of sampling points in the azimuth direction. Indicates the first Echoes from sampling points in each azimuth direction Indicates the transpose operation; Represents the target scattering coefficient. The number of sampling points for the target scattering coefficient. Indicates the first Target scattering coefficients at each sampling point in each azimuth direction; Indicates additive noise. Indicates the first Noise at each sampling point in each direction; Represented as a convolution matrix derived from the antenna pattern function, specifically:

[0053]

[0054] in For antenna beam sampling vector, This represents the number of sampling points for the antenna pattern. Indicates the first The antenna sampling function for each azimuth sampling point has the following relationship:

[0055]

[0056] Since interference occurs randomly, it is assumed that the modulation of the antenna pattern only affects the energy of the interference and does not form a convolutional relationship like that of an echo. Therefore, the echo model under interference conditions is as follows:

[0057]

[0058] in This is an interference signal. Indicates the first Interference signals from sampling points in each azimuth direction. Next, extending the echo model to the full-range cell yields...

[0059]

[0060] in This represents the echo signal across the entire range of cells. The number of sampling points in the distance direction. Indicates the first The echo vector at a distance from the sampling point; Represents the target scattering coefficient across the entire range cell. Indicates the first The target scattering vector at each distance sampling point; This represents additive noise across the entire distance cell. Indicates the first A noise vector at a distance from each sampling point; This represents the interference signal across the entire range of cells. Indicates the first The interference vectors at each sampling point are then transformed into the range-time domain-azimuth time domain using an inverse Fourier transform, yielding:

[0061]

[0062] in This represents the interference signal in the range-time domain versus the azimuth-time domain, where Indicates the first Interference signals at a distance from the sampling point ; The normalized inverse Fourier transform matrix is ​​as follows:

[0063]

[0064] in Represents the imaginary unit. Represents the natural constant.

[0065] Step 2: Construct a sparse regularization reconstruction framework.

[0066] In forward-looking scanning radar super-resolution imaging, the interference-free observation model can be expressed as:

[0067]

[0068] To reconstruct the target scattering coefficients, the least squares method is used to solve the following optimization problem:

[0069]

[0070] in This represents the solved target scattering coefficient. Representation matrix Norm, This represents the square operation. By taking the derivative and setting it to zero, we can obtain the analytical solution to the above expression:

[0071]

[0072] in This represents the target scattering coefficient obtained based on the least squares method. The observation model... Substituting, we get:

[0073]

[0074] in It is a noise amplification matrix. From the perspective of matrix theory, due to the system measurement matrix... The severe ill-conditioning of convolution inversion amplifies noise during the solution process, leading to instability. Therefore, it is necessary to add constraint terms to the least squares problem to alleviate the ill-conditioning and transform it into a benign problem.

[0075] Based on the above optimization problem formula, adding a regularization constraint term, it becomes:

[0076]

[0077] in It is a least squares constraint, also known as a data fidelity term. It is a regularization constraint term. It is a regularization parameter used to adjust the strength of the regularization term.

[0078] In real-world scenarios of forward-looking radar imaging, targets of interest typically exhibit a sparse distribution within the imaging area. However... Norms are widely used to characterize the sparsity properties of a target, therefore this invention selects... The norm, acting as a sparse constraint on the solution, further transforms into an optimization problem of sparse regularized reconstruction:

[0079]

[0080] in Representation matrix Norm. By introducing Norm regularization constraints effectively suppress the image quality degradation caused by noise amplification on the one hand; on the other hand, by leveraging its inherent sparsity-induced properties, it enables the solution to converge in the sparsity direction, thereby improving the azimuth resolution.

[0081] Step 3: Constructing a joint sparse constraint reconstruction model.

[0082] Under interference, the azimuth convolution relationship is disrupted, leading to a sharp increase in reconstruction error for sparse regularized reconstruction. Interference exhibits sparsity in the range-time domain. Due to the randomness of interference in the azimuth direction, the interference signal can be considered sparse in both the two-dimensional range-time and azimuth-time domains. Therefore, sparse regularized reconstruction can be transformed into solving the following optimization problem:

[0083]

[0084] in This is a least squares constraint, also known as a data fidelity term; This is a sparse constraint term for interference, used to constrain the sparsity of interference and suppress it. This is a sparse constraint term for target scattering, used to constrain the sparsity of target scattering, thereby achieving azimuth super-resolution. This is the interference regularization parameter.

[0085] Step 4: Solve using a combination of Fast Iterative Soft Thresholding (FISTA) and Alternating Direction Multiplier Method (ADMM).

[0086] Solving the joint sparse constraint reconstruction model can be viewed as solving a two-layer minimum absolute value shrinkage and selection operator (LASSO) problem.

[0087]

[0088] The first layer is to solve the interference. To address the problem, this invention employs the Fast Iterative Soft Thresholding (FISTA) method, which can retain non-zero components and zero out small components. Since the interference and target echoes differ significantly, this method effectively separates "strong interference" from "weak echoes." The second layer involves solving for target scattering. To address this problem, this invention selects the ADMM method. This method achieves convergence through alternating solutions, and compared to FISTA, it better protects weak targets instead of directly setting them to zero. The specific solution process is as follows:

[0089] (1) Solving for interference The original problem is transformed into:

[0090]

[0091] Among them, the fidelity term function It is a convex function and differentiable; regularization term function It is a convex function but not differentiable. For Differentiation yields:

[0092]

[0093] in The fidelity function represents the pair of terms. The differential, ,in Let be the identity matrix. The above formula can be transformed into:

[0094]

[0095] in For the optimal result of interference, Step size, For the first The result of the second iteration. Based on the derivation, we get:

[0096]

[0097] intermediate variables , .set up

[0098]

[0099] For intermediate functions Solving by taking the partial derivative yields the following results.

[0100]

[0101] in

[0102]

[0103] in It is a soft threshold function. For the threshold, Represent the sign function. Calculate the iterative results using the Iterative Soft Thresholding (ISTA) method. To further accelerate the iteration of the ISTA method, the Nesterov acceleration algorithm is introduced. The specific iterative process of this algorithm is as follows:

[0104]

[0105] in For momentum parameters, Indicates the first The next iteration is the decision interference matrix. Intermediate variables set.

[0106] (2) Solving for target scattering The original problem is transformed into:

[0107]

[0108] Introducing auxiliary variables The above formula can be transformed into:

[0109]

[0110] Constructing the augmented Lagrangian function yields:

[0111]

[0112] in It is the introduced dual variable. These are the Lagrange multiplier parameters. Solve them alternately. .

[0113] Solve subproblem 1:

[0114]

[0115] right Differentiation yields

[0116]

[0117] Solving for the given information yields the following results:

[0118]

[0119] Solve subproblem 2:

[0120]

[0121] Transforming the original problem into a set of separable problems yields:

[0122]

[0123] set up

[0124]

[0125] right Solving by taking the partial derivative, we get:

[0126]

[0127] By shifting the direction, we can obtain:

[0128]

[0129] Solving for the given information yields:

[0130]

[0131] Solve subproblem 3:

[0132]

[0133] The three sub-problems are solved until convergence, yielding the final target scattering coefficient and interference signal.

[0134] To demonstrate the effectiveness of this invention, simulation experiments were conducted on the Matlab 2019b platform.

[0135] The method flow of this invention is as follows:

[0136] enter: ;

[0137] Hyperparameters: , , , ;

[0138] initialization: , , , , ;

[0139] cycle:

[0140] Solve :

[0141] ,

[0142] Solve :

[0143] ,

[0144] Until convergence;

[0145] Output: , .

[0146] Table 1 presents the simulation parameters for anti-jamming super-resolution imaging of forward-looking scanning radar. Figure 2 It is a point target simulation scenario.

[0147] Table 1. Simulation parameters for anti-jamming super-resolution imaging with forward-looking radar:

[0148] Parameter name value speed of light 3 x 10 8 m / s carrier frequency 10GHz Transmitted signal pulse width 10us Transmitted signal frequency modulation bandwidth 50MHz Sampling frequency 100MHz Main lobe width 3° Scan speed 100° Pulse repetition frequency 200Hz Scan range -10°~10° Slope distance 6000m

[0149] The acquired echo data was processed using various methods to obtain... Figure 3 (a) and Figure 4 (a) in the figure gives the real beam echo under interference conditions, where Figure 3 In (a), ten percent of the azimuth pulses were randomly selected to be added as interference. Figure 4 In (a), five percent of the azimuth pulses were continuously selected to add interference.

[0150] Figure 3 (b) shows the super-resolution results of the Iterative Adaptive Method (IAA). IAA has weak anti-interference ability and tends to concentrate interference in certain directions during the solution process. Since the interference disrupts the convolution relationship, IAA is unable to reconstruct the target. Figure 3 (c) shows the Lucy super-resolution results. Due to the presence of interference, the echo convolution relationship is disrupted, causing the Lucy method to fail. Figure 3 (d) in the figure shows the L1 regularized super-resolution results. Under interference, the method can barely achieve target reconstruction, but the interference suppression effect is also poor. Figure 3 Figure (e) shows the SPICE super-resolution results. As can be seen from the figure, the Sparse Iterative Covariance Estimation (SPICE) method has a certain anti-interference ability. It has achieved good suppression of interference and reconstruction of the target. However, due to the destruction of the convolution relationship, the SPICE method has resulted in target loss in the reconstruction results. Figure 3 (f) in the figure shows the results of the method of the present invention. It can be seen from the results that the method proposed in this invention can effectively suppress interference and achieve target scattering reconstruction, thus significantly improving the azimuth resolution.

[0151] When interference occurs randomly in the azimuth direction, its disruption to the convolution relationship is relatively limited, and some traditional super-resolution methods have shown a certain degree of anti-interference capability. To further verify the effectiveness of this invention, in Figure 4 In (a), five percent of the continuous azimuth pulses were selected to introduce interference. Figure 4Figures (b), (c), (d), (e), and (f) illustrate the IAA, Lucy super-resolution method, L1 regularized super-resolution method, SPICE super-resolution method, and the super-resolution method of this invention, respectively. Simulation results show that traditional super-resolution methods cannot effectively suppress continuously occurring interference, resulting in compressed bright lines in the reconstruction results. The figures also show that the portion of the target not covered by interference is reconstructed to a certain extent. For target echoes continuously covered by interference, the convolution relationship is severely disrupted, causing traditional super-resolution methods to fail and preventing effective reconstruction of the target scattering function. The method proposed in this invention, by applying regularization constraints to both interference and target scattering, suppresses interference, reconstructs the disrupted azimuth convolution relationship, and constrains the space of the target scattering function solution, thus suppressing noise amplification and effectively achieving anti-interference super-resolution imaging.

[0152] To further quantify the analysis, Mean Square Error (MSE) and Structural Similarity (SSIM) were introduced as evaluation metrics. MSE is defined as follows:

[0153]

[0154] in, Indicates the distance from the sampling points. This indicates the number of azimuth sampling points. and Let represent the true target scattering coefficient and the recovered target scattering coefficient, respectively. The formula for calculating SSIM is as follows:

[0155]

[0156] in, This indicates that the mean of the subscripts is calculated. This indicates the calculation of the standard deviation of the subscript. This indicates the calculation of the correlation coefficient for the subscript, where the subscript is... and These represent the original target scattering coefficient distribution and the super-resolution reconstructed target scattering coefficient distribution, respectively. SSIM is used to quantitatively calculate the similarity between the super-resolution processing result and the original target scene, and its value ranges from 0 to 1. The larger the SSIM value, the closer the super-resolution processing result is to the original target scene; when the SSIM value is 1, it means that the two are completely identical.

[0157] Tables 2 and 3 present the MSE and SSIM results of multi-point target scene simulation processing under different interference distributions. Combining Tables 2 and 3, the traditional IAA method exhibits excellent super-resolution performance, but its weak anti-interference capability results in poor performance in both metrics. Overall, the method proposed in this invention achieves better performance under both interference distributions.

[0158] Table 2. MSE values ​​from simulation results under interference conditions:

[0159] Super-resolution methods 10% random interference / dB 5% continuous interference / dB Lucy -85 -86 IAA -76 -71 L1 regularization -87 -81 SPICE -94 -83 The method proposed in this paper -94 -95

[0160] Table 3 SSIM values ​​from simulation results under interference conditions:

[0161] Super-resolution methods 10% random interference 5% continuous interference Lucy 0.8338 0.9706 IAA 0.2250 0.1844 L1 regularization 0.8618 0.9662 SPICE 0.6192 0.9418 The method proposed in this paper 0.9884 0.9930

[0162] The results above demonstrate that the joint sparse prior constraints proposed in this invention exhibit excellent performance in suppressing interference and achieving azimuth super-resolution. Those skilled in the art can make relevant applications based on the scanning radar anti-jamming super-resolution imaging method based on joint sparse constraints disclosed in this invention, and such knowledge remains within the scope of protection of this invention.

Claims

1. A scanning radar anti-jamming super-resolution imaging method based on joint sparse constraints, characterized in that, Includes the following steps: Step 1: Based on the echo signal of the forward-looking area of ​​the scanning radar under interference environment, establish an echo convolution model, which is specifically represented by adding random interference signal to the convolution relationship between the target scattering vector and the antenna pattern; Step 2: Construct a sparse regularized reconstruction model, specifically by using the least squares method to solve for the target scattering coefficients and introducing a model based on... Sparsity regularization constraints of norms; Step 3: Transform the sparse regularized reconstruction model into a joint sparse constraint reconstruction model that solves for the target scattering coefficient and the interference signal; Step 4: Solve the joint sparse constraint reconstruction model using the fast iterative soft thresholding method and the alternating direction multiplier method.

2. The scanning radar anti-jamming super-resolution imaging method based on joint sparse constraints according to claim 1, characterized in that, The sparse regularized reconstruction model is represented as follows: ； in, This represents the solved target scattering coefficient. This represents the echo signal across the entire range of cells. Represents the target scattering coefficient across the entire range cell. Represented as a convolution matrix written from the antenna pattern function, It is a regularization parameter. Representation matrix Norm, Representation matrix Norm.

3. The scanning radar anti-jamming super-resolution imaging method based on joint sparse constraints according to claim 2, characterized in that, The joint sparse constraint reconstruction model is represented as follows: ； in, This represents the interference signal in the range-time domain versus the azimuth-time domain. For the normalized inverse Fourier transform matrix, For interference regularization parameters; To interfere with the sparse constraint term, This is a sparse constraint term for target scattering.

4. The scanning radar anti-jamming super-resolution imaging method based on joint sparsity constraints according to claim 3, characterized in that, Step four is specifically solved jointly in the following way: Solving the joint sparse constraint reconstruction model can be viewed as a two-layer minimum absolute value contraction and operator selection problem: ； The first layer is to solve for the interference signal. The problem is solved using the fast iterative soft thresholding method. The second layer involves solving the target scattering coefficient. The problem is solved using the alternating direction multiplier method; the specific solution process is as follows: Solving for interference signals Then, the original problem is transformed into: ； Among them, the fidelity term function It is a convex function and differentiable; regularization term function It is a convex function but not differentiable; for Differentiating, we get: ； in The fidelity function represents the pair of terms. The derivative, after derivation and solution, yields: ； in For the optimal result of interference, It is a soft threshold function. Step size, superscript Indicates the first The next iteration; Find the iterative results of the iterative soft thresholding algorithm. ; Solve for the target scattering coefficient Then, the original problem is transformed into: ； Introducing auxiliary variables and dual variables Constructing the augmented Lagrange function : ； in These are the Lagrange multiplier parameters, for The subproblems are constructed and solved alternately. After the solutions converge, the final target scattering coefficient and interference signal are obtained.

5. The scanning radar anti-jamming super-resolution imaging method based on joint sparse constraints according to claim 4, characterized in that, The pair The subproblems are constructed and solved alternately as follows: Solve subproblem 1: ; right Differentiating gives ; Solving for the given information ;in It is the identity matrix; Solve subproblem 2: ; Transforming the original problem into a set of separable problems yields... ; , This represents the number of sampling points in the distance direction. set up ; right Solving for the partial derivative yields the following results. ; By moving direction ; Solving for the given information ; Solve subproblem 3: .

6. The scanning radar anti-jamming super-resolution imaging method based on joint sparse constraints according to claim 5, characterized in that, The Nesterov acceleration algorithm is introduced to speed up the iteration of the soft threshold method.

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