A Multi-Parameter Learning Real Aperture Radar Super-Resolution Imaging Method

Abstract

This invention discloses a multi-parameter learning real aperture radar super-resolution imaging method, applied in the field of radar imaging technology. Addressing the difficulties in selecting multiple parameter types and the limitations in imaging performance caused by fixed parameters in traditional regularized super-resolution imaging methods, this invention first decomposes the sparse constraint optimization problem into three sub-problems based on the traditional split Bregman algorithm. Second, it differentiates the different types of parameters in the sub-problems to achieve differentiated correction of different azimuth units in the real beam. Finally, it expands the traditional iterative process into a network layer structure, learning from data to achieve adaptive updates of multiple parameter types. Compared with traditional methods, this improves the target angular resolution capability in sparse scenes.

Description

Technical Field

[0001] This invention belongs to the field of radar imaging technology, and specifically relates to a multi-parameter learning real aperture radar super-resolution imaging method. Background Technology

[0002] Real aperture radar can acquire all-around target detection information through beam scanning, but its angular resolution is limited by the antenna size and is usually low.

[0003] The echo sequence of a scanning radar along the angular direction can be modeled as a convolution relationship between the target scattering coefficient and the antenna pattern modulation function. Therefore, its angular resolution can be improved by using deconvolution methods. Among them, regularization-based methods can achieve good reconstruction performance, but they face the problem of multiple parameter selection. Traditional methods have limitations such as high computational complexity and limited parameter selection. Pei et al. applied deep neural networks to radar super-resolution imaging, but the interpretability of this data-driven deep learning method is poor. Furthermore, Lai et al. proposed ISTA-Net, which combines traditional algorithms with deep networks for super-resolution imaging in complex scenes. It shows good reconstruction performance on simulated data, but its adaptability to scenes and its ability to distinguish sparse targets are still insufficient. Summary of the Invention

[0004] To address the challenges of selecting multiple parameters in traditional regularized super-resolution methods and the limitations on imaging performance caused by fixed parameters, this invention proposes a multi-parameter learning real aperture radar super-resolution imaging method.

[0005] The technical solution adopted in this invention is: a multi-parameter learning real aperture radar super-resolution imaging method, comprising:

[0006] Step 1: Preprocess the raw echo signal acquired by the radar to obtain the real beam echo, which is represented as the convolution of the antenna pattern and the target scattering coefficient;

[0007] Step 2: Establish a least squares problem with the target scattering coefficient as the solution objective, and decompose the problem using sparse constraint optimization; then use the split Bregman algorithm to introduce auxiliary and dual variables, decouple the original problem into three subproblems, and solve the target scattering coefficient, auxiliary variables and dual variables respectively;

[0008] Step 3: Construct a K-layer cascaded deep unfolded network to solve the three sub-problems. Each layer of the network corresponds to one iteration, including a target scattering reconstruction module, a threshold filtering module, and a dual correction module.

[0009] The target scattering reconstruction module solves subproblem 1 based on the output results of the previous threshold filtering module and the dual correction module;

[0010] The threshold filtering module solves sub-problem 2 based on the output of the target scattering reconstruction module of the current layer and the output of the dual correction module of the previous layer;

[0011] The dual correction module solves sub-problem 3 based on the outputs of the current layer target scattering reconstruction module and the threshold filtering module;

[0012] Step 4: Input the real beam echo data into the network for forward propagation, calculate the loss function based on the reconstruction error between the target scattering coefficient output by the network and the target's true scattering coefficient; finally, iteratively update multiple types of parameters based on the loss function.

[0013] Furthermore, step 2 is detailed as follows:

[0014] A least-squares problem is established with the target scattering coefficient as the solution objective. This problem is then decomposed using sparse constraints, resulting in the following optimization problem:

[0015]

[0016] in, To estimate the target scattering coefficient, The scattering coefficients of the real target are... For real beam echo, Represents the antenna measurement matrix. For regularization parameters; express The square of the norm, express Norm;

[0017] Then, the split Bregman algorithm is used to introduce auxiliary variable d and dual variable b, decoupling the original problem into three subproblems:

[0018]

[0019] Where the superscript k indicates the k-th iteration, d represents the auxiliary variable, and b represents the dual variable. This is the penalty parameter.

[0020] Furthermore, the deep unfolded network is specifically as follows:

[0021] The target scattering reconstruction module uses azimuth units to expand the penalty parameters into a high-dimensional penalty matrix and the regularization parameters into a high-dimensional regularization weighting matrix, and then solves for the target scattering coefficients; the calculation formula of the target scattering reconstruction module is as follows:

[0022]

[0023] in, For a high-dimensional penalty matrix, It is a high-dimensional regularized weighted matrix;

[0024] The threshold filtering module includes a threshold generation module (TG) and a residual correction module (RC). The input variables are the outputs of the current layer's target scattering reconstruction module and the previous layer's dual correction module. The threshold generation module performs global max pooling and average pooling on the input variables, then concatenates the extracted feature maps and processes them through convolutional layers to extract discriminative representations. An activation function is then used to generate an attention weight map to dynamically adjust the threshold. The processing result is output through the threshold generation function. The residual correction module's input variables undergo convolution operations and activation functions, and the output is then corrected using a residual correction term. Auxiliary variables are handled by the threshold filtering module. The calculation formula can be expressed as:

[0025]

[0026] in, This represents the auxiliary variable in the k-th network layer. Indicates the module's input variables. This represents the activation function. This indicates that a convolution kernel of size 1×3 is being performed; threshold is the designed threshold parameter, and its expression is:

[0027]

[0028] in, This represents the concatenation function. This indicates max pooling. This indicates average pooling;

[0029] The dual correction module extends the step size parameter of subproblem 3 during iteration into a learnable step size sequence. In the step size parameter learning, the activation function is used to adaptively adjust the slope and intercept to constrain the step size sequence to achieve convergence.

[0030] The dual correction module is represented as:

[0031] ;

[0032] in, The step size sequence in the k-th network layer is expressed as:

[0033] ;

[0034] in, This represents the step size parameter of the i-th azimuth unit in the k-th network layer.

[0035] Furthermore, the training process of the deep unfolded network treats the network as a mapping function with hyperparameters. Iterative updates of multiple types of parameters in the multi-type parameter set A are performed by minimizing the loss function and backpropagating gradients. These parameters include a high-dimensional penalty matrix, a high-dimensional regularized weighting matrix, a threshold parameter, and a step size sequence, expressed as:

[0036] ;

[0037] in, This represents the updated set of multiple parameter types. The training dataset is constructed using a radar forward-looking imaging model to generate real radar beam echoes. This represents the target scattering coefficient reconstructed from the echo s by the deep unfolded network under a multi-type parameter set A.

[0038] The beneficial effects of this invention are as follows: First, the method of this invention decouples the sparse constraint optimization problem of real aperture radar forward-looking super-resolution imaging into three solvable sub-problems based on the split Bregman algorithm. Second, the decoupled sub-problems are mapped to a target scattering reconstruction module, a threshold filtering module, and a dual correction module, respectively. Furthermore, differentiated designs are implemented based on the characteristics of multiple parameter types, extending the traditionally fixed regularization parameters into high-dimensional learnable parameters. Finally, gradient backpropagation is used to perform end-to-end optimization with the goal of minimizing reconstruction error, achieving the learning of multiple parameter types. Compared with traditional regularization methods, this invention overcomes the problems of multi-parameter selection and parameter fixation in traditional methods, exhibiting superior super-resolution reconstruction performance for sparse scenarios. Attached Figure Description

[0039] Figure 1 This is a diagram illustrating the working principle of a scanning radar.

[0040] Figure 2 This is the overall network structure diagram of the present invention.

[0041] Figure 3 This is a diagram of the single-layer network structure of the present invention.

[0042] Figure 4 The simulated beam pattern is shown at a signal-to-noise ratio of 15dB.

[0043] Figure 5 The images show the processing results of different super-resolution methods at a signal-to-noise ratio of 15 dB; where (a) is... The processing result of the -IRN method, (b) is The results of the SplitBregman method are shown in (c) and (d) respectively.

[0044] Figure 6Figures show the processing results of measured data using different super-resolution methods; where (a) is the real beam echo, and (b) is... The processing result of the -IRN method, (c) is - The processing result of the SplitBregman method, and (d) is the processing result of the IAA method.

[0045] Figure 7 This is a diagram showing the processing results of the measured data using the method of the present invention. Detailed Implementation

[0046] To facilitate understanding of the technical content of this invention by those skilled in the art, the following description, in conjunction with the accompanying drawings, further illustrates the invention.

[0047] This invention is verified using simulation experiments and real-world measurements. All steps and conclusions have been verified correctly using PyCharm 2024. The method of this invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0048] A multi-parameter learning method for real aperture radar super-resolution imaging, the specific implementation steps of which are as follows:

[0049] Step 1: Preprocess the raw echo signal acquired by the radar to obtain the real beam echo. ;

[0050] In forward-looking imaging with real aperture radar, the radar beam operates in scanning mode. The geometric model of radar beam scanning imaging is as follows: Figure 1 As shown. The radar is located at coordinates (0, 0, H), where H is the radar's height above the ground. The radar platform moves along the y-axis at a speed of v, and the antenna scanning speed is ω. The target is located at point P. Let be the azimuth angle of the target relative to the radar at the initial moment. The initial elevation angle of the target relative to the radar. This indicates the initial distance between the radar and the target. The radar scans the target while in motion. Let be the azimuth angle at time t. Let be the pitch angle at time t. Let be the distance at time t. The received echo is modulated by a linear frequency modulated waveform and the antenna pattern, producing the following echo model:

[0051]

[0052] in, This represents the two-dimensional target echo at target point P. For the distance to the dimensional fast time, For azimuth angle, For two-way echo delay, This represents the scattering coefficient of target point P. This indicates the antenna radiation pattern. To adjust the frequency, The duration of the pulse. The carrier frequency is used. After pulse compression and range migration correction, a real-beam echo can be obtained. This can be represented as the convolution of the antenna pattern and the target scattering coefficient:

[0053]

[0054] in This represents the received echo signal matrix. The target scattering coefficient matrix, This represents the target scattering coefficient at the Nth azimuth sampling point. For the noise matrix, This represents the noise at the Nth azimuth sampling point; N represents the number of azimuth sampling points. This represents the antenna measurement matrix.

[0055] Step 2: Establish the target scattering coefficient To solve the objective least squares problem, a sparse constraint optimization problem decomposition is used; then, the split Bregman algorithm is used to introduce auxiliary variables d and dual variables b, decoupling the original problem into three subproblems.

[0056] Due to the ill-posedness of the antenna measurement matrix, the target cannot be directly inverted from the noise-contaminated echo. To alleviate this ill-posedness, a regularization method is introduced:

[0057]

[0058] in, To estimate the target scattering coefficient, The scattering coefficients of the real target are... The variable that minimizes the objective function. The value; express The square of the norm, where It is an introduced regularization term used to constrain the range of the solution space. This is the regularization parameter.

[0059] Because the target distribution in the forward-looking area of ​​traditional real-aperture radar is sparse, sparsity constraints are applied to limit the solution space of the target scattering coefficients and enhance azimuth resolution. By introducing sparsity constraints, the regularization term is... The optimization problem can be represented as:

[0060]

[0061] in, express Norm. Sparse constraints can be used to improve azimuth resolution, but... The non-convex property of the norm poses a significant challenge to solving this convex optimization problem. Therefore, the split Bregman algorithm is introduced, which separates variables to... The non-convex property of the norm is transformed into three convex subproblems.

[0062] First, introduce auxiliary variables. The original expression can be transformed into:

[0063]

[0064] After decoupling, it can be transformed into an unconstrained problem, as shown in the following expression:

[0065]

[0066] in, As a penalty parameter, let ,in To optimize the objective function of the problem, based on the Bregman distance, the above equation can be expressed as:

[0067]

[0068] in, Indicates the Bregman distance. for The auxiliary variable for the kth iteration. for The auxiliary variable for the k-th iteration, where the superscript k indicates the k-th iteration. The expression is:

[0069]

[0070] in, for The gradient, where the superscript i represents the i-th azimuth unit. The expression is:

[0071]

[0072] Let dual variables , , The expression can be simplified to:

[0073]

[0074]

[0075] The unconstrained problem can then be transformed into:

[0076]

[0077] replace The iterative formula for the split Bregman algorithm can be expressed as:

[0078]

[0079] The above solution strategy contains three variables, namely , and It can be broken down into the following subproblems:

[0080]

[0081] Step 3: Deep unfolding network design; The iterative solution process in Step 3 is mapped to a K-layer cascaded network structure, with each layer corresponding to one iteration, and containing three core modules: a target scattering reconstruction module based on sub-problem 1, a threshold filtering module based on sub-problem 2, and a dual correction module based on sub-problem 3.

[0082] Traditional split-Bregman algorithms employ globally fixed parameters to facilitate manual parameter selection, which inherently limits the algorithm's flexibility. To address this issue, this paper proposes a split-Bregman super-resolution network based on multi-type parameter learning. By constructing a mapping relationship between multi-type parameters and echo data, the three sub-problems of the traditional algorithm are divided into different modules. Differentiated multi-type parameters are designed for each module, forming a learnable set of multi-type parameters. , by high-dimensional penalty matrix High-dimensional regularized weighted matrix Threshold parameters and step size sequence The network is composed of parameters that are updated iteratively within and between network layers in a data-driven manner. The parameter design and iteration process for each module are as follows:

[0083] Constructing a target scattering reconstruction module The solution to subproblem 1 can be expressed as:

[0084]

[0085] Among them, the penalty parameter It is used to correct the distribution of singular values ​​in the matrix and alleviate the noise amplification problem in the inversion process.

[0086] In real beam echoes, noise levels vary across different azimuth angle cells. Therefore, the traditional fixed penalty parameter... Extended to a high-dimensional penalty matrix Γ to achieve differentiated correction of different azimuth angle units in different iteration layers, the penalty matrix of the k-th layer network. It can be represented as:

[0087]

[0088] Where N represents the angular dimension of the echo data, Describes the constructor for a diagonal matrix. This represents the penalty weight of the i-th azimuth unit in the k-th layer of the network.

[0089] Similarly, the regularization parameter λ is expanded into a high-dimensional regularization weighting matrix. To adjust the weights of the data fidelity terms for different azimuth angle units, the regularization weighting matrix of the k-th layer network is used. It can be represented as:

[0090]

[0091] This represents the regularization parameter of the i-th azimuth unit in the k-th layer network. In summary, the calculation formula for the target scattering reconstruction module is:

[0092]

[0093] Construct a threshold filtering module .make Subproblem 2 can be represented as:

[0094]

[0095] in, For noisy data, the above equation can be viewed as a total variation denoising problem. This solution is typically approximated using a threshold operator, expressed as:

[0096]

[0097] in, Indicates the threshold generation function, subscript The threshold parameter is represented by the following expression for the threshold generation function:

[0098]

[0099] in, Refers to general variables; This indicates taking the absolute value. Denotes the positive part function, Represents a symbolic function.

[0100] However, in the traditional splitting Bregman algorithm, the threshold parameter It is fixed and cannot be updated during iterations, nor can it be adjusted for different azimuth angles. Furthermore, The output is limited to three discrete values ​​[−1, 0, 1], making it unsuitable for the noise characteristics of units with different azimuth angles, which may lead to noise accumulation or signal attenuation. Therefore, this paper constructs a dynamic network architecture, namely the Data Cleaning Block (DCB). The Data Cleaning Block (DCB) is as follows: Figure 3 As shown, it consists of a threshold generation module (TG) and a residual correction module (RC). The TG module first performs global max pooling and average pooling on the input variables, then concatenates the extracted feature maps and processes them through convolutional layers to extract discriminative representations, and then uses... The activation function generates an attention weight map to dynamically adjust the threshold, and the final processing result is then... Output; The RC module first performs convolution operations on the input variables to extract feature representations, and then passes them through an activation function. To enhance nonlinear representation capabilities, a residual correction term is then learned to correct the output of the TG module. The input variables for both the TG and RC modules are the sum of the scattering coefficient estimate from the output of the target scattering reconstruction module at the k-th network layer and the dual variable from the output of the (k-1)-th network layer.

[0101] Auxiliary variables in the threshold filtering module The calculation formula can be expressed as:

[0102]

[0103] in, This represents the auxiliary variable in the k-th network layer. Indicates the module's input variables. This represents the activation function. This indicates that a convolution kernel of size 1×3 is being performed; threshold is a newly designed threshold parameter, the expression of which is:

[0104]

[0105] in, This represents the concatenation function. This indicates max pooling. This indicates that average pooling is used.

[0106] Constructing a dual correction module The step size parameter of subproblem 3 is fixed at 1 during iteration. This is expanded into a learnable step-size sequence to adapt to parameter update requirements at different iteration stages. Furthermore, an activation function is used in the step-size parameter learning process. The slope and intercept are adaptively adjusted to constrain the step size sequence to achieve convergence. Subproblem 3 can be represented as:

[0107]

[0108] in, The step size sequence in the k-th network layer is expressed as:

[0109]

[0110] in, This represents the step size parameter of the i-th azimuth unit in the k-th network layer.

[0111] The overall network architecture is as follows Figure 2 As shown, the number of unfolded layers K is set to 10, and sparse reconstruction of the target scattering coefficient is achieved by iterating alternately between the three network modules.

[0112] Step 4: Establish the loss function; input the real beam echo data The input network is used for forward propagation, and the loss function is calculated based on the reconstruction error between the network's target scattering coefficient output and the target's true scattering coefficient. Finally, the various types of parameters are iteratively updated based on the loss function.

[0113] In radar super-resolution imaging tasks, the main objective of this invention is to recover the target scattering coefficient from observation echoes affected by noise, and the loss function... It can be defined as the reconstruction error between the network reconstruction result and the true scattering coefficient of the target, and can be expressed as:

[0114]

[0115] in, Indicates that the network is based on the echo The reconstructed target scattering coefficients Let E be the scattering coefficient of the target in the real scene. The number of pixels in the image.

[0116] The training process can be viewed as a mapping function with hyperparameters. By minimizing a predefined loss function and backpropagating gradients, the various types of parameters in the multi-type parameter set A are iteratively updated, which can be represented as:

[0117]

[0118] in, This represents the updated set of multiple parameter types. The training dataset is constructed using a radar forward-looking imaging model to generate real radar beam echoes.

[0119] Step 5: Performance verification.

[0120] To verify the effectiveness of the method of the present invention, simulation data and measured data were used for verification. The simulation parameters are shown in Table 1.

[0121] Table 1 Simulation System Parameters

[0122] parameter numerical values carrier frequency 9.6GHz bandwidth 45MHz Antenna scanning speed 50° / s Main lobe beamwidth 5.1° Pulse repetition frequency 1000Hz Scan range -10°~10°

[0123] Figure 4 The simulation scene at a signal-to-noise ratio of 15dB is shown. The original simulation scene is as follows: Figure 4 As shown in (a), two targets with different amplitudes are located at -0.55° and 0.55° respectively, with an azimuth interval smaller than the beamwidth. The echo of a one-dimensional point target scene is as follows: Figure 4 As shown in (b), the real beam echo is aliased, making it impossible to distinguish between the two targets. Figure 5 (a) in the middle is Norm Iterative Reweighting Method The reconstruction results of -IRN will produce false targets. Norm splitting Bregman method ( The reconstruction results of the SplitBregman method and the Iterative Adaptive Method (IAA) are as follows: Figure 5 (b) and Figure 5 As shown in (c), the two targets can be separated to some extent, but the magnitude loss is relatively large. Figure 5 (d) in the figure shows the processing result of the method of the present invention, which can effectively distinguish adjacent targets while maintaining a narrow reconstruction beamwidth.

[0124] To verify the effectiveness of the method of the present invention, actual measurement data was used for verification. Figure 6 In (a), the echo is a real beam. Due to the limitation of the radar system's angular resolution, the two ships within the red rectangular area cannot be effectively distinguished. Figure 6 (b) The IRN method can distinguish ships, but due to its sparsity, the reconstruction results contain a large number of false targets. Figure 6 (c) shown in The SplitBregman method can distinguish targets, but it produces artifacts. Figure 6 In the diagram, (d) represents the reconstruction result using the IAA method, which exhibits high sidelobes. The reconstruction result of the method of this invention is as follows: Figure 7 As shown, it can effectively distinguish ships and reconstruct a narrower target width, while effectively suppressing artifacts, demonstrating excellent noise robustness.

[0125] In summary, this invention proposes a multi-parameter learning real aperture radar super-resolution imaging method. By establishing a mapping relationship between multiple types of parameters and real beam echoes, it achieves multi-type parameter selection in sparse scenes, thereby solving the problems of multi-type parameter selection and parameter fixation in traditional regularization methods. Experimental results show that, for sparse scenes, the method of this invention outperforms existing methods in both simulation and measured data, exhibiting superior performance in parameter selection capability and imaging quality.

[0126] Those skilled in the art will recognize that the embodiments described herein are for the purpose of helping to understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of the claims of the invention.

Claims

1. A method for multi-parameter learning real-aperture radar super-resolution imaging, characterized in that, The method comprises the following steps: Step 1: preprocessing the original echo signal obtained by the radar to obtain real beam echo, which is represented as the convolution of antenna pattern and target scattering coefficient; Step 2: establishing a least square problem for solving the target scattering coefficient, and decomposing the problem into three sub-problems by using sparse constraint optimization; then introducing auxiliary variables and dual variables by using a split Bregman algorithm to decouple the original problem into three sub-problems, and solving the target scattering coefficient, the auxiliary variables and the dual variables respectively; Step 3: constructing a K-level cascaded deep unfolding network to solve the three sub-problems, each layer of the network corresponding to an iteration, and comprising a target scattering reconstruction module, a threshold filtering module and a dual correction module; The target scattering reconstruction module solves the sub-problem 1 based on the output of the threshold filtering module and the dual correction module of the previous layer; The threshold filtering module solves the sub-problem 2 based on the output of the target scattering reconstruction module of the current layer and the output of the dual correction module of the previous layer; The dual correction module solves the sub-problem 3 based on the output of the target scattering reconstruction module and the threshold filtering module of the current layer; Step 4: inputting the real beam echo data into the network for forward propagation, calculating a loss function based on the reconstruction error between the target scattering coefficient output by the network and the real target scattering coefficient, and finally updating the multiple types of parameters of the deep unfolding network based on the loss function; The step 2 is specifically as follows: The least square problem for solving the target scattering coefficient is established, and the obtained optimization problem is represented as follows: ； wherein, is an estimated target scattering coefficient, is a true target scattering coefficient, is a real beam echo, denotes an antenna measurement matrix, is a regularization parameter; denotes the square of the L2 norm, denotes the L2 norm; Then the split Bregman algorithm is used to introduce auxiliary variables d and dual variables b, and the original problem is decoupled into three sub-problems: ； where the superscript k denotes the kth iteration, d denotes the auxiliary variable, and b denotes the dual variable, is a penalty parameter.

2. The method of claim 1, wherein, The deep unfolding network is specifically as follows: The target scattering reconstruction module expands the penalty parameter into a high-dimensional penalty matrix and expands the regularization parameter into a high-dimensional regularization weight matrix by using the azimuth angle unit, and then solves the target scattering coefficient; The threshold filtering module comprises a threshold generation module TG and a residual correction module RC, and the input variables are the output of the target scattering reconstruction module of the current layer and the output of the dual correction module of the previous layer; the threshold generation module performs global maximum pooling and average pooling on the input variables, then splices the extracted feature maps and processes them through a convolution layer to extract discriminative representations, and then generates an attention weight map by using an activation function to realize dynamic adjustment of the threshold, and the processing result is output through a threshold generation function; the input variables of the residual correction module are processed through convolution operation and activation function, and then the output is corrected through a residual correction term; The dual correction module expands the step parameter of the sub-problem 3 in iteration into a learnable step sequence, and in the step parameter learning, uses an activation function to adaptively adjust the slope and intercept to constrain the step sequence to achieve convergence.

3. The method of claim 2, wherein, The calculation formula of the target scattering reconstruction module is: ； wherein, is a high-dimensional penalty matrix, is a high-dimensional regularization weighting matrix; The calculation formula of the auxiliary variable in the threshold filtering module is: ； wherein, denotes an auxiliary variable in the k-th network layer, denotes an input variable of the module, denotes an activation function, denotes a convolution kernel operation with a size of 1 x 3; threshold is a designed threshold parameter, and its expression is: ； wherein, denotes a concatenation function, denotes max-pooling, denotes average-pooling; The dual correction module is represented as: ； wherein denotes the sequence of steps in the k-th network layer, which is expressed as: ； wherein represents a step size parameter for the i-th azimuthal unit in the k-th network layer.

4. The method of claim 3, wherein, The training process of the deep unfolding network regards the network as a mapping function with hyperparameters, and iteratively updates the multi-type parameters in the multi-type parameter set A, including the high-dimensional penalty matrix, the high-dimensional regularization weighting matrix, the threshold parameter, and the step sequence, by minimizing the loss function and gradient backpropagation, and is expressed as: ； wherein, denotes the updated multi-type parameter set, denotes the training data set, and the radar real beam echo is generated by using the radar forward imaging model to construct, denotes the target scattering coefficient reconstructed by the deep unfolding network under the multi-type parameter set A according to the echo s.

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