Fast extraction of scattering center parameters of SAR target based on depth unfolding

Abstract

The application provides a SAR target scattering center parameter fast extraction method, and mainly solves the problems of slow speed and low precision of a traditional SAR target scattering center parameter extraction method; firstly, the application models a scattering center parameter solving problem based on a sparse representation theory; then, a SAR target scattering center parameter extraction problem model based on a semi-quadratic splitting method is constructed, a deep unfolding network is constructed according to an optimization process based on the semi-quadratic splitting method, and the SAR target scattering center parameter is extracted by using the deep unfolding network; compared with a traditional method, the method constructs a deep unfolding network based on the semi-quadratic splitting method and a scattering center model, and realizes efficient and interpretable SAR target scattering center parameter extraction.

Description

A Fast Extraction Method for SAR Target Scattering Center Parameters Based on Depth Unfolding Technical Field

[0001] This invention belongs to the field of artificial intelligence technology, specifically relating to a method for rapid extraction of SAR target scattering center parameters based on depth unfolding. Background Technology

[0002] Synthetic Aperture Radar (SAR) is a ground-based detection system that actively transmits and receives electromagnetic waves. It is capable of all-weather, all-day, high-resolution imaging, making it suitable for target reconnaissance, monitoring, and identification. It has also been widely applied in Earth sciences, climate change research, environmental and Earth system monitoring, marine resource utilization, and planetary exploration, demonstrating high application value. In recent years, the number of SAR images has increased dramatically, making intelligent interpretation of SAR images based on deep learning a popular research direction. Because SAR target scattering center models have the ability to parameterize target features, increasing research focuses on extracting SAR target scattering center parameters and applying them to SAR target interpretation. Current methods for extracting SAR target scattering center parameters suffer from the following problems:

[0003] 1. Traditional SAR target scattering center parameter extraction methods are slow. Traditional SAR target scattering center parameter extraction methods are usually based on iterative optimization algorithms, which often require hundreds or thousands of iterations to obtain the SAR target scattering center parameters.

[0004] 2. Traditional SAR target scattering center parameter extraction methods have low accuracy. Traditional SAR target scattering center parameter extraction methods rely on manually adjusted hyperparameters, such as the step size and threshold in soft thresholding iteration algorithms. The setting of these hyperparameters significantly affects the algorithm performance, resulting in insufficient accuracy of the optimization results and poor generalization in practical applications.

[0005] To address the above problems, this invention proposes an efficient method for extracting SAR target scattering center parameters based on depth unfolding. Summary of the Invention

[0006] To address the issues of slow speed and low accuracy in traditional SAR target scattering center parameter extraction methods, this invention proposes a rapid SAR target scattering center parameter extraction method based on depth unfolding.

[0007] A method for fast extraction of SAR target scattering center parameters based on depth unfolding includes the following steps:

[0008] Step 1: Based on sparse representation theory, the problem of extracting SAR target scattering center parameters is transformed into an optimization problem of sparse coefficient vectors;

[0009] Step 2: The process of solving the optimization problem of sparse coefficient vectors using the semi-quadratic splitting method;

[0010] Step 3: Solving the optimization problem of constructing sparse coefficient vectors based on the semi-quadratic splitting method; Constructing a prior embedding deep unfolding network;

[0011] Step 4: Extract SAR target scattering center parameters using a priori embedding depth unfolding network.

[0012] Furthermore, based on sparse representation theory, the steps to transform the SAR target scattering center parameter extraction problem into an optimization problem of sparse coefficient vectors are as follows:

[0013] Step 1.1: Construct a SAR target scattering center model based on geometric diffraction theory and physical optics theory;

[0014] Step 1.2: Based on sparse representation theory and SAR target scattering center model, the problem of extracting SAR target scattering center parameters is transformed into an optimization problem of sparse coefficient vector.

[0015] Furthermore, the steps for constructing the SAR target scattering center model based on geometric diffraction theory and physical optics theory are as follows:

[0016] According to geometric diffraction theory and physical optics theory, the SAR target response at a small angle is the sum of the responses of K SAR target scattering centers. Therefore, the SAR target scattering center model is:

[0017]

[0018] Where f is the frequency vector of the synthetic aperture radar. f is the azimuth vector of the synthetic aperture radar; c The center frequency; For radar echo signals, The imaginary unit is θ, c represents the speed of light, exp represents an exponential function with the natural constant e as the base; K is the number of SAR target scattering centers, and Θ represents the set of parameters of K SAR target scattering centers; Θ = {θ1, θ2, ... θ} K};θ i It is the set of parameters of the scattering center of the i-th SAR target, where i ranges from [1, K]; θ i ={A i ,α i ,x i ,y i}, A i Let x be the echo amplitude of the i-th SAR target scattering center. iLet y be the range coordinate of the i-th SAR target scattering center. i Let α be the azimuth coordinate of the i-th SAR target scattering center. i α is the frequency dependence factor of the i-th SAR target scattering center; i Selected from the set of frequency-dependent factors.

[0019] Furthermore, the set of frequency-dependent factors is {-1,-0.5,0,0.5,1}.

[0020] Furthermore, based on sparse representation theory and the SAR target scattering center model, the steps to transform the SAR target scattering center parameter extraction problem into an optimization problem of a sparse coefficient vector are as follows:

[0021] According to sparse representation theory, the SAR target scattering center model in step 1.1 is expressed as:

[0022]

[0023] in, Radar echo signal The vectorized form of z is a sparse coefficient vector, and z corresponds to the SAR target scattering center model. This represents a signal domain dictionary containing information about the location of the SAR target scattering center. Corresponding to the SAR target scattering center model x is the range vector; y is the azimuth vector; A is the echo amplitude vector; α is the frequency dependence factor vector;

[0024] Signal domain dictionary Represented by column:

[0025]

[0026] For signal domain dictionary The column, x h Let y represent the h-th element of the distance vector x. w Represents the w-th element of the azimuth vector y; signal domain dictionary The dimension is PQ×HW, which is the signal domain dictionary. The frequency vector f of the synthetic aperture radar is formed by uniformly sampling P times within the frequency range, and the azimuth vector of the synthetic aperture radar is formed by uniformly sampling Q times within the azimuth range. The range vector x is formed by uniformly sampling H times within the range direction, and the azimuth vector y is formed by uniformly sampling W times within the azimuth direction; vec means converting the matrix into a one-dimensional vector.

[0027] For the signal domain dictionary Perform an inverse Fourier transform on each column to convert the signal domain dictionary from the signal domain to the image domain, obtaining the image domain dictionary Φ; the image domain dictionary is represented as a sparse diagonal matrix, where the SAR target scattering centers corresponding to each column are concentrated near the diagonal;

[0028] According to the inverse Fourier transform, equation (1-2) is transformed into an image-domain SAR target scattering center model based on sparse representation theory. The image-domain SAR target scattering center model based on sparse representation theory is expressed as follows:

[0029] s=Φz (1-5)

[0030] Where s represents the radar echo signal in the image domain; Φ represents the image domain dictionary in the image domain;

[0031] The problem of extracting SAR target scattering center parameters is transformed into an optimization problem of the sparse coefficient vector z:

[0032]

[0033] in, This means optimizing z to find the objective function ||s-Φz||. 2 +λ||z||1 yields the minimum z value; λ is a hyperparameter that balances data fidelity and sparsity.

[0034] Furthermore, the steps in solving the optimization problem of constructing a sparse coefficient vector using the semi-quadratic splitting method are as follows:

[0035] The semi-quadratic splitting method is used to solve the compressed sensing problem, which is transformed into an optimization problem as shown in equation (2-1):

[0036]

[0037] Where B is a matrix of size m×n, ω is an n-dimensional vector, b is an m-dimensional measurement vector, and b is used to represent the observed value of the signal;

[0038] The solution process for the optimization problem of constructing a sparse coefficient vector using the semi-quadratic splitting method is as follows:

[0039] To simplify gradient calculation, the original objective function is scaled to obtain the standard form of the objective function:

[0040]

[0041] In the formula, Φ is the image domain dictionary, s is the radar echo signal in the image domain, and z is the sparse coefficient vector;

[0042] The semi-quadratic splitting method introduces an auxiliary variable u, which equivalently transforms the standard form objective function into an objective function with the auxiliary variable u:

[0043]

[0044] In the formula This means optimizing z and u to find an objective function that incorporates auxiliary variables. Find the minimum z and u values; the subject to u = z is an equality constraint that ensures that z and u are equal in the optimal solution.

[0045] Furthermore, a quadratic penalty function is applied to the objective function that introduces auxiliary variables. Relaxing the constraints transforms the equality constraint u = z into a soft constraint, yielding the objective function after constraint relaxation:

[0046]

[0047] In the formula, μ is the penalty term hyperparameter; the semi-quadratic splitting method alternately optimizes z and u in the iteration to approximate the optimal solution of the objective function after relaxing the constraints; the iterative alternating optimization process is expressed as:

[0048]

[0049] z k Let u be the sparse coefficient vector obtained in the k-th iteration. k The auxiliary variable obtained in the k-th iteration;

[0050] in, This means optimizing z to find the objective function. The z-value that yields the minimum value This means optimizing u to find the objective function. The value of u that yields the minimum value; k and k-1 represent the number of iterations;

[0051] According to the normal equation Solve for z to obtain z k :

[0052]

[0053] The normal equation is:

[0054] (Φ * Φ+μI)z k=Φ * s+μu k-1 (2-7)

[0055] Where, Φ * Let Φ denote the conjugate transpose of Φ, and I be the identity matrix;

[0056] u is solved using the soft threshold iterative algorithm. k :

[0057] u k =S ρ (u k-1 +tΦ * (z k -Φu k-1 (2-8)

[0058] Where t and S ρ (·) represent the step size hyperparameter and the soft thresholding function, respectively. The complex soft thresholding function is expressed as:

[0059] S ρ (v)=sign(v)max(|v|-ρ,0), (2-9)

[0060]

[0061] Where v is a complex number, ρ is the threshold hyperparameter, and |v| represents the modulus of the complex number v;

[0062] The semi-quadratic splitting method is used to solve the problem of extracting SAR target scattering center parameters, resulting in a sparse coefficient vector z. k and auxiliary variable u k , z k Let u be the sparse coefficient vector obtained in the k-th iteration. k This is the auxiliary variable obtained in the k-th iteration.

[0063] Furthermore, the process of solving the optimization problem based on the semi-quadratic splitting method to construct sparse coefficient vectors involves the following steps in constructing the prior embedding deep unfolding network:

[0064] Step 3.1: Construct a prior embedding deep unfolded network;

[0065] To address the problem of extracting SAR target scattering center parameters, a prior embedding depth unfolding network based on the semi-quadratic splitting method is constructed, which combines the depth unfolding method and the semi-quadratic splitting method with the image domain dictionary to provide SAR target scattering center location information.

[0066] The prior embedding deep unfolded network consists of N identical stages, which are cascaded together; the hyperparameters of each stage include μ. d ρ d and td The range of d is [1, N]. The input of the prior embedding deep unfolding network is the radar echo signal in the image domain, and the output is the sparse coefficient vector z of the Nth stage. N and the auxiliary variable u in stage N N ;

[0067] Based on the solution process of the optimization problem of constructing sparse coefficient vectors using the semi-quadratic splitting method described in step 2, the prior embedding depth unfolding network of the d-th stage is represented as:

[0068]

[0069] In the formula, μ d ρ d and t d z is the learnable parameter for the d-th stage; d Let u be the sparse coefficient vector of the d-th stage of the prior embedding deep unfolded network. d , which are auxiliary variables for the d-th stage of the prior embedding deep unrolled network; d represents the d-th stage of the prior embedding deep unrolled network, and d-1 represents the d-1-th stage of the prior embedding deep unrolled network;

[0070] Step 3.2: Construct the loss function for the prior embedding deep unfolded network;

[0071] During the training of the prior embedding deep unfolding network, the input SAR image is converted into a one-dimensional vector through vectorization to obtain the radar echo signal s in the image domain, which serves as the input to the prior embedding deep unfolding network. The prior embedding deep unfolding network can progressively extract the SAR target scattering center information; the sparse coefficient vector z in the Nth stage... N The reconstructed image vector s is obtained by matrix multiplication with the image domain dictionary Φ. reconstruct s reconstruct =Φz N ;

[0072] Combining the constraints of the semi-quadratic splitting method, the loss function of the prior embedding deep unfolded network includes residual loss, regularization loss, penalty loss and total loss function;

[0073] Residual loss L residual for:

[0074] L residual =||ss reconstruct ||2(3-3)

[0075] Residual loss L residual Ensure the reconstruction of graph vectors s reconstruct Consistency with the radar echo signal s in the image domain;

[0076] Regularization loss L regular for:

[0077] L regular =λ r ||u N ||1(3-4)

[0078] In the formula λ r To constrain the auxiliary variable u in stage N N The sparsity hyperparameter, the regularization loss L regular Ensure the auxiliary variable u in stage N N sparsity;

[0079] Penalty Loss L penalty for:

[0080] L penalty =λ p ||z N -u N ||2(3-5)

[0081] In the formula λ p To constrain the auxiliary variable u in stage N N With the sparse coefficient vector z of the Nth stage N Consistency hyperparameters, penalty loss L penalty Ensure the auxiliary variable u in stage N N With the sparse coefficient vector z of the Nth stage N Consistency between them;

[0082] The total loss function is L total :

[0083] L total =L residual +L regular +L penalty (3-6)

[0084] That is, the total loss function is the sum of the residual loss, the regularization term loss, and the penalty term loss.

[0085] Furthermore, the step of extracting SAR target scattering center parameters using a priori embedding depth unrolling network is as follows:

[0086] Step 4.1: Train the prior embedding deep unfolding network;

[0087] Step 4.1.1: Data Preprocessing:

[0088] The training set images are cropped to obtain 80×80 pixel input images, and L2 normalization is performed on the input images. The normalized input images are then vectorized into one-dimensional vectors to obtain the radar echo signal s in the image domain.

[0089] Step 4.1.2: Train the prior embedding deep unfolding network:

[0090] The training set images undergo data preprocessing to obtain radar echo signals s in the image domain, which are used as input to the prior embedding deep unrolling network. The d-th stage of the prior embedding deep unrolling network is as follows:

[0091]

[0092] In the formula z d Let u be the sparse coefficient vector of the d-th stage of the prior embedding deep unfolded network. d μ is an auxiliary variable for the d-th stage of the prior embedding deep unfolded network. d , ρ d and t d Let z be the learnable parameters for the d-th stage; after N stages, the sparse coefficient vector z for the N-th stage is obtained. N and the auxiliary variable u in stage N N ;z N The reconstructed image vector s is obtained by matrix multiplication with the image domain dictionary Φ. reconstruct s reconstruct =Φz N ; Reconstruct graph vectors s reconstruct The difference between the radar echo signal s in the image domain and L is achieved through residual Constraints are imposed through L regular constraint u N The sparsity, through L penalty Keep z N with u N The consistency is specifically represented as follows:

[0093] L residual =||ss reconstruct ||2(4-3)

[0094] L regular =λ r ||u N ||1(4-4)

[0095] L penalty =λ p ||z N -u N ||2(4-5)

[0096] L total =L residual +L regular +L penalty (4-6)

[0097] Total loss function L total By L residual L regular and L penalty Together they form; when the total loss function L total If the network stabilizes after multiple iterations, meaning the loss value no longer decreases, the prior embedding depth unfolding network is considered to have converged. The learnable parameters of each stage of the prior embedding depth unfolding network at this point are saved for subsequent SAR target scattering center parameter extraction.

[0098] Step 4.2: Extraction of SAR target scattering center parameters;

[0099] Load the learned parameters for each stage stored in the prior embedding deep unrolling network;

[0100] After the data preprocessing in step 4.1.1, the test set images are input into the model to obtain the sparse coefficient vector z of the Nth stage. N ;

[0101] According to z N The SAR target scattering center parameters are obtained through inversion: x K y K A K α K K is the number of SAR target scattering centers;

[0102] Where, x K Let x represent a vector containing the range coordinates of the scattering centers of K SAR targets. K = [x1,x2,…,x i ,…x K ], x i Let y be the range coordinate of the i-th SAR target scattering center; K Let y represent a vector containing the azimuth coordinates of the scattering centers of K SAR targets. K =[y1,y2,…,y i ,…y K ], y i Let A be the azimuth coordinate of the scattering center of the i-th SAR target; K A represents a vector containing the echo amplitudes of the scattering centers of K SAR targets. K =[A1,A2,…,A i ,…A K A i α is the echo amplitude of the i-th SAR target scattering center; K Let α represent a vector containing K frequency dependence factors of the SAR target scattering center. K =[α1,α2,…,α i ,…,α K ], α iThe frequency dependence factor of the scattering center of the i-th SAR target;

[0103] To obtain the SAR target scattering center parameter set θ of the i-th SAR target scattering center i First, determine the scattering center of the i-th SAR target at z. N The index value is mapped to an 80×80 grid to obtain the pixel position of the i-th SAR target scattering center; then, based on the initial sampled value of the pixel position, the range coordinate x of the i-th SAR target scattering center is obtained. i and azimuth coordinates y i For index values ​​in z N The absolute value of the corresponding value is taken to obtain the echo amplitude A of the i-th SAR target scattering center. i ; Calculate the index value in z N The phase angle corresponding to the value in the equation, wherein the unit of the phase angle is radians;

[0104] Elements are sequentially selected from the frequency dependence factor set {-1, -0.5, 0, 0.5, 1}. The element with the smallest absolute difference between the selected element and the phase angle is taken as the frequency dependence factor α of the i-th SAR target scattering center. i ;

[0105] x i y i A i α i This refers to the scattering center parameter of the i-th SAR target.

[0106] This invention proposes a fast method for extracting SAR target scattering center parameters based on semi-quadratic splitting depth unfolding, which has the following beneficial effects:

[0107] (1) To address the slow extraction speed of traditional iterative algorithms, this invention first establishes an optimization model based on the SAR target scattering center model and sparse representation theory; then, based on the depth unfolding method, the semi-quadratic split iterative optimization algorithm is unfolded into a neural network, and a loss function is designed to automatically update the parameters through gradient descent; finally, the neural network is trained and the model parameters are saved for use in extracting SAR target scattering center parameters from the test set. The inference time of the soft threshold iterative algorithm is approximately 73.6324 seconds, while the method proposed in this invention reduces the inference time to 0.2358 seconds, which is approximately 312 times more efficient than the soft threshold iterative algorithm.

[0108] (2) To address the low accuracy problem of traditional algorithms, the proposed method for rapid extraction of SAR target scattering center parameters uses a neural network to automatically learn model parameters, thus avoiding accuracy loss due to improper parameter settings. Regarding image reconstruction quality, the peak signal-to-noise ratio (PSNR) of the approximate message passing algorithm is 39.17 dB, while the proposed method improves the PSNR to 39.82 dB, an increase of 0.65 dB. Attached Figure Description

[0109] Figure 1 is a flowchart of the rapid extraction method for SAR target scattering center parameters of the present invention;

[0110] Figure 2 is a schematic diagram of the prior embedding depth unfolded network structure of the present invention;

[0111] Figure 3 shows the image reconstruction results of the present invention, where (a) is the original image and (b) is the reconstructed image. Detailed Implementation

[0112] A fast method for extracting SAR target scattering center parameters based on depth unfolding includes the following steps:

[0113] Step 1: Based on sparse representation theory, the problem of extracting SAR target scattering center parameters is transformed into an optimization problem of sparse coefficient vectors;

[0114] Step 1.1: Construct a SAR target scattering center model based on geometric diffraction theory and physical optics theory;

[0115] According to geometric diffraction theory and physical optics theory, the SAR target response at a small angle is the sum of the responses of K SAR target scattering centers. Therefore, the SAR target scattering center model is:

[0116]

[0117] Where f is the frequency vector of the synthetic aperture radar. f is the azimuth vector of the synthetic aperture radar; c The center frequency; For radar echo signals, The imaginary unit is Θ, where c represents the speed of light, exp represents an exponential function with the natural constant e as its base, K is the number of SAR target scattering centers, and Θ = {θ1, θ2, ... θ}. K} represents the set consisting of K SAR target scattering center parameter sets; θ i It is the set of parameters of the scattering center of the i-th SAR target, where i ranges from [1, K]; θ i ={A i ,α i ,x i ,y i}, A i Let x be the echo amplitude of the i-th SAR target scattering center. i Let y be the range coordinate of the i-th SAR target scattering center. i Let α be the azimuth coordinate of the i-th SAR target scattering center. i Let be the frequency dependence factor of the i-th SAR target scattering center; the frequency dependence factor is selected from the frequency dependence factor set, which is {-1,-0.5,0,0.5,1}.

[0118] Step 1.2: Based on sparse representation theory and SAR target scattering center model, the problem of extracting SAR target scattering center parameters is transformed into an optimization problem of sparse coefficient vector;

[0119] Radar echo signals are sparse in the SAR target scattering center parameter space. The idea of ​​sparse signal representation is used to effectively analyze and extract SAR target scattering center parameters.

[0120] According to sparse representation theory, the SAR target scattering center model in step 1.1 is expressed as:

[0121]

[0122] in, Radar echo signal The vectorized form of z is a sparse coefficient vector, and z corresponds to the SAR target scattering center model. This represents a signal domain dictionary containing information about the location of the SAR target scattering center. Corresponding to the SAR target scattering center model x is the range vector; y is the azimuth vector; A is the echo amplitude vector; α is the frequency dependence factor vector;

[0123] Signal domain dictionary Represented by column:

[0124]

[0125] For signal domain dictionary The column, x h Let y represent the h-th element of the distance vector x. w Represents the w-th element of the azimuth vector y; signal domain dictionary The dimension is PQ×HW, which is the signal domain dictionary. The frequency vector f of the synthetic aperture radar is formed by uniformly sampling P times within the frequency range, and the azimuth vector of the synthetic aperture radar is formed by uniformly sampling Q times within the azimuth range. The range vector x is formed by uniformly sampling H times within the range direction, and the azimuth vector y is formed by uniformly sampling W times within the azimuth direction; vec means converting the matrix into a one-dimensional vector.

[0126] For the signal domain dictionary Perform an inverse Fourier transform on each column to convert the signal domain dictionary from the signal domain to the image domain, obtaining the image domain dictionary Φ; the image domain dictionary is represented as a sparse diagonal matrix, where the SAR target scattering centers corresponding to each column are concentrated near the diagonal;

[0127] Therefore, the problem of extracting SAR target scattering center parameters is essentially a matching problem;

[0128] According to the inverse Fourier transform, equation (1-2) is transformed into an image-domain SAR target scattering center model based on sparse representation theory. The image-domain SAR target scattering center model based on sparse representation theory is expressed as follows:

[0129] s=Φz (1-5)

[0130] Where s represents the radar echo signal in the image domain; Φ represents the image domain dictionary in the image domain;

[0131] The problem of extracting SAR target scattering center parameters is transformed into an optimization problem of the sparse coefficient vector z:

[0132]

[0133] in, This means optimizing z to find the objective function ||s-Φz||. 2 +λ||z||1 yields the minimum value of z; λ is a hyperparameter that balances data fidelity and sparsity.

[0134] Step 2: Construct the solution process for the optimization problem of constructing a sparse coefficient vector using the semi-quadratic splitting method;

[0135] The semi-quadratic splitting method is used to solve the compressed sensing problem, which is transformed into the following optimization problem:

[0136]

[0137] Where B is a matrix of size m×n, ω is an n-dimensional vector, b is an m-dimensional measurement vector, and b is used to represent the observed value of the signal;

[0138] The optimization problem solved by the semi-quadratic splitting method is consistent with the problem of extracting SAR target scattering center parameters in step 1.2, which is transformed into an optimization problem of sparse coefficient vectors. Therefore, the problem of extracting SAR target scattering center parameters is transformed into a compressed sensing problem, and the semi-quadratic splitting method is used to solve the problem of extracting SAR target scattering center parameters.

[0139] The solution process for the optimization problem of constructing a sparse coefficient vector using the semi-quadratic splitting method is as follows:

[0140] To simplify gradient calculation, the original objective function is scaled to obtain the standard form of the objective function:

[0141]

[0142] In the formula, Φ is the image domain dictionary, s is the radar echo signal in the image domain, and z is the sparse coefficient vector;

[0143] The semi-quadratic splitting method introduces an auxiliary variable u, which equivalently transforms the standard form objective function into an objective function with the auxiliary variable u:

[0144]

[0145] In the formula This means optimizing z and u to find an objective function that incorporates auxiliary variables. Find the minimum z and u values; the subject to u = z is an equality constraint that ensures that z and u are equal in the optimal solution.

[0146] Furthermore, a quadratic penalty function is applied to the objective function that introduces auxiliary variables. Relaxing the constraints transforms the equality constraint u = z into a soft constraint, yielding the objective function after constraint relaxation:

[0147]

[0148] In the formula, μ is the penalty term hyperparameter; the semi-quadratic splitting method alternately optimizes z and u in the iteration to approximate the optimal solution of the objective function after relaxing the constraints; the iterative alternating optimization process is expressed as:

[0149]

[0150] z k Let u be the sparse coefficient vector obtained in the k-th iteration. k The auxiliary variable obtained in the k-th iteration;

[0151] in, This means optimizing z to find the objective function. The z-value that yields the minimum value This means optimizing u to find the objective function. The value of u that yields the minimum value; k, k-1 represent the number of iterations;

[0152] According to the normal equation Solve for z to obtain z k :

[0153]

[0154] The normal equation is:

[0155] (Φ * Φ+μI)z k =Φ * s+μu k-1 (2-7)

[0156] Where, Φ * Let Φ denote the conjugate transpose of Φ, and I be the identity matrix;

[0157] u is solved using the soft threshold iterative algorithm. k :

[0158] u k =S ρ (u k-1 +tΦ * (z k -Φu k-1 (2-8)

[0159] Where t and S ρ (·) represent the step size hyperparameter and the soft thresholding function, respectively. The complex soft thresholding function is expressed as:

[0160] S ρ (v)=sign(v)max(|v|-ρ,0), (2-9)

[0161]

[0162] Where v is a complex number, ρ is the threshold hyperparameter, and |v| represents the modulus of the complex number v;

[0163] The semi-quadratic splitting method is used to solve the problem of extracting SAR target scattering center parameters, resulting in a sparse coefficient vector z. k and auxiliary variable u k , z k Let u be the sparse coefficient vector obtained in the k-th iteration. k The auxiliary variable obtained in the k-th iteration;

[0164] Step 3: Solving the optimization problem of constructing sparse coefficient vectors based on the semi-quadratic splitting method; Constructing a prior embedding deep unfolding network;

[0165] Step 3.1: Construct a prior embedding deep unfolded network;

[0166] In the traditional semi-quadratic splitting method, the penalty term hyperparameter μ, the threshold hyperparameter ρ, and the step size hyperparameter t are usually manually selected based on prior information. These hyperparameters remain unchanged during the algorithm iteration process, and a large number of iteration update steps are required, resulting in a slow convergence speed.

[0167] Deep unfolding is a method that combines iterative optimization and deep learning. The core idea of ​​deep unfolding is to unfold the iterative steps of traditional optimization algorithms into the hierarchical structure of neural networks. By dynamically learning hyperparameters and compressing the iterative process, an end-to-end trainable deep unfolded network can be constructed.

[0168] To address the problem of extracting SAR target scattering center parameters, a prior embedding depth unfolding network based on the semi-quadratic splitting method is constructed, which combines the depth unfolding method and the semi-quadratic splitting method with the image domain dictionary to provide SAR target scattering center location information.

[0169] The prior embedding deep unfolded network consists of N identical stages, which are cascaded together; the hyperparameter of each stage is μ. d ρ d and t d The range of d is [1, N]. The input of the prior embedding deep unfolding network is the radar echo signal in the image domain, and the output is the sparse coefficient vector z of the Nth stage. N and the auxiliary variable u in stage N N ;

[0170] Based on the solution process of the optimization problem of constructing sparse coefficient vectors using the semi-quadratic splitting method described in step 2, the prior embedding depth unfolding network of the d-th stage is represented as:

[0171]

[0172] In the formula, μ d , ρ d and t d z is the learnable parameter for the d-th stage; d Let u be the sparse coefficient vector of the d-th stage of the prior embedding deep unfolded network. d , which are auxiliary variables for the d-th stage of the prior embedding deep unrolled network; d represents the d-th stage of the prior embedding deep unrolled network, and d-1 represents the d-1-th stage of the prior embedding deep unrolled network;

[0173] The specific structure of the d-th stage of the prior embedding deep unfolded network is shown in Figure 2.

[0174] Compared to the traditional semi-quadratic split algorithm, the prior embedding deep unfolding network based on the semi-quadratic split method does not rely on manually designed hyperparameters and uses the backpropagation algorithm to automatically update the learnable parameters; the number of parameters and inference time of the prior embedding deep unfolding network depend on the size of N.

[0175] Step 3.2: Construct the loss function for the prior embedding deep unfolded network;

[0176] During the training of the prior embedding deep unfolding network, the input SAR image is converted into a one-dimensional vector through vectorization to obtain the radar echo signal s in the image domain, which serves as the input to the prior embedding deep unfolding network. The prior embedding deep unfolding network can progressively extract the SAR target scattering center information; the sparse coefficient vector z in the Nth stage... N The reconstructed image vector s is obtained by matrix multiplication with the image domain dictionary Φ. reconstruct s reconstruct =Φz N ;

[0177] Combining the constraints of the semi-quadratic splitting method, the loss function of the prior embedding deep unfolded network includes residual loss, regularization loss, penalty loss and total loss function;

[0178] Residual loss L residual for:

[0179] L residual =||ss reconstruct ||2(3-3)

[0180] Residual loss ensures the reconstruction of graph vectors s reconstruct Consistency with the radar echo signal s in the image domain;

[0181] Regularization loss L regular for:

[0182] L regular =λ r ||u N ||1(3-4)

[0183] In the formula λ r To constrain the auxiliary variable u in stage N N The sparsity hyperparameter, the regularization loss L regular Ensure the auxiliary variable u in stage N N sparsity;

[0184] Penalty Loss L penalty for:

[0185] L penalty =λ p ||z N -u N ||2(3-5)

[0186] In the formula λ p To constrain the auxiliary variable u in stage N N With the sparse coefficient vector z of the Nth stage N Consistency hyperparameters, penalty loss L penalty Ensure the auxiliary variable u in stage N N With the sparse coefficient vector z of the Nth stage N Consistency between them;

[0187] The total loss function is L total :

[0188] L total =L residual +L regular +L penalty (3-6)

[0189] Step 4: Extract SAR target scattering center parameters using a priori embedding depth unrolling network;

[0190] Step 4.1: Train the prior embedding deep unfolding network;

[0191] Step 4.1.1: Data Preprocessing:

[0192] The training set images are cropped to obtain 80×80 pixel input images, which are then L2 normalized. The normalized input images are then vectorized into one-dimensional vectors to obtain the radar echo signal s in the image domain.

[0193] Step 4.1.2: Train the prior embedding deep unfolding network:

[0194] The training set images undergo data preprocessing to obtain radar echo signals s in the image domain, which are used as input to the prior embedding deep unrolling network. The d-th stage of the prior embedding deep unrolling network is as follows:

[0195]

[0196] In the formula z d Let u be the sparse coefficient vector of the d-th stage of the prior embedding deep unfolded network. d μ is an auxiliary variable for the d-th stage of the prior embedding deep unfolded network. d , ρ d and t dLet z be the learnable parameters for the d-th stage; after N stages, the sparse coefficient vector z for the N-th stage is obtained. N and the auxiliary variable u in stage N N ;z N The reconstructed image vector s is obtained by matrix multiplication with the image domain dictionary Φ. reconstruct s reconstruct =Φz N ; through L residual Constraint Reconstruction Graph Vectors s reconstruct The difference between the radar echo signal s in the image domain and L regular constraint u N The sparsity, through L penalty Keep z N with u N The consistency is specifically represented as follows:

[0197] L residual =||ss reconstruct ||2(4-3)

[0198] L regular =λ r ||u N ||1(4-4)

[0199] L penalty =λ p ||z N -u N ||2(4-5)

[0200] L total =L residual +L regular +L penalty (4-6)

[0201] Total loss function L total By L residual L regular and L penalty Together they form; when the total loss function L total If the network stabilizes after multiple iterations, meaning the loss value no longer decreases, the prior embedding depth unfolding network is considered to have converged. The learnable parameters of each stage of the prior embedding depth unfolding network at this point are saved for subsequent SAR target scattering center parameter extraction.

[0202] Step 4.2: Extraction of SAR target scattering center parameters and image reconstruction;

[0203] Step 4.2.1: Extraction of SAR target scattering center parameters:

[0204] Load the learned parameters for each stage stored in the prior embedding deep unrolling network;

[0205] After the data preprocessing in step 4.1.1, the test set images are input into the model to obtain the sparse coefficient vector z of the Nth stage. N ;

[0206] According to z N The SAR target scattering center parameters are obtained through inversion: x K y K A K α K K is the number of SAR target scattering centers;

[0207] Where, x K Let x represent a vector containing the range coordinates of the scattering centers of K SAR targets. K = [x1,x2,…,x i ,…x K ], x i Let y be the range coordinate of the i-th SAR target scattering center; K Let y represent a vector containing the azimuth coordinates of the scattering centers of K SAR targets. K =[y1,y2,…,y i ,…y K ], y i Let A be the azimuth coordinate of the scattering center of the i-th SAR target; K A represents a vector containing the echo amplitudes of the scattering centers of K SAR targets. K =[A1,A2,…,A i ,…A K A i α is the echo amplitude of the i-th SAR target scattering center; K Let α represent a vector containing K frequency dependence factors of the SAR target scattering center. K =[α1,α2,…,α i ,…,α K ], α i The frequency dependence factor of the scattering center of the i-th SAR target;

[0208] To obtain the SAR target scattering center parameter set θ of the i-th SAR target scattering center i First, determine the scattering center of the i-th SAR target at z. N The index value is mapped to an 80×80 grid to obtain the pixel position of the i-th SAR target scattering center; then, based on the initial sampled value of the pixel position, the range coordinate x of the i-th SAR target scattering center is obtained. i azimuth coordinate y i For index values ​​in z N The absolute value of the corresponding value is taken to obtain the echo amplitude A of the i-th SAR target scattering center.i ; Calculate the index value in z N The phase angle corresponding to the value in the equation, wherein the unit of the phase angle is radians;

[0209] Elements are selected sequentially from the set of frequency dependence factors α {-1, -0.5, 0, 0.5, 1}. The element with the smallest absolute difference between the selected element and the phase angle is taken as the frequency dependence factor α of the i-th SAR target scattering center. i ;

[0210] x i y i A i α i That is, the scattering center parameter of the i-th SAR target;

[0211] Step 4.2.2: Image reconstruction and image quality assessment;

[0212] Based on the sparse coefficient vector z of the Nth stage N The reconstructed graph vector s is obtained from the image domain dictionary Φ. reconstruct :

[0213] s reconstruct =Φz N (4-7)

[0214] Reconstruct the graph vectors s reconstruct The reconstructed image is obtained by restoring the image to a two-dimensional form.

[0215] Peak signal-to-noise ratio (PSNR) is used to evaluate the quality of the reconstruction results, with the unit being decibels (dB). A higher PSNR indicates better reconstructed image quality. The formula for calculating PSNR is:

[0216]

[0217] MSE is the mean squared error. The smaller the mean squared error, the better the quality of the reconstructed image.

[0218] The formula for calculating the mean square error is:

[0219]

[0220] Where s (l) This represents the l-th element of the radar echo signal s in the image domain. Represents the reconstructed graph vector s reconstruct The l-th element, where l ranges from [1, L]; L is the reconstructed graph vector s. reconstruct Length;

[0221] PSNR is Peak Signal-to-Noise Ratio;

[0222] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0223] Example 1: Referring to Figure 1, a method for rapid extraction of SAR target scattering center parameters based on depth unfolding is described. The process includes:

[0224] Step 1: Based on sparse representation theory, the problem of extracting SAR target scattering center parameters is transformed into an optimization problem of sparse coefficient vectors;

[0225] Step 1.1: Construct a SAR target scattering center model based on geometric diffraction theory and physical optics theory;

[0226] According to geometric diffraction theory and physical optics theory, the SAR target response at a small angle is the sum of the responses of K SAR target scattering centers. Therefore, the SAR target scattering center model is:

[0227]

[0228] Where f is the frequency vector of the synthetic aperture radar. f is the azimuth vector of the synthetic aperture radar; c The center frequency; For radar echo signals, The imaginary unit is Θ, where c represents the speed of light, exp represents an exponential function with the natural constant e as its base, K is the number of SAR target scattering centers, and Θ = {θ1, θ2, ... θ}. K} represents the set consisting of K SAR target scattering center parameter sets; θ i It is the set of parameters of the scattering center of the i-th SAR target, where i ranges from [1, K]; θ i ={A i ,α i ,x i ,y i}, A i Let x be the echo amplitude of the i-th SAR target scattering center. i Let y be the range coordinate of the i-th SAR target scattering center. i Let α be the azimuth coordinate of the i-th SAR target scattering center. i Let be the frequency dependence factor of the i-th SAR target scattering center; the frequency dependence factor is selected from the set {-1,-0.5,0,0.5,1}.

[0229] Table 1: Different α values i The scatterer structure corresponding to the value

[0230] αi Scattering structure: -1 angular diffraction, apex diffraction, -0.5 edge diffraction, 0-point scattering, hyperboloid reflection, straight-edge specular reflection, 0.5 monoboloid reflection, 1-plate normal reflection, dihedral reflection, trihedral reflection. surface

[0231] Step 1.2: Based on sparse representation theory and SAR target scattering center model, the problem of extracting SAR target scattering center parameters is transformed into an optimization problem of sparse coefficient vector;

[0232] Radar echo signals are sparsity in the SAR target scattering center parameter space. The idea of ​​sparse signal representation is used to effectively analyze and extract SAR target scattering center parameters.

[0233] According to sparse representation theory, the SAR target scattering center model in step 1.1 is expressed as:

[0234]

[0235] in, Radar echo signal The vectorized form of , where z is a sparse coefficient vector, corresponding to the SAR target scattering center model. This represents the signal domain dictionary containing SAR target scattering center location information, corresponding to the SAR target scattering center model. x is the range vector; y is the azimuth vector; A is the echo amplitude vector; α is the frequency dependence factor vector;

[0236] Signal domain dictionary Represented by column:

[0237]

[0238] For signal domain dictionary The column, x h Let y represent the h-th element of the distance vector x. w Represents the w-th element of the azimuth vector y; signal domain dictionary The dimension is PQ×HW, which is the signal domain dictionary. The frequency vector f of the synthetic aperture radar is formed by uniformly sampling P times within the frequency range, and the azimuth vector of the synthetic aperture radar is formed by uniformly sampling Q times within the azimuth range. The range vector x is formed by uniformly sampling H times within the range direction, and the azimuth vector y is formed by uniformly sampling W times within the azimuth direction; vec means converting the matrix into a one-dimensional vector.

[0239] For the signal domain dictionary Perform an inverse Fourier transform on each column to convert the signal domain dictionary from the signal domain to the image domain, obtaining the image domain dictionary Φ; the image domain dictionary is represented as a sparse diagonal matrix, where the SAR target scattering centers corresponding to each column are concentrated near the diagonal;

[0240] Therefore, the problem of extracting SAR target scattering center parameters is essentially a matching problem;

[0241] According to the inverse Fourier transform, equation (1-2) is transformed into an image-domain SAR target scattering center model based on sparse representation theory. The image-domain SAR target scattering center model based on sparse representation theory is expressed as follows:

[0242] s=Φz (1-5)

[0243] Where s represents the radar echo signal in the image domain; Φ represents the image domain dictionary in the image domain;

[0244] The problem of extracting SAR target scattering center parameters is transformed into an optimization problem of the sparse coefficient vector z:

[0245]

[0246] in, This means optimizing z to find the objective function ||s-Φz||. 2 +λ||z||1 yields the minimum value of z; λ is a hyperparameter that balances data fidelity and sparsity.

[0247] This example is based on the open-source MSTAR (The Moving and Stationary Target Acquisition and Recognition) vehicle target recognition dataset collected and released by Sandia National Laboratories in the United States. In the MSTAR dataset, the targets are concentrated in the 80×80 region in the center of the image. Therefore, the sampling times P, Q, H, and W are all set to 80. The hyperparameter settings of the signal domain dictionary are shown in Table 2.

[0248] Table 2: Signal Domain Dictionary Hyperparameter Settings

[0249]

[0250]

[0251] The signal domain dictionary is converted into an image domain dictionary using the inverse Fourier transform. The image domain dictionary has a dimension of 6400×6400. The image domain dictionary is saved as a .mat file for easy reading and use later.

[0252] Step 2: Construct the solution process for the optimization problem of constructing a sparse coefficient vector using the semi-quadratic splitting method;

[0253] The semi-quadratic splitting method is often used to solve compressed sensing problems. Solving compressed sensing problems is transformed into the following optimization problem:

[0254]

[0255] Where B is a matrix of size m×n, ω is an n-dimensional vector, b is an m-dimensional measurement vector, and b is used to represent the observed value of the signal;

[0256] The optimization problem solved by the semi-quadratic splitting method is consistent with the problem of extracting SAR target scattering center parameters in step 1.2, which is transformed into an optimization problem of sparse coefficient vectors. Therefore, the problem of extracting SAR target scattering center parameters is transformed into a compressed sensing problem, and the semi-quadratic splitting method is used to solve the problem of extracting SAR target scattering center parameters.

[0257] The solution process for the optimization problem of constructing a sparse coefficient vector using the semi-quadratic splitting method is as follows:

[0258] To simplify gradient calculation, the original objective function is scaled to obtain the standard form of the objective function:

[0259]

[0260] In the formula, Φ is the image domain dictionary, s is the radar echo signal in the image domain, and z is the sparse coefficient vector;

[0261] The semi-quadratic splitting method introduces an auxiliary variable u, which equivalently transforms the standard form objective function into an objective function with the auxiliary variable u:

[0262]

[0263] In the formula This means optimizing z and u to find an objective function that incorporates auxiliary variables. Find the minimum z and u values; the subject to u = z is an equality constraint that ensures that z and u are equal in the optimal solution.

[0264] Furthermore, a quadratic penalty function is applied to the objective function that introduces auxiliary variables. Relaxing the constraints transforms the equality constraint u = z into a soft constraint, yielding the objective function after constraint relaxation:

[0265]

[0266] In the formula, μ is the penalty term hyperparameter; the semi-quadratic splitting method alternately optimizes z and u in the iteration to approximate the optimal solution of the objective function after relaxing the constraints; the iterative alternating optimization process is expressed as:

[0267]

[0268] z k Let u be the sparse coefficient vector obtained in the k-th iteration. k The auxiliary variable obtained in the k-th iteration;

[0269] in, This means optimizing z to find the objective function. The z-value that yields the minimum value This means optimizing u to find the objective function. The value of u that yields the minimum value; k, k-1 represent the number of iterations;

[0270] According to the normal equation Solve for z to obtain z k :

[0271]

[0272] The normal equation is:

[0273] (Φ * Φ+μI)z k =Φ * s+μu k-1 (2-7)

[0274] Where, Φ * Let Φ denote the conjugate transpose of Φ, and I be the identity matrix;

[0275] u is solved using the soft threshold iterative algorithm. k :

[0276] u k =S ρ (u k-1 +tΦ * (z k -Φu k-1 (2-8)

[0277] Where t and S ρ(·) represent the step size hyperparameter and the soft thresholding function, respectively. The complex soft thresholding function is expressed as:

[0278] S ρ (v)=sign(v)max(|v|-ρ,0), (2-9)

[0279]

[0280] Where v is a complex number, ρ is the threshold hyperparameter, and |v| represents the modulus of the complex number v;

[0281] The semi-quadratic splitting method is used to solve the problem of extracting SAR target scattering center parameters, resulting in a sparse coefficient vector z. k and auxiliary variable u k , z k Let u be the sparse coefficient vector obtained in the k-th iteration. k The auxiliary variable obtained in the k-th iteration;

[0282] Step 3: Solving the optimization problem of constructing sparse coefficient vectors based on the semi-quadratic splitting method; Constructing a prior embedding deep unfolding network;

[0283] Step 3.1: Construct a prior embedding deep unfolded network;

[0284] In the traditional semi-quadratic splitting method, the penalty term hyperparameter μ, the threshold hyperparameter ρ, and the step size hyperparameter t are usually manually selected based on prior information. These hyperparameters remain unchanged during the algorithm iteration process, and a large number of iteration update steps are required, resulting in a slow convergence speed.

[0285] Deep unfolding is a method that combines iterative optimization and deep learning. The core idea of ​​deep unfolding is to unfold the iterative steps of traditional optimization algorithms into the hierarchical structure of neural networks. By dynamically learning hyperparameters and compressing the iterative process, an end-to-end trainable deep unfolded network can be constructed.

[0286] To address the problem of extracting SAR target scattering center parameters, a prior embedding depth unfolding network based on the semi-quadratic splitting method is constructed, which combines the depth unfolding method and the semi-quadratic splitting method with the image domain dictionary to provide SAR target scattering center location information.

[0287] The prior embedding deep unfolded network consists of N identical stages, which are cascaded together; the hyperparameter of each stage is μ. d ρ d and t d The range of d is [1, N]. The input of the prior embedding deep unfolding network is the radar echo signal in the image domain, and the output is the sparse coefficient vector z of the Nth stage. N and the auxiliary variable u in stage NN ;

[0288] Based on the solution process of the optimization problem of constructing sparse coefficient vectors using the semi-quadratic splitting method described in step 2, the prior embedding depth unfolding network of the d-th stage is represented as:

[0289]

[0290] In the formula, μ d , ρ d and t d z is the learnable parameter for the d-th stage; d Let u be the sparse coefficient vector of the d-th stage of the prior embedding deep unfolded network. d , which are auxiliary variables for the d-th stage of the prior embedding deep unrolled network; d represents the d-th stage of the prior embedding deep unrolled network, and d-1 represents the d-1-th stage of the prior embedding deep unrolled network;

[0291] The specific structure of the d-th stage of the prior embedding deep unfolded network is shown in Figure 2.

[0292] Compared to the traditional semi-quadratic split algorithm, the prior embedding deep unfolding network based on the semi-quadratic split method does not rely on manually designed hyperparameters and uses the backpropagation algorithm to automatically update the learnable parameters; the number of parameters and inference time of the prior embedding deep unfolding network depend on the size of N.

[0293] Step 3.2: Construct the loss function for the prior embedding deep unfolded network;

[0294] During the training of the prior embedding deep unfolding network, the input SAR image is converted into a one-dimensional vector through vectorization to obtain the radar echo signal s in the image domain, which serves as the input to the prior embedding deep unfolding network. The prior embedding deep unfolding network can progressively extract the SAR target scattering center information; the sparse coefficient vector z in the Nth stage... N The reconstructed image vector s is obtained by matrix multiplication with the image domain dictionary Φ. reconstruct s reconstruct =Φz N Reconstructing graph vectors s through constraints reconstruct Parameter optimization is performed based on the difference between the radar echo signal s in the image domain and the actual signal s.

[0295] Combining the constraints of the semi-quadratic splitting method, the loss function of the prior embedding deep unfolded network includes residual loss, regularization loss, penalty loss and total loss function;

[0296] Residual loss L residual for:

[0297] L residual=||ss reconstruct ||2(3-3)

[0298] Residual loss ensures the reconstruction of graph vectors s reconstruct Consistency with input s;

[0299] Regularization loss L regular for:

[0300] L regular =λ r ||u N ||1(3-4)

[0301] In the formula λ r To constrain the auxiliary variable u in stage N N The sparsity hyperparameter, the regularization loss L regular Ensure the auxiliary variable u in stage N N sparsity;

[0302] Penalty Loss L penalty for:

[0303] L penalty =λ p ||z N -u N ||2(3-5)

[0304] In the formula λ p To constrain the auxiliary variable u in stage N N With the sparse coefficient vector z of the Nth stage N Consistency hyperparameters, penalty loss L penalty Ensure the auxiliary variable u in stage N N With the sparse coefficient vector z of the Nth stage N Consistency between them;

[0305] The total loss function is L total :

[0306] L total =L residual +L regular +L penalty (3-6)

[0307] Step 4: Extract SAR target scattering center parameters using a priori embedding depth unrolling network;

[0308] Step 4.1: Train the prior embedding deep unfolding network;

[0309] Step 4.1.1: Data Preprocessing:

[0310] The training set images are cropped to obtain 80×80 pixel input images, which are then L2 normalized. The normalized input images are then vectorized into one-dimensional vectors to obtain the radar echo signal s in the image domain.

[0311] Step 4.1.2: Train the prior embedding deep unfolding network:

[0312] The training set images undergo data preprocessing to obtain radar echo signals s in the image domain, which are used as input to the prior embedding deep unrolling network. The d-th stage of the prior embedding deep unrolling network is as follows:

[0313]

[0314] In the formula z d Let u be the sparse coefficient vector of the d-th stage of the prior embedding deep unfolded network. d μ is an auxiliary variable for the d-th stage of the prior embedding deep unfolded network. d , ρ d and t d Let z be the learnable parameters for the d-th stage; after N stages, the sparse coefficient vector z for the N-th stage is obtained. N and the auxiliary variable u in stage N N ;z N The reconstructed image vector s is obtained by matrix multiplication with the image domain dictionary Φ. reconstruct s reconstruct =Φz N ; through L residual Constraint Reconstruction Graph Vectors s reconstruct The difference between the radar echo signal s in the image domain and L regular constraint u N The sparsity, through L penalty Keep z N with u N The consistency is specifically represented as follows:

[0315] L residual =||ss reconstruct ||2(4-3)

[0316] L regular =λ r ||u N ||1(4-4)

[0317] L penalty =λ p ||z N -u N ||2(4-5)

[0318] L total =Lresidual +L regular +L penalty (4-6)

[0319] During model training, the AdamW optimizer was used, with a stability coefficient of 1×10⁻⁶. -6 The weight decay coefficient is set to 0.005. The OneCycleLR learning rate scheduler is used to design a periodic learning rate adjustment strategy for the optimizer. The learning rate first increases linearly to its maximum value (5 times the initial learning rate) in each training cycle, and then gradually decreases over the remaining training cycles according to the cosine annealing strategy until training is complete.

[0320] When calculating the loss function, λ p The value is 100, λ r The value is 200. When the total loss function L total If the network stabilizes after multiple iterations, meaning the loss value no longer decreases, the prior embedding depth unfolding network is considered to have converged. The learnable parameters of each stage of the prior embedding depth unfolding network at this point are saved for subsequent SAR target scattering center parameter extraction.

[0321] Step 4.2: Extraction of SAR target scattering center parameters and image reconstruction:

[0322] Step 4.2.1: Extraction of SAR target scattering center parameters:

[0323] Load the learned parameters for each stage stored in the prior embedding deep unrolling network;

[0324] After the data preprocessing in step 4.1.1, the test set images are input into the model to obtain the sparse coefficient vector z of the Nth stage. N ;

[0325] According to z N The SAR target scattering center parameters are obtained through inversion: x K y K A K α K K is the number of SAR target scattering centers;

[0326] Where, x K Let x represent a vector containing the range coordinates of the scattering centers of K SAR targets. K = [x1,x2,…,x i ,…x K ], x i Let y be the range coordinate of the i-th SAR target scattering center; K Let y represent a vector containing the azimuth coordinates of the scattering centers of K SAR targets. K =[y1,y2,…,yi ,…y K ], y i Let A be the azimuth coordinate of the scattering center of the i-th SAR target; K A represents a vector containing the echo amplitudes of the scattering centers of K SAR targets. K =[A1,A2,…,A i ,…A K A i α is the echo amplitude of the i-th SAR target scattering center; K Let α represent a vector containing K frequency dependence factors of the SAR target scattering center. K =[α1,α2,…,α i ,…,α K ], α i The frequency dependence factor of the scattering center of the i-th SAR target;

[0327] To obtain the SAR target scattering center parameter set θ of the i-th SAR target scattering center i First, determine the scattering center of the i-th SAR target at z. N The index value is mapped to an 80×80 grid to obtain the pixel position of the i-th SAR target scattering center; then, based on the initial sampled value of the pixel position, the range coordinate x of the i-th SAR target scattering center is obtained. i and azimuth coordinates y i For index values ​​in z N The absolute value of the corresponding value is taken to obtain the echo amplitude A of the i-th SAR target scattering center. i ; Calculate the index value in z N The phase angle corresponding to the value in the equation, wherein the unit of the phase angle is radians;

[0328] Elements are selected sequentially from the set of frequency dependence factors α {-1, -0.5, 0, 0.5, 1}. The element with the smallest absolute difference between the selected element and the phase angle is taken as the frequency dependence factor α of the i-th SAR target scattering center. i ;

[0329] x i y i A i α i That is, the scattering center parameter of the i-th SAR target;

[0330] (2) Image reconstruction and image quality assessment:

[0331] Based on the sparse coefficient vector z of the Nth stage N The reconstructed graph vector s is obtained from the image domain dictionary Φ. reconstruct :

[0332] s reconstruct =Φz N (4-7)

[0333] Reconstruct the graph vectors s reconstruct The reconstructed image is obtained by restoring the image to a two-dimensional form.

[0334] Peak signal-to-noise ratio (PSNR) is used to evaluate the quality of the reconstruction results, with the unit being decibels (dB). A higher PSNR indicates better reconstructed image quality. The formula for calculating PSNR is:

[0335]

[0336] MSE is the mean squared error. The smaller the mean squared error, the better the quality of the reconstructed image.

[0337] The formula for calculating the mean square error is:

[0338]

[0339] Where s (l) This represents the l-th element of the radar echo signal s in the image domain. Represents the reconstructed graph vector s reconstruct The l-th element, where l ranges from [1, L]; L is the reconstructed graph vector s. reconstruct Length;

[0340] PSNR is Peak Signal-to-Noise Ratio;

[0341] Example 2: Unlike Example 1, this example is designed to verify the effectiveness of the rapid extraction method for SAR target scattering center parameters as described in Example 1.

[0342] 1. Simulation conditions;

[0343] This invention is based on simulation using the PyTorch framework on an Intel(R) i9-10900X 3.7GHz CPU, 256GB of memory, four Nvidia GTX3090 GPUs, and an Ubuntu 18.04 operating system. The dataset used in the experiment is the MSTAR dataset.

[0344] 2. Simulation content;

[0345] The fast extraction method for SAR target scattering center parameters described in Example 1 was tested, and the results are shown in Table 3. The peak signal-to-noise ratio and inference time of the proposed method are compared with those of the traditional approximate message passing algorithm, orthogonal matching pursuit algorithm and soft thresholding iteration algorithm.

[0346] Table 3: Comparison of Peak Signal-to-Noise Ratio and Inference Time

[0347] Methods: Unit approximation message passing algorithm, orthogonal matching pursuit algorithm, soft thresholding iterative algorithm. The peak signal-to-noise ratio (PSNR) of the proposed method is 39.17 (Bb), 38.05 (Bb), 38.31 (Bb), and 39.82 (Bb). Inference time is 84.53 (Sb), 1106.18 (Sb), 3973.63 (Sb), and 240.2358 (Sb). surface

[0348] The reconstruction result is shown in Figure 3.

Claims

1. A method for rapid extraction of SAR target scattering center parameters based on depth unfolding, characterized in that, The process includes the following steps: Step 1: Based on sparse representation theory, the problem of extracting SAR target scattering center parameters is transformed into an optimization problem of sparse coefficient vectors; Step 2: The solution process of the optimization problem of sparse coefficient vectors is constructed using the semi-quadratic splitting method; Step 3: Based on the solution process of the optimization problem of sparse coefficient vectors constructed using the semi-quadratic splitting method, a prior embedding depth expansion network is constructed; Step 4: The SAR target scattering center parameters are extracted using the prior embedding depth expansion network.

2. The method for rapid extraction of SAR target scattering center parameters based on depth unfolding according to claim 1, characterized in that, Based on sparse representation theory, the steps to transform the problem of extracting SAR target scattering center parameters into the optimization problem of sparse coefficient vectors are as follows: Step 1.1: Construct a SAR target scattering center model based on geometric diffraction theory and physical optics theory; Step 1.2: Based on sparse representation theory and the SAR target scattering center model, transform the problem of extracting SAR target scattering center parameters into the optimization problem of sparse coefficient vectors.

3. The method for rapid extraction of SAR target scattering center parameters based on depth unfolding according to claim 2, characterized in that, The steps for constructing a SAR target scattering center model based on geometric diffraction theory and physical optics theory are as follows: According to geometric diffraction theory and physical optics theory, the SAR target response at a small angle is... The sum of the responses of each SAR target scattering center; therefore, the SAR target scattering center model is: (1-1) Wherein, For the frequency vector of the synthetic aperture radar, This is the azimuth vector of the synthetic aperture radar; The center frequency; For radar echo signals, The imaginary unit is , c represents the speed of light, and exp represents an exponential function with the natural constant e as the base. The number of SAR target scattering centers. Indicates by A set consisting of a set of SAR target scattering center parameters; ； It is the first A set of SAR target scattering center parameters The range is ； ， For the first The echo amplitude of the scattering center of the SAR target For the first Range coordinates of the scattering center of a SAR target For the first The azimuth coordinates of the scattering center of the SAR target For the first Frequency dependence factor of each SAR target scattering center; Selected from the set of frequency-dependent factors.

4. The method for rapid extraction of SAR target scattering center parameters based on depth unfolding according to claim 2, characterized in that, Based on sparse representation theory and the SAR target scattering center model, the steps to transform the SAR target scattering center parameter extraction problem into an optimization problem of a sparse coefficient vector are as follows: According to sparse representation theory, the SAR target scattering center model in step 1.1 is expressed as: (1-2) Among them, Radar echo signal The vectorized form, It is a sparse coefficient vector. Corresponding to the SAR target scattering center model ； This represents a signal domain dictionary containing information about the location of the SAR target scattering center. Corresponding to the SAR target scattering center model ； It is a distance vector; A is the azimuth vector; A is the echo amplitude vector; A vector of frequency-dependent factors; For the frequency vector of the synthetic aperture radar, Center frequency; c represents the speed of light; signal domain dictionary Represented by column: （1-3） （1-4） For signal domain dictionary The list, Represents the distance vector The One element, Represents the azimuth vector The One element; signal domain dictionary The dimension is That is, the signal domain dictionary Uniform sampling within the frequency range The frequency vector that constitutes the synthetic aperture radar Uniform sampling within the azimuth angle range The azimuth vector that constitutes the synthetic aperture radar. Uniform sampling within the distance range This constitutes the distance vector. Uniform sampling within the azimuth direction This constitutes the azimuth vector. ;vec represents converting a matrix into a one-dimensional vector; for the signal domain dictionary Perform an inverse Fourier transform on each column to convert the signal domain dictionary from the signal domain to the image domain, obtaining the image domain dictionary. The image domain dictionary is represented as a sparse diagonal matrix, where the SAR target scattering centers corresponding to each column are concentrated near the diagonal. According to the inverse Fourier transform, equation (1-2) is transformed into an image domain SAR target scattering center model based on sparse representation theory. The image domain SAR target scattering center model based on sparse representation theory is represented as follows: (1-5) Among them, Represents radar echo signals in the image domain; Represents an image domain dictionary in the image domain; transforms the problem of extracting SAR target scattering center parameters into extracting sparse coefficient vectors. Optimization issues: (1-6) Among them, Indicates to Optimize to find the original objective function Get the minimum value value; To balance the hyperparameters between data fidelity and sparsity.

5. The method for rapid extraction of SAR target scattering center parameters based on depth unfolding according to claim 1, characterized in that, The steps of solving the optimization problem using the semi-quadratic splitting method to construct a sparse coefficient vector are as follows: The semi-quadratic splitting method is used to solve the compressed sensing problem, and the solution of the compressed sensing problem is transformed into the optimization problem of equation (2-1): (2-1) Wherein, It is of size m A matrix of size n It is an n-dimensional vector. It is an m-dimensional measurement vector. The observations used to represent the signal; the solution process for the optimization problem of constructing a sparse coefficient vector using the semi-quadratic splitting method is as follows: To simplify gradient calculation, the original objective function is scaled to obtain the standard form of the objective function: In equation (2-2), For image domain dictionary, For radar echo signals in the image domain, A sparse coefficient vector; the semi-quadratic splitting method introduces auxiliary variables. The standard form of the objective function is equivalently transformed into an objective function that incorporates auxiliary variables: In equation (2-3) Indicates to and Optimize to find the objective function that introduces auxiliary variables. Get the minimum value Value and Value; subject to As an equality constraint, ensure and They are equal at the optimal solution; further, a quadratic penalty function is applied to the objective function that introduces auxiliary variables. Relaxing constraints, removing equality constraints Converting to soft constraints yields the objective function after constraint relaxation: In equation (2-4), The hyperparameter is used as a penalty term; the semi-quadratic splitting method alternately optimizes it in iterations. and The iterative and alternating optimization process approximates the optimal solution of the objective function after relaxing the constraints. （2-5） For the first The sparse coefficient vector obtained from the next iteration. For the first The auxiliary variables obtained from the next iteration; among them... Indicates to Optimize to find the objective function Get the minimum value value, Indicates to Optimize to find the objective function Get the minimum value value; and -1 indicates the iteration number; according to the normal equation... Solve, and obtain ： (2-6) Wherein, the normal equation is: (2-7) Among them, express The conjugate transpose of . The identity matrix is ​​solved using a soft thresholding iterative algorithm. ： (2-8) Among them, and Let these be the step size hyperparameter and the soft thresholding function, respectively. The soft thresholding function for complex numbers is expressed as: （2-9） (2-10) where v is a complex number, For threshold hyperparameters, The modulus of the complex number v is represented; the semi-quadratic splitting method is used to solve the problem of extracting SAR target scattering center parameters, resulting in a sparse coefficient vector. and auxiliary variables ， For the first The sparse coefficient vector obtained from the next iteration. For the first The auxiliary variables obtained from the next iteration.

6. The method for rapid extraction of SAR target scattering center parameters based on depth unfolding according to claim 1, characterized in that, The solution process for the optimization problem based on the semi-quadratic splitting method to construct a sparse coefficient vector involves the following steps for building a priori embedding depth expansion network: Step 3.1: Constructing a priori embedding depth expansion network; For the SAR target scattering center parameter extraction problem, based on the depth expansion method and the semi-quadratic splitting method, combined with the SAR target scattering center location information provided by the image domain dictionary, a priori embedding depth expansion network based on the semi-quadratic splitting method is constructed; the priori embedding depth expansion network includes... The same stage, The same cascaded stages; the hyperparameters of each stage include 、 and ； The range is [1, The prior embedding deep unfolding network takes radar echo signals in the image domain as input and outputs the first... sparse coefficient vector of the stage and the Auxiliary variables of the stage According to the solution process of the optimization problem of constructing sparse coefficient vectors using the semi-quadratic splitting method described in step 2, the first... The prior embedding deep unfolded network representation for each stage is as follows: （3-1） In equation (3-2), 、 and For the first Learnable parameters for each stage; For prior embedding deep unfolded network The sparse coefficient vector of each stage For prior embedding deep unfolded network Auxiliary variables for each stage; The first in the prior embedding deep unfolded network represents the first... stage, -1 indicates the first digit of the prior embedding deep unfolded network. -1 stage; Step 3.2: Construct the loss function of the prior embedding deep unfolding network; During the training process of the prior embedding deep unfolding network, the input SAR image is converted into a one-dimensional vector through vectorization operations to obtain the radar echo signal in the image domain. ， As input to the prior embedding deep unfolding network; the prior embedding deep unfolding network can progressively extract SAR target scattering center information; No. sparse coefficient vector of the stage With image domain dictionary The reconstructed image vectors are obtained through matrix multiplication. ， Combining the constraints of the semi-quadratic splitting method, the loss function of the prior embedding deep unfolded network includes residual loss, regularization loss, penalty loss, and total loss function; residual loss for: (3-3) Residual loss Ensure the reconstruction of graph vectors Radar echo signals in the image domain Consistency between them; regularization loss for: In equation (3-4) To constrain the first Auxiliary variables of the stage The sparsity hyperparameters, regularization loss Ensure the Auxiliary variables of the stage Sparsity; Penalty term loss for: In equation (3-5) To constrain the first Auxiliary variables of the stage With the sparse coefficient vector of the stage Consistency hyperparameters, penalty loss Ensure the Auxiliary variables of the stage With the sparse coefficient vector of the stage Consistency between them; the total loss function is ： (3-6) That is, the total loss function is the sum of residual loss, regularization loss and penalty loss.

7. The method for rapid extraction of SAR target scattering center parameters based on depth unfolding according to claim 1, characterized in that, The steps for extracting SAR target scattering center parameters using a prior embedding deep unrolling network are as follows: Step 4.1: Train the prior embedding deep unrolling network; Step 4.1.1: Data preprocessing: The training set images are cropped to obtain 80×80 pixel input images, and the input images are processed... Normalization; the normalized input image is then vectorized into a one-dimensional vector to obtain the radar echo signal in the image domain. ； Step 4.1.2: Training the prior embedding deep unfolded network: The training set images are preprocessed to obtain radar echo signals in the image domain. ， As input to the prior embedding deep unrolling network; the first... The stages are as follows: （4-1） In equation (4-2) For prior embedding deep unfolded network The sparse coefficient vector of each stage For prior embedding deep unfolded network Auxiliary variables for each stage ， and For the first Learnable parameters for each stage; go through After the first stage, we obtain the second stage. sparse coefficient vector of the stage and the Auxiliary variables of the stage ； With image domain dictionary The reconstructed image vectors are obtained through matrix multiplication. ， ； Reconstructing Graph Vectors Radar echo signals in the image domain The differences between them are through To impose constraints, through constraint The sparsity, through Keep and The consistency is specifically represented as follows: (4-3) (4-4) (4-5) (4-6) Total Loss Function Depend on ， and Together they form; when the total loss function The prior embedding depth unrolling network is considered to have converged when it stabilizes after multiple iterations, i.e., the loss value no longer decreases. The learnable parameters of each stage of the prior embedding depth unrolling network are saved for subsequent SAR target scattering center parameter extraction. Step 4.2: SAR target scattering center parameter extraction; The saved learnable parameters of each stage are loaded onto the prior embedding depth unrolling network. The test set images, after data preprocessing in step 4.1.1, are input into the model to obtain the... sparse coefficient vector of the stage ;according to Inversion yields SAR target scattering center parameters: ， ， ， ， The number of SAR target scattering centers; where, Indicates inclusion The vector of the range coordinates of the scattering center of a SAR target. ， For the first The range coordinates of the SAR target scattering center; Indicates inclusion A vector representing the azimuth coordinates of the scattering center of a SAR target. ， For the first Azimuth coordinates of the scattering center of a SAR target; Indicates inclusion The vector of the echo amplitude of the SAR target scattering center. ， For the first The echo amplitude of the scattering center of a SAR target; Indicates inclusion A vector of frequency-dependent factors of the SAR target scattering center. ， For the first The frequency dependence factor of the SAR target scattering center; to obtain the SAR target scattering center frequency dependence factor; SAR target scattering center parameter set for each SAR target scattering center First, determine the number The scattering center of the SAR target is at The index value in the matrix is ​​mapped to an 80×80 grid to obtain the index value. The pixel position of the SAR target scattering center is obtained based on the initial sampled value of the pixel position. Range coordinates of the SAR target scattering center and azimuth coordinates For index values ​​in Take the absolute value of the corresponding value in the middle to get the first... Echo amplitude of the SAR target scattering center ; Calculate the index value in The phase angle corresponding to the value in the set of frequency-dependent factors, wherein the phase angle is in radians; Select elements sequentially, and take the element with the smallest absolute difference between the selected element and the phase angle as the first element. Frequency dependence factor of each SAR target scattering center ； 、 、 、 That is, the first SAR target scattering center parameters.

8. The method for rapid extraction of SAR target scattering center parameters based on depth unfolding according to claim 3, characterized in that, The set of frequency-dependent factors is: 。 9. A terminal device, comprising a processor, a memory, and a computer program stored in the memory; characterized in that... When the processor executes the computer program, it implements a method for rapid extraction of SAR target scattering center parameters based on depth unfolding, as described in any one of claims 1-8.

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