SAR target scattering center parameter rapid extraction method based on depth expansion

Abstract

The invention provides an SAR target scattering center parameter rapid extraction method, and mainly solves the problem that a traditional SAR target scattering center parameter extraction method is slow in speed and low in precision. The method comprises the following steps: modeling a scattering center parameter solving problem based on a sparse representation theory; constructing an SAR target scattering center parameter extraction problem model based on a semi-quadratic splitting method, constructing a deep expansion network according to an optimization process based on the semi-quadratic splitting method, and extracting SAR target scattering center parameters by using the deep expansion network; compared with a traditional method, the method has the advantages that the deep expansion network is constructed based on the semi-quadratic splitting method and the scattering center model, and efficient and explainable SAR target scattering center parameter extraction is achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of artificial intelligence, and specifically relates to a method for quickly extracting SAR target scattering center parameters based on deep unfolding. Background Technique

[0002] Synthetic Aperture Radar (SAR) is a ground detection system that actively emits and receives electromagnetic waves. It can provide all-weather, all-day, and high-resolution imaging, and is suitable for target reconnaissance, monitoring, and identification. At the same time, it has been widely used in fields such as earth science, climate change research, environmental and earth system monitoring, marine resource utilization, and planetary exploration, and has high application value. In recent years, the number of SAR images has increased sharply, and carrying out intelligent interpretation tasks of SAR images based on deep learning has become one of the popular research directions in the field. Since the SAR target scattering center model has the ability to parameterize target features, more and more research has focused on the extraction of SAR target scattering center parameters and their application to the interpretation of SAR targets. Currently, the following problems exist in the methods for extracting SAR target scattering center parameters:

[0003] 1. The traditional method for extracting SAR target scattering center parameters is slow. The traditional methods for extracting SAR target scattering center parameters usually rely on iterative optimization algorithms, and these algorithms often require hundreds or thousands of iterations to obtain the SAR target scattering center parameters.

[0004] 2. The traditional method for extracting SAR target scattering center parameters has low accuracy. The traditional methods for extracting SAR target scattering center parameters rely on manually adjusted hyperparameters, such as the step size and threshold in the soft threshold iteration algorithm. The setting of these hyperparameters will significantly affect the algorithm performance, resulting in insufficient accuracy of the optimization results and poor generalization in practical applications.

[0005] To solve the above problems, the present invention designs an efficient method for extracting SAR target scattering center parameters based on deep unfolding. Summary of the Invention

[0006] To solve the problems of slow speed and low accuracy of the traditional method for extracting SAR target scattering center parameters, the present invention proposes a method for quickly extracting SAR target scattering center parameters based on deep unfolding.

[0007] A method for quickly extracting SAR target scattering center parameters based on deep unfolding includes the following steps:

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

[0009] Step 2: Use the half - quadratic splitting method to construct the solution process of the optimization problem for the sparse coefficient vector;

[0010] Step 3: Based on the solution process of the optimization problem for the sparse coefficient vector constructed by the half - quadratic splitting method, construct a prior - embedded deep unfolding network;

[0011] Step 4: Use the prior - embedded deep unfolding network to extract the SAR target scattering center parameters.

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

[0013] Step 1.1: According to the geometric diffraction theory and physical optics theory, construct a SAR target scattering center model;

[0014] Step 1.2: Based on the sparse representation theory and the SAR target scattering center model, convert the SAR target scattering center parameter extraction problem into an optimization problem for the sparse coefficient vector.

[0015] Furthermore, the steps to construct the SAR target scattering center model according to the geometric diffraction theory and physical optics theory are as follows:

[0016] According to the geometric diffraction theory and physical optics theory, the SAR target response at small angles 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, is the azimuth angle vector of the synthetic aperture radar; f c is the center frequency; is the radar echo signal, is the imaginary unit, c represents the speed of light, exp represents the exponential function with the natural constant e as the base; K is the number of SAR target scattering centers, Θ represents the set composed of K SAR target scattering center parameter sets; Θ = {θ1, θ2, … θ K}; θ i is the i - th SAR target scattering center parameter set, and the range of i is [1, K]; θ i = {A i , α i , x i , y i}, A i is the echo amplitude of the i - th SAR target scattering center, x i is the range - direction coordinate of the i - th SAR target scattering center, y iis the azimuth coordinate of the i-th SAR target scattering center, α i is the frequency-dependent factor of the i-th SAR target scattering center; α i is selected from a 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 the sparse representation theory and the SAR target scattering center model, the steps to convert the SAR target scattering center parameter extraction problem into an optimization problem of the sparse coefficient vector are as follows:

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

[0022]

[0023] where is the vectorized form of the radar echo signal z is the sparse coefficient vector, and z corresponds to the signal domain dictionary representing the position information of the SAR target scattering center, corresponds to the x is the range vector; y is the azimuth vector; A is the echo amplitude vector; α is the frequency-dependent factor vector;

[0024] The signal domain dictionary is represented column by column as:

[0025]

[0026] is the column of the signal domain dictionary x h represents the h-th element of the range vector x, and y w represents the w-th element of the azimuth vector y; the dimension of the signal domain dictionary is PQ×HW, that is, the signal domain dictionary uniformly samples P times within the frequency range to form the frequency vector f of the synthetic aperture radar, and uniformly samples Q times within the azimuth angle range to form the azimuth angle vector of the synthetic aperture radar uniformly samples H times within the range direction to form the range vector x, and uniformly samples W times within the azimuth direction to form the azimuth vector y; vec represents converting the matrix into a one-dimensional vector.

[0027] For the signal domain dictionary Perform the inverse Fourier transform on each column to transform 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, convert Equation (1-2) into an image-domain SAR target scattering center model based on the sparse representation theory. The representation form of the image-domain SAR target scattering center model based on the sparse representation theory is:

[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] Convert the SAR target scattering center parameter extraction problem into an optimization problem for the sparse coefficient vector z:

[0032]

[0033] where, denotes optimizing z to find the value of z that minimizes the original objective function ||s - Φz|| 2 + λ||z||1; λ is a hyperparameter that balances data fidelity and sparsity.

[0034] Furthermore, the steps of the solution process for constructing the optimization problem of the sparse coefficient vector using the half-quadratic splitting method are as follows:

[0035] The half-quadratic splitting method is used to solve the compressed sensing problem. The solution of the compressed sensing problem is transformed into the optimization problem of 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 constructing the optimization problem of the sparse coefficient vector using the half-quadratic splitting method is as follows:

[0039] To simplify the gradient calculation, scale the original objective function to obtain the objective function in standard form:

[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 \(u\) to equivalently transform the objective function in standard form into an objective function with an auxiliary variable:

[0043]

[0044] In the formula denotes optimizing \(z\) and \(u\) to find the values of \(z\) and \(u\) that minimize the objective function with the introduced auxiliary variable ; subject to \(u = z\) as an equality constraint to ensure that \(z\) and \(u\) are equal at the optimal solution;

[0045] Further, use the quadratic penalty function for the objective function with the introduced auxiliary variable to relax the constraint, converting the equality constraint \(u = z\) into a soft constraint, and obtaining the objective function after relaxation:

[0046]

[0047] In the formula, \(\mu\) 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 relaxation; the iterative alternating optimization process is expressed as:

[0048]

[0049] \(z\) k is the sparse - coefficient vector obtained in the \(k\) - th iteration, and \(u\) k is the auxiliary variable obtained in the \(k\) - th iteration;

[0050] Among them, denotes optimizing \(z\) to find the value of \(z\) that minimizes the objective function , denotes optimizing \(u\) to find the value of \(u\) that minimizes the objective function ; \(k\) and \(k - 1\) represent the iteration numbers;

[0051] Solve for \(z\) k :

[0052]

[0053] Among them, the normal equation is:

[0054] \((\varPhi\) * \(\varPhi+\mu I)z\) k \(=\varPhi\) * \(s+\mu u\) k-1 (2 - 7)

[0055] Among them, \(\varPhi\) * denotes the conjugate transpose of \(\varPhi\), and \(I\) is the identity matrix;

[0056] Solve for u through the soft threshold iteration algorithm k :[[]]

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

[0058] where t and S ρ (·) are the step size hyperparameter and the soft threshold function respectively, and the soft threshold function of a complex number 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] Solve the SAR target scattering center parameter extraction problem using the half-quadratic splitting method to obtain the sparse coefficient vector z k and the auxiliary variable u k , z k is the sparse coefficient vector obtained in the k-th iteration, and u k is the auxiliary variable obtained in the k-th iteration.

[0063] Furthermore, the steps to construct the prior-embedded depth unfolding network for the solution process of the optimization problem of constructing the sparse coefficient vector based on the half-quadratic splitting method are as follows:

[0064] Step 3.1: Construct the prior-embedded depth unfolding network;

[0065] For the SAR target scattering center parameter extraction problem, based on the depth unfolding method and the half-quadratic splitting method, combined with the image domain dictionary to provide the SAR target scattering center position information, construct a prior-embedded depth unfolding network based on the half-quadratic splitting method;

[0066] The prior-embedded depth unfolding network includes N identical stages, and the N identical stages are cascaded; the hyperparameters of each stage include μ d , ρ d and t d ; the range of d is [1, N]; the input of the prior-embedded depth unfolding network is the radar echo signal in the image domain, and the output is the sparse coefficient vector z N and the auxiliary variable u N in the N-th stage;

[0067] According to the solution process of the optimization problem for constructing the sparse coefficient vector using the half - quadratic splitting method described in step 2, the prior - embedding depth - unfolding network in the d - th stage is expressed as:

[0068]

[0069] where μ d , ρ d and t d are learnable parameters in the d - th stage; z d is the sparse coefficient vector of the prior - embedding depth - unfolding network in the d - th stage, and u d is the auxiliary variable of the prior - embedding depth - unfolding network in the d - th stage; d represents the d - th stage of the prior - embedding depth - unfolding network, and d - 1 represents the (d - 1) - th stage of the prior - embedding depth - unfolding network;

[0070] Step 3.2: Construct the loss function of the prior - embedding depth - unfolding network;

[0071] During the training process of the prior - embedding depth - unfolding network, the input SAR image is converted into a one - dimensional vector through a vectorization operation to obtain the radar echo signal s in the image domain, and s is used as the input of the prior - embedding depth - unfolding network; the prior - embedding depth - unfolding network can gradually extract the SAR target scattering center information; the sparse coefficient vector z N in the N - th stage and the image - domain dictionary Φ obtain the reconstructed map vector s reconstruct through matrix multiplication operation, s reconstruct = Φz N ;

[0072] Combined with the constraint conditions of the half - quadratic splitting method, the loss function of the prior - embedding depth - unfolding network includes residual loss, regularization - term loss, penalty - term loss, and total loss function;

[0073] The residual loss L residual is:

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

[0075] The residual loss L residual ensures the consistency between the reconstructed map vector s reconstruct and the radar echo signal s in the image domain;

[0076] The regularization - term loss L regular is:

[0077] L regular = λ r ||u N ||1 (3 - 4)

[0078] where λ r is the hyperparameter that constrains the sparsity of the auxiliary variable u in the Nth stage, and the regularization term loss L N ensures the sparsity of the auxiliary variable u in the Nth stage; regular The penalty term loss L N is:

[0079] L penalty is:

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

[0081] where λ p is the hyperparameter that constrains the consistency between the auxiliary variable u in the Nth stage and the sparse coefficient vector z in the Nth stage. The penalty term loss L N ensures the consistency between the auxiliary variable u in the Nth stage and the sparse coefficient vector z in the Nth stage; N The total loss function is L penalty : N The total loss function is the sum of the residual loss, the regularization term loss, and the penalty term loss. That is, N L

[0082] = L total + L

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

[0084] Specifically, the steps of using the prior-embedded deep unfolding network to extract the SAR target scattering center parameters are as follows:

[0085] Step 4.1: Train the prior-embedded deep unfolding network;

[0086] Step 4.1.1: Data preprocessing:

[0087] The training set images are cropped to obtain input images of 80×80 pixels, and the input images are L2-normalized. The normalized input images are converted into one-dimensional vectors through vectorization operations to obtain the radar echo signals s in the image domain;

[0088] Step 4.1.2: Train the prior-embedded deep unfolding network:

[0089]

[0090] ​The training set images are preprocessed to obtain the radar echo signal s in the image domain, and s is used as the input to the prior-embedded deep unfolding network. The d-th stage of the prior-embedded deep unfolding network is as follows:

[0091]

[0092] where z d is the sparse coefficient vector at the d-th stage of the prior-embedded deep unfolding network, u d is the auxiliary variable at the d-th stage of the prior-embedded deep unfolding network, μ d , ρ d and t d are the learnable parameters at the d-th stage. After N stages, the sparse coefficient vector z N and the auxiliary variable u N at the N-th stage are obtained. z N and the image domain dictionary Φ are multiplied through matrix multiplication to obtain the reconstructed image vector s reconstruct , s reconstruct =Φz N ; The difference between the reconstructed image vector s reconstruct and the radar echo signal s in the image domain is constrained by L residual , and the sparsity of u regular is constrained by L N , and the consistency between z penalty and u N is maintained by L N , which is specifically expressed as follows:

[0093] L residual =||s - s 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] The total loss function L total is composed of L residual , L regular and L penalty ; When the total loss function Ltotal It converges in successive iterations, that is, the loss value no longer decreases, and it is considered that the prior embedded depth unfolding network converges; save the learnable parameters of each stage of the prior embedded depth unfolding network at this time for subsequent extraction of SAR target scattering center parameters;

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

[0099] Load the saved learnable parameters of each stage on the prior embedded depth unfolding network;

[0100] The test set image is input into the model after data preprocessing in Step 4.1.1 to obtain the sparse coefficient vector z N ;

[0101] According to z N invert to obtain SAR target scattering center parameters: x K , y K , A K , α K , where K is the number of SAR target scattering centers;

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

[0103] To obtain the SAR target scattering center parameter set θ of the i-th SAR target scattering centeri , first determine the index value of the $i$-th SAR target scattering center in $z$ N , map the index value to an $80\times80$ grid to obtain the pixel position of the $i$-th SAR target scattering center; then, according to the initial sampling value of the pixel position, obtain the range coordinate $x$ of the $i$-th SAR target scattering center i and the azimuth coordinate $y$ i ; take the absolute value of the value corresponding to the index value in $z$ N to obtain the echo amplitude $A$ of the $i$-th SAR target scattering center i ; calculate the phase angle of the value corresponding to the index value in $z$ N , and the unit of the phase angle is radians;

[0104] Successively select elements from the set of frequency-dependent factors $\{-1, -0.5, 0, 0.5, 1\}$, and take the value with the smallest absolute value of the difference between the selected element and the phase angle as the frequency-dependent factor $\alpha$ of the $i$-th SAR target scattering center i ;

[0105] $x$ i , $y$ i , $A$ i , $\alpha$ i are the parameters of the $i$-th SAR target scattering center.

[0106] The present invention proposes a fast extraction method for SAR target scattering center parameters based on the depth unfolding of the half-quadratic splitting method, which has the following beneficial effects:

[0107] (1) Aiming at the problem of slow extraction speed of traditional iterative algorithms, the present 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 half-quadratic splitting iterative optimization algorithm is unfolded into a neural network, and a loss function is designed to automatically update the parameters through the gradient descent method; finally, the neural network is trained and the model parameters are saved for the extraction of SAR target scattering center parameters in the test set. The inference time of the soft threshold iterative algorithm is about 73.6324 seconds, and the method proposed by the present invention shortens the inference time to 0.2358 seconds. Compared with the soft threshold iterative algorithm, the inference efficiency is improved by about 312 times.

[0108] (2) Aiming at the problem of low extraction accuracy of traditional algorithms, the fast extraction method for SAR target scattering center parameters proposed by the present invention automatically learns the model parameters through a neural network, avoiding the accuracy loss caused by improper parameter settings. In terms of the quality of the reconstructed image, the peak signal-to-noise ratio of the approximate message passing algorithm is 39.17 dB, and the method proposed by the present invention improves the peak signal-to-noise ratio to 39.82 dB, an increase of 0.65 dB. Description of the Drawings

[0109] Figure 1 This is the flowchart of the method for rapidly extracting SAR target scattering center parameters of the present invention;

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

[0111] Figure 3 This is the image reconstruction result diagram of the present invention, where (a) is the original image; (b) is the reconstructed image. Specific implementation manner

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

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

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

[0115] According to the geometric diffraction theory and the physical optics theory, the SAR target response at small angles 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, is the azimuth angle vector of the synthetic aperture radar; f c is the center frequency; is the radar echo signal, is the imaginary unit, c represents the speed of light, exp represents the exponential function with the natural constant e as the base; K is the number of SAR target scattering centers, Θ = {θ1, θ2,... θ K} represents a set composed of K SAR target scattering center parameter sets; θ i is the i-th SAR target scattering center parameter set, and the range of i is [1, K]; θ i = {A i , α i , x i , y i}, A i is the echo amplitude of the i-th SAR target scattering center, x i is the range coordinate of the i-th SAR target scattering center, y i is the azimuth coordinate of the i-th SAR target scattering center, α iis the frequency-dependent factor of the i-th SAR target scattering center; the frequency-dependent factor is selected from a set of frequency-dependent factors, and the set of frequency-dependent factors is {-1, -0.5, 0, 0.5, 1};

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

[0119] The radar echo signal has 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;

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

[0121]

[0122] where is the vectorized form of the radar echo signal , z is the sparse coefficient vector, and z corresponds to the represents the signal domain dictionary containing the position information of the SAR target scattering center, corresponds to the x is the range vector; y is the azimuth vector; A is the echo amplitude vector; α is the frequency-dependent factor vector;

[0123] The signal domain dictionary is represented by columns as:

[0124]

[0125] is the column of the signal domain dictionary , x h represents the h-th element of the range vector x, and y w represents the w-th element of the azimuth vector y; the dimension of the signal domain dictionary is PQ × HW, that is, the signal domain dictionary is uniformly sampled P times in the frequency range to form the frequency vector f of the synthetic aperture radar, and is uniformly sampled Q times in the azimuth angle range to form the azimuth angle vector of the synthetic aperture radar is uniformly sampled H times in the range direction to form the range vector x, and is uniformly sampled W times in the azimuth direction to form the azimuth vector y; vec represents converting a matrix into a one-dimensional vector.

[0126] For the signal domain dictionary Perform the inverse Fourier transform on each column, convert the signal domain dictionary from the signal domain to the image domain, and obtain 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 SAR target scattering center parameter extraction is essentially a matching problem;

[0128] According to the inverse Fourier transform, convert Equation (1-2) into an image domain SAR target scattering center model based on the sparse representation theory. The representation form of the image domain SAR target scattering center model based on the sparse representation theory is:

[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] Convert the SAR target scattering center parameter extraction problem into an optimization problem for the sparse coefficient vector z:

[0132]

[0133] where, represents optimizing z to find the z value that minimizes the original objective function ||s - Φz|| 2 + λ||z||1; λ is a hyperparameter that balances data fidelity and sparsity;

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

[0135] The semi - quadratic splitting method is used to solve the compressive sensing problem. The solution of the compressive sensing problem 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 optimization problem of converting the SAR target scattering center parameter extraction problem into an optimization problem for the sparse coefficient vector in Step 1.2; Therefore, convert the SAR target scattering center parameter extraction problem into a compressive sensing problem and use the semi - quadratic splitting method to solve the SAR target scattering center parameter extraction problem;

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

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

[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 to equivalently transform the objective function in standard form into an objective function with an auxiliary variable:

[0144]

[0145] In the formula represents optimizing z and u to find the values of z and u that minimize the objective function with the introduced auxiliary variable ; subject to u = z as an equality constraint to ensure that z and u are equal at the optimal solution;

[0146] Further, the quadratic penalty function is used to relax the constraint, converting the equality constraint u = z into a soft constraint to obtain the objective function after 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 relaxation; the iterative alternating optimization process is expressed as:

[0149]

[0150] z k is the sparse coefficient vector obtained in the k - th iteration, and u k is the auxiliary variable obtained in the k - th iteration;

[0151] Among them, represents optimizing z to find the value of z that minimizes the objective function , represents optimizing u to find the value of u that minimizes the objective function ; k, k - 1 represent the iteration times;

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

[0153]

[0154] Among them, the normal equation is:

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

[0156] Wherein, Φ * represents the conjugate transpose of Φ, and I is the identity matrix;

[0157] Solve for u through the soft - thresholding iteration algorithm k :

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

[0159] Wherein, t and S ρ (·) are the step - size hyperparameter and the soft - thresholding function respectively. The soft - thresholding function for complex numbers 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] Solve the problem of SAR target scattering center parameter extraction using the semi - quadratic splitting method to obtain the sparse coefficient vector z k and the auxiliary variable u k , z k is the sparse coefficient vector obtained in the k - th iteration, and u k is the auxiliary variable obtained in the k - th iteration;

[0164] Step 3: Construct a prior - embedded depth - unfolding network based on the solution process of the optimization problem of the sparse coefficient vector constructed by the semi - quadratic splitting method;

[0165] Step 3.1: Construct a prior - embedded depth - unfolding 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 selected manually based on prior information. These hyperparameters remain unchanged during the algorithm iteration process, and a large number of iterative update steps are required, resulting in a slow convergence speed;

[0167] The deep unfolding method is a method that combines iterative optimization and deep learning. The core idea of the deep unfolding method is to unfold the iterative steps of traditional optimization algorithms into the hierarchical structure of a neural network, and construct an end-to-end trainable deep unfolding network by dynamically learning hyperparameters and compressing the iterative process.

[0168] For the problem of SAR target scattering center parameter extraction, based on the deep unfolding method and the half-quadratic splitting method, combined with the image domain dictionary to provide the SAR target scattering center position information, a prior-embedded deep unfolding network based on the half-quadratic splitting method is constructed;

[0169] The prior-embedded deep unfolding network includes N identical stages, and the N identical stages are cascaded; the hyperparameters of each stage are μ d , ρ d and t d ; the range of d is [1, N]; the input of the prior-embedded deep unfolding network is the radar echo signal in the image domain, and the output is the sparse coefficient vector z N and the auxiliary variable u N in the Nth stage;

[0170] According to the solution process of the optimization problem of constructing the sparse coefficient vector using the half-quadratic splitting method described in step 2, the prior-embedded deep unfolding network of the dth stage is expressed as:

[0171]

[0172] where μ d , ρ d and t d are the learnable parameters of the dth stage; z d is the sparse coefficient vector of the dth stage of the prior-embedded deep unfolding network, and u d is the auxiliary variable of the dth stage of the prior-embedded deep unfolding network; d represents the dth stage of the prior-embedded deep unfolding network, and d - 1 represents the (d - 1)th stage of the prior-embedded deep unfolding network;

[0173] The specific structure of the dth stage of the prior-embedded deep unfolding network refers to Figure 2 .

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

[0175] Step 3.2: Construct the loss function of the prior-embedded deep unfolding network;

[0176] During the training process of the prior embedded depth unfolding network, the input SAR image is converted into a one-dimensional vector through a vectorization operation to obtain the radar echo signal s in the image domain. s serves as the input of the prior embedded depth unfolding network. The prior embedded depth unfolding network can gradually extract the SAR target scattering center information. The sparse coefficient vector z at the Nth stage N and the image domain dictionary Φ are multiplied through matrix multiplication to obtain the reconstructed map vector s reconstruct , s reconstruct = Φz N ;

[0177] Combined with the constraint conditions of the semi-quadratic splitting method, the loss function of the prior embedded depth unfolding network includes residual loss, regularization term loss, penalty term loss, and total loss function;

[0178] The residual loss L residual is:

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

[0180] The residual loss ensures the consistency between the reconstructed map vector s reconstruct and the radar echo signal s in the image domain;

[0181] The regularization term loss L regular is:

[0182] L regular = λ r ||u N ||1 (3 - 4)

[0183] where λ r is the hyperparameter that constrains the sparsity of the auxiliary variable u N at the Nth stage. The regularization term loss L regular ensures the sparsity of the auxiliary variable u N at the Nth stage;

[0184] The penalty term loss L penalty is:

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

[0186] where λ p is the hyperparameter that constrains the consistency between the auxiliary variable u N at the Nth stage and the sparse coefficient vector z N at the Nth stage. The penalty term loss L penalty ensures the consistency between the auxiliary variable u NConsistency with the sparse coefficient vector z in the Nth stage N ;

[0187] The total loss function is L total :

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

[0189] Step 4: Use the prior-embedded depth unfolding network to extract the SAR target scattering center parameters;

[0190] Step 4.1: Train the prior-embedded depth unfolding network;

[0191] Step 4.1.1: Data preprocessing:

[0192] The training set images are cropped to obtain input images of 80×80 pixels, and the input images are L2-normalized. The normalized input images are converted into one-dimensional vectors through vectorization operations to obtain the radar echo signal s in the image domain;

[0193] Step 4.1.2: Train the prior-embedded depth unfolding network:

[0194] The training set images are preprocessed to obtain the radar echo signal s in the image domain, and s is used as the input of the prior-embedded depth unfolding network; The dth stage of the prior-embedded depth unfolding network is:

[0195]

[0196] where z d is the sparse coefficient vector in the dth stage of the prior-embedded depth unfolding network, u d is the auxiliary variable in the dth stage of the prior-embedded depth unfolding network, μ d , ρ d and t d are the learnable parameters in the dth stage; After N stages, the sparse coefficient vector z N and the auxiliary variable u N in the Nth stage are obtained; z N and the image domain dictionary Φ are multiplied through matrix operations to obtain the reconstructed image vector s reconstruct , s reconstruct = Φz N ; The difference between the reconstructed image vector s residual and the radar echo signal s in the image domain is constrained by L reconstruct , and the sparsity of u regular is constrained by L N , and z penalty is maintained by LN Consistency with u N is specifically expressed as follows:

[0197] L residual = ||s - s 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] The total loss function L total is composed of L residual , L regular and L penalty jointly; when the total loss function L total tends to be stable in consecutive multiple iterations, that is, the loss value no longer decreases, it is considered that the prior embedded depth unfolding network converges; save the learnable parameters of each stage of the prior embedded depth unfolding network at this time for subsequent SAR target scattering center parameter extraction;

[0202] Step 4.2: SAR target scattering center parameter extraction and image reconstruction;

[0203] Step 4.2.1: SAR target scattering center parameter extraction:

[0204] Load the learnable parameters of each stage saved on the prior embedded depth unfolding network;

[0205] The test set image is input into the model after being pre - processed in Step 4.1.1, and the sparse coefficient vector z N ;

[0206] According to z N invert to obtain the SAR target scattering center parameters: x K , y K , A K , α K , where K is the number of SAR target scattering centers;

[0207] Among them, x K represents a vector containing the range - direction coordinates of K SAR target scattering centers, xK = [x1, x2, …, x i , … x K , where x i is the range coordinate of the i-th SAR target scattering center; y K represents a vector containing the azimuth coordinates of K SAR target scattering centers, y K = [y1, y2, …, y i , … y K , where y i is the azimuth coordinate of the i-th SAR target scattering center; A K represents a vector containing the echo amplitudes of K SAR target scattering centers, A K = [A1, A2, …, A i , … A K , where A i is the echo amplitude of the i-th SAR target scattering center; α K represents a vector containing the frequency-dependent factors of K SAR target scattering centers, α K = [α1, α2, …, α i , …, α K , where α i is the frequency-dependent factor of the i-th SAR target scattering center;

[0208] To obtain the SAR target scattering center parameter set θ i of the i-th SAR target scattering center, first determine the index value of the i-th SAR target scattering center in z N , map the index value to an 80×80 grid to obtain the pixel position of the i-th SAR target scattering center; then, based on the initial sampling value of the pixel position, obtain the range coordinate x i and the azimuth coordinate y i of the i-th SAR target scattering center; take the absolute value of the value corresponding to the index value in z N to obtain the echo amplitude A i of the i-th SAR target scattering center; calculate the phase angle of the value corresponding to the index value in z N , where the unit of the phase angle is radians;

[0209] Successively select elements from the set of frequency-dependent factors α {-1, -0.5, 0, 0.5, 1}, and the value with the smallest absolute difference from the phase angle is used as the frequency-dependent factor α i of the i-th SAR target scattering center;

[0210] x i , y i , A i , α iThat is, the scattering center parameters of the $i$-th SAR target;

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

[0212] Based on the sparse coefficient vector $z$ of the $N$-th stage N and the image domain dictionary $\varPhi$, obtain the reconstructed image vector $s$ reconstruct :

[0213] $s$ reconstruct $= \varPhi z$ N (4-7)

[0214] Restore the reconstructed image vector $s$ reconstruct to a two-dimensional image to obtain the reconstructed image;

[0215] Use the peak signal-to-noise ratio (PSNR) to evaluate the quality of the reconstruction result, with the unit of decibels (dB); the higher the peak signal-to-noise ratio, the better the quality of the reconstructed image. The calculation formula for the peak signal-to-noise ratio is:

[0216]

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

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

[0219]

[0220] where $s$ (l) represents the $l$-th element of the radar echo signal $s$ in the image domain, represents the $l$-th element of the reconstructed image vector $s$ reconstruct , and the range of $l$ is $[1, L]$; $L$ is the length of the reconstructed image vector $s$ reconstruct ;

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

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

[0223] Embodiment 1: Referring to Figure 1 A fast extraction method for SAR target scattering center parameters based on deep unfolding shown in the figure, the process includes:

[0224] Step 1: Based on the sparse representation theory, convert the SAR target scattering center parameter extraction problem into an optimization problem of a sparse coefficient vector;

[0225] Step 1.1: According to the geometric diffraction theory and physical optics theory, construct a SAR target scattering center model;

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

[0227]

[0228] where f is the frequency vector of the synthetic aperture radar, is the azimuth angle vector of the synthetic aperture radar; f c is the center frequency; is the radar echo signal, is the imaginary unit, c represents the speed of light, exp represents the exponential function with the natural constant e as the base; K is the number of SAR target scattering centers, Θ = {θ1, θ2, … θ K} represents a set composed of the parameter sets of K SAR target scattering centers; θ i is the parameter set of the i-th SAR target scattering center, and the range of i is [1, K]; θ i = {A i , α i , x i , y i}, A i is the echo amplitude of the i-th SAR target scattering center, x i is the range coordinate of the i-th SAR target scattering center, y i is the azimuth coordinate of the i-th SAR target scattering center, α i is the frequency-dependent factor of the i-th SAR target scattering center; the frequency-dependent factor is selected from the set {-1, -0.5, 0, 0.5, 1}.

[0229] Table 1: Scattering body structures corresponding to different α i values

[0230] <![CDATA[α i > Scatterer structure -1 Corner diffraction, apex diffraction -0.5 Edge diffraction 0 Point scattering, hyperbolic reflection, straight-edge specular reflection 0.5 Single-curved surface reflection 1 Flat normal reflection, dihedral angle reflection, trihedral angle reflection

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

[0232] The radar echo signal has sparsity in the SAR target scattering center parameter space, and the idea of sparse signal representation is used to effectively analyze and extract SAR target scattering center parameters;

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

[0234]

[0235] where, Radar echo signal The vectorized form of z is the sparse coefficient vector, corresponding to the SAR target scattering center model Represents the signal domain dictionary containing the 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 The columns are represented as:

[0237]

[0238] Signal domain dictionary Column, x h Represents the hth element of the distance vector x, y w Represents the w-th element of the azimuth vector y; signal domain dictionary The dimension is PQ×HW, that 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 in the range direction, and the azimuth vector y is formed by uniformly sampling W times in the range of the azimuth direction; vec represents the conversion of the matrix into a one-dimensional vector;

[0239] Signal Domain Dictionary Perform inverse Fourier transform on each column of , convert the signal domain dictionary from the signal domain to the image domain, and obtain the image domain dictionary Φ; the image domain dictionary is represented as a sparse diagonal matrix, in which the SAR target scattering center corresponding to each column is concentrated near the diagonal line;

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

[0241] According to the inverse Fourier transform, equation (1-2) is converted into the 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:

[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 SAR target scattering center parameter extraction problem is converted into an optimization problem of the sparse coefficient vector z:

[0245]

[0246] Among them, represents optimizing z to find the value of z that minimizes the original objective function ||s - Φz|| 2 + λ||z||1; 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 published by Sandia National Laboratories in the United States. In the MSTAR dataset, the targets are concentrated in the 80×80 area in the center of the image. Therefore, the sampling times P, Q, H, and W are all set to 80, and the hyperparameters of the signal domain dictionary are set as shown in Table 2.

[0248] Table 2: Hyperparameter settings of the signal domain dictionary

[0249]

[0250]

[0251] According to the inverse Fourier transform, the signal domain dictionary is converted into an image domain dictionary, and the dimension of the image domain dictionary is 6400×6400. The image domain dictionary is saved as a mat format file for subsequent reading and use.

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

[0253] The half-quadratic splitting method is often used to solve the compressed sensing problem. The solution of the compressed sensing problem is transformed into the following optimization problem:

[0254]

[0255] Among them, 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 half-quadratic splitting method is consistent with the optimization problem of converting the SAR target scattering center parameter extraction problem in Step 1.2 into an optimization problem of a sparse coefficient vector; therefore, the SAR target scattering center parameter extraction problem is converted into a compressed sensing problem, and the half-quadratic splitting method is used to solve the SAR target scattering center parameter extraction problem;

[0257] The solution process of constructing the optimization problem of the sparse coefficient vector by the half - quadratic splitting method is as follows:

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

[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 half - quadratic splitting method introduces an auxiliary variable u to equivalently transform the objective function in the standard form into the objective function with the introduced auxiliary variable:

[0262]

[0263] In the formula represents optimizing z and u to find the z - value and u - value that minimize the objective function with the introduced auxiliary variable ; subject to u = z as the equality constraint to ensure that z and u are equal at the optimal solution;

[0264] Further, the quadratic penalty function is used to relax the constraint, converting the equality constraint u = z into a soft constraint to obtain the objective function after relaxation of the constraint:

[0265]

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

[0267]

[0268] z k is the sparse coefficient vector obtained in the k - th iteration, and u k is the auxiliary variable obtained in the k - th iteration;

[0269] Among them, represents optimizing z to find the z - value that minimizes the objective function ; represents optimizing u to find the u - value that minimizes the objective function ; k, k - 1 represent the iteration times;

[0270] According to the normal equation, solve to obtain z k :

[0271]

[0272] Among them, the normal equation is:

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

[0274] Among them, Φ * represents the conjugate transpose of Φ, and I is the identity matrix;

[0275] Solve u through the soft - thresholding iteration algorithm k :

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

[0277] Among them, t and S ρ (·) are the step - size hyperparameter and the soft - thresholding function respectively. The soft - thresholding function of complex numbers is expressed as:

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

[0279]

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

[0281] Use the half - quadratic splitting method to solve the problem of extracting SAR target scattering center parameters, and obtain the sparse coefficient vector z k and the auxiliary variable u k , z k is the sparse coefficient vector obtained in the k - th iteration, and u k is the auxiliary variable obtained in the k - th iteration;

[0282] Step 3: Based on the solution process of constructing the optimization problem of the sparse coefficient vector by the half - quadratic splitting method, construct a prior - embedded deep unfolding network;

[0283] Step 3.1: Construct a prior - embedded deep unfolding network;

[0284] In the traditional half - quadratic splitting method, the penalty - term hyperparameter μ, the threshold hyperparameter ρ, and the step - size hyperparameter t are usually selected manually 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] The deep unfolding method is a method that combines iterative optimization and deep learning. The core idea of the deep unfolding method is to unfold the iterative steps of traditional optimization algorithms into the hierarchical structure of a neural network, and construct an end-to-end trainable deep unfolding network by dynamically learning hyperparameters and compressing the iterative process.

[0286] Aiming at the problem of SAR target scattering center parameter extraction, based on the deep unfolding method and the half-quadratic splitting method, and combining the image domain dictionary to provide the SAR target scattering center position information, a prior-embedded deep unfolding network based on the half-quadratic splitting method is constructed;

[0287] The prior-embedded deep unfolding network includes N identical stages, and the N identical stages are cascaded; the hyperparameters of each stage are μ d 、ρ d and t d ; the range of d is [1, N]; the input of the prior-embedded deep unfolding network is the radar echo signal in the image domain, and the output is the sparse coefficient vector z N and the auxiliary variable u N ;

[0288] According to the solution process of the optimization problem of constructing the sparse coefficient vector using the half-quadratic splitting method described in step 2, the prior-embedded deep unfolding network of the d-th stage is expressed as:

[0289]

[0290] In the formula, μ d , ρ d and t d are the learnable parameters of the d-th stage; z d is the sparse coefficient vector of the d-th stage of the prior-embedded deep unfolding network, and u d is the auxiliary variable of the d-th stage of the prior-embedded deep unfolding network; d represents the d-th stage of the prior-embedded deep unfolding network, and d - 1 represents the (d - 1)-th stage of the prior-embedded deep unfolding network;

[0291] The specific structure of the d-th stage of the prior-embedded deep unfolding network refers to Figure 2 .

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

[0293] Step 3.2: Construct the loss function of the prior-embedded deep unfolding network;

[0294] During the training process of the prior embedded depth unfolding network, the input SAR image is converted into a one-dimensional vector through a vectorization operation to obtain the radar echo signal s in the image domain. s serves as the input to the prior embedded depth unfolding network. The prior embedded depth unfolding network can gradually extract the SAR target scattering center information. The sparse coefficient vector z in the Nth stage N and the image domain dictionary Φ are multiplied through matrix multiplication to obtain the reconstructed image vector s reconstruct , s reconstruct = Φz N ; The parameters are optimized by constraining the difference between the reconstructed image vector s reconstruct and the radar echo signal s in the image domain;

[0295] Combined with the constraint conditions of the semi - quadratic splitting method, the loss function of the prior embedded depth unfolding network includes residual loss, regularization term loss, penalty term loss, and total loss function;

[0296] The residual loss L residual is:

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

[0298] The residual loss ensures the consistency between the reconstructed image vector s reconstruct and the input s;

[0299] The regularization term loss L regular is:

[0300] L regular = λ r ||u N ||1 (3 - 4)

[0301] where λ r is the hyperparameter that constrains the sparsity of the auxiliary variable u N in the Nth stage. The regularization term loss L regular ensures the sparsity of the auxiliary variable u N in the Nth stage;

[0302] The penalty term loss L penalty is:

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

[0304] where λ p is the hyperparameter that constrains the consistency between the auxiliary variable u N in the Nth stage and the sparse coefficient vector z N in the Nth stage. The penalty term loss Lpenalty Ensure the auxiliary variable u in the Nth stage N and the sparse coefficient vector z in the Nth stage N to be consistent;

[0305] The total loss function is L total :

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

[0307] Step 4: Use the prior-embedded depth unfolding network to extract the SAR target scattering center parameters;

[0308] Step 4.1: Train the prior-embedded depth unfolding network;

[0309] Step 4.1.1: Data preprocessing:

[0310] The training set images are center-cropped to obtain input images of 80×80 pixels, and the input images are L2-normalized. The normalized input images are converted into one-dimensional vectors through vectorization operations to obtain the radar echo signal s in the image domain;

[0311] Step 4.1.2: Train the prior-embedded depth unfolding network:

[0312] The training set images are preprocessed to obtain the radar echo signal s in the image domain, and s is used as the input of the prior-embedded depth unfolding network; The dth stage of the prior-embedded depth unfolding network is:

[0313]

[0314] where z d is the sparse coefficient vector in the dth stage of the prior-embedded depth unfolding network, u d is the auxiliary variable in the dth stage of the prior-embedded depth unfolding network, μ d , ρ d and t d are the learnable parameters in the dth stage; After N stages, the sparse coefficient vector z N and the auxiliary variable u N in the Nth stage are obtained; z N and the image domain dictionary Φ are multiplied through matrix operations to obtain the reconstructed image vector s reconstruct , s reconstruct = Φz N ; The difference between the reconstructed image vector s residual and the radar echo signal s in the image domain is constrained by L reconstruct , and u is constrained by L regular ​N The sparsity, through L penalty Keep z N and u N The consistency is specifically expressed as follows:

[0315] L residual = ||s - s 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 = L residual + L regular + L penalty (4 - 6)

[0319] During model training, the AdamW optimizer is adopted, the stabilization coefficient is set to 1×10 -6 , and 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 linearly increases to the maximum value (the maximum value is 5 times the initial learning rate) within each training epoch, and then gradually decreases according to the cosine annealing strategy in the remaining training epochs until the training is completed.

[0320] When calculating the loss function, λ p is set to 100, and λ r is set to 200. When the total loss function L total tends to be stable in consecutive multiple iterations, that is, the loss value no longer decreases, it is considered that the prior embedded depth unfolding network converges; save the learnable parameters of each stage of the prior embedded depth unfolding network at this time for subsequent SAR target scattering center parameter extraction;

[0321] Step 4.2: SAR target scattering center parameter extraction and image reconstruction:

[0322] Step 4.2.1: SAR target scattering center parameter extraction:

[0323] Load the learnable parameters of each stage saved on the prior embedded depth unfolding network;

[0324] The test set images are input into the model after being preprocessed in Step 4.1.1 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 by inversion: x K , y K , A K , α K , where K is the number of SAR target scattering centers;

[0326] Among them, x K represents a vector containing the range coordinates of K SAR target scattering centers, x K = [x1, x2, …, x i , … x K , x i is the range coordinate of the i-th SAR target scattering center; y K represents a vector containing the azimuth coordinates of K SAR target scattering centers, y K = [y1, y2, …, y i , … y K , y i is the azimuth coordinate of the i-th SAR target scattering center; A K represents a vector containing the echo amplitudes of K SAR target scattering centers, A K = [A1, A2, …, A i , … A K , A i is the echo amplitude of the i-th SAR target scattering center; α K represents a vector containing the frequency-dependent factors of K SAR target scattering centers, α K = [α1, α2, …, α i , …, α K , α i is the frequency-dependent factor of the i-th SAR target scattering center;

[0327] To obtain the SAR target scattering center parameter set θ i of the i-th SAR target scattering center, first determine the index value of the i-th SAR target scattering center in z N , map the index value to an 80×80 grid to obtain the pixel position of the i-th SAR target scattering center; then, according to the initial sampling value of the pixel position, obtain the range coordinate x i and azimuth coordinate y i of the i-th SAR target scattering center; take the absolute value of the value corresponding to the index value in z N to obtain the echo amplitude A i of the i-th SAR target scattering center; calculate the phase angle of the value corresponding to the index value in z N , and the unit of the phase angle is radians;

[0328] Select elements from the set of frequency-dependent factors α {-1, -0.5, 0, 0.5, 1} in sequence, and take the value with the smallest absolute value of the difference between the selected element and the phase angle as the frequency-dependent factor α of the i-th SAR target scattering center. i ;

[0329] x i 、y i 、A i 、α i are the parameters of the i-th SAR target scattering center;

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

[0331] According to the sparse coefficient vector z N of the N-th stage and the image domain dictionary Φ, obtain the reconstructed image vector s reconstruct :

[0332] s reconstruct = Φz N (4-7)

[0333] Restore the reconstructed image vector s reconstruct to a two-dimensional image to obtain the reconstructed image;

[0334] Use the peak signal-to-noise ratio PSNR to evaluate the quality of the reconstruction result, with the unit of decibels (dB); the higher the peak signal-to-noise ratio, the better the quality of the reconstructed image. The calculation formula of the peak signal-to-noise ratio is:

[0335]

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

[0337] The calculation formula of the mean square error is:

[0338]

[0339] where s (l) represents the l-th element of the radar echo signal s in the image domain, represents the l-th element of the reconstructed image vector s reconstruct , and the range of l is [1, L]; L is the length of the reconstructed image vector s reconstruct ;

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

[0341] Example 2: Different from the above Example 1, to verify the effectiveness of the SAR target scattering center parameter fast extraction method described in Example 1, this example is designed for verification:

[0342] 1. Simulation conditions;

[0343] This invention conducts simulation using the Pytorch framework on a central processing unit of Intel(R) i9-10900X 3.7GHz CPU, with 256G of memory, 4 Nvidia GTX3090 GPUs, and the Ubuntu 18.04 operating system. In the experiment, the dataset used is the MSTAR dataset.

[0344] 2. Simulation content;

[0345] Test the fast extraction method for SAR target scattering center parameters described in Embodiment 1. The results are shown in Table 3, which presents a comparison of the peak signal-to-noise ratio and inference time between the method in this paper and the traditional approximate message passing algorithm, orthogonal matching pursuit algorithm, and soft threshold iteration algorithm.

[0346] Table 3: Comparison results of peak signal-to-noise ratio and inference time

[0347] Method Unit Approximate message passing algorithm Orthogonal matching pursuit algorithm Soft thresholding iteration algorithm Method of this paper Peak signal-to-noise ratio Decibel 39.17 38.05 38.31 39.82 Inference time Second 84.5331 106.1839 73.6324 0.2358

[0348] The reconstruction results are as Figure 3 shown.

Claims

1. A fast extraction method for SAR target scattering center parameters based on deep unfolding, characterized in that, It includes the following steps: Step 1: Based on the sparse representation theory, convert the problem of extracting SAR target scattering center parameters into an optimization problem of a sparse coefficient vector; Step 2: Use the half - quadratic splitting method to construct the solution process of the optimization problem of the sparse coefficient vector; Step 3: Based on the solution process of the optimization problem of the sparse coefficient vector constructed by the half - quadratic splitting method, construct a prior - embedded depth - unfolding network; Step 4: Use the prior - embedded depth - unfolding network to extract SAR target scattering center parameters.

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

3. A fast extraction method for SAR target scattering center parameters based on deep unfolding according to claim 2, characterized in that, The steps to construct a SAR target scattering center model according to the geometric diffraction theory and physical optics theory are as follows: According to the geometric diffraction theory and physical optics theory, the SAR target response at small angles is the sum of the responses of K SAR target scattering centers. Therefore, the SAR target scattering center model is: where f is the frequency vector of the synthetic aperture radar, is the azimuth angle vector of the synthetic aperture radar; f c is the center frequency; is the radar echo signal, is the imaginary unit, c represents the speed of light, and exp represents the exponential function with the natural constant e as the base; K is the number of SAR target scattering centers, and Θ represents the set composed of K SAR target scattering center parameter sets; Θ = {θ1, θ2, … θ K}; θ i is the i-th SAR target scattering center parameter set, and the range of i is [1, K]; θ i = {A i , α i , x i , y i}, A i is the echo amplitude of the i-th SAR target scattering center, x i is the range coordinate of the i-th SAR target scattering center, y i is the azimuth coordinate of the i-th SAR target scattering center, and α i is the frequency dependence factor of the i-th SAR target scattering center; α i is selected from the set of frequency dependence factors.

4. A method for quickly extracting SAR target scattering center parameters based on deep unfolding according to claim 2, characterized in that Based on the sparse representation theory and the SAR target scattering center model, the steps to convert the problem of extracting SAR target scattering center parameters into an optimization problem for the sparse coefficient vector are as follows: According to the sparse representation theory, the SAR target scattering center model in Step 1.1 is expressed as: Among them, is the vectorized form of the radar echo signal, z is the sparse coefficient vector, and z corresponds to the SAR target scattering center model, represents the signal domain dictionary containing the position information of the SAR target scattering center, corresponding to the x is the range vector; y is the azimuth vector; A is the echo amplitude vector; α is the frequency-dependent factor vector; Signal domain dictionary Represented column by column as: is the signal domain dictionary is the column of, x h represents the h-th element of the range vector x, y w represents the w-th element of the azimuth vector y; the signal domain dictionary has a dimension of PQ×HW, that is, the signal domain dictionary is uniformly sampled P times within the frequency range to form the frequency vector f of the synthetic aperture radar, and is uniformly sampled Q times within the azimuth angle range to form the azimuth angle vector of the synthetic aperture radar is uniformly sampled H times within the range direction to form the range vector x, and is uniformly sampled W times within the azimuth direction to form the azimuth vector y; vec represents converting a matrix into a one-dimensional vector; Perform an inverse Fourier transform on each column of the signal domain dictionary to convert the signal domain dictionary from the signal domain to the image domain and obtain 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; According to the inverse Fourier transform, convert Equation (1 - 2) into an image - domain SAR target scattering center model based on the sparse representation theory. The expression form of the image - domain SAR target scattering center model based on the sparse representation theory is: s = Φz (1 - 5) where s represents the radar echo signal in the image domain; Φ represents the image - domain dictionary in the image domain; Convert the problem of extracting SAR target scattering center parameters into an optimization problem for the sparse coefficient vector z: Among them, represents optimizing z to find the value of z that minimizes the original objective function ||s - Φz|| 2 + λ||z||1; λ is a hyperparameter that balances data fidelity and sparsity.

5. A fast extraction method for SAR target scattering center parameters based on deep unfolding according to claim 1, characterized in that, The steps to use the half - quadratic splitting method to construct the solution process of the optimization problem of the sparse coefficient vector are as follows: The half - quadratic splitting method is used to solve the compressed sensing problem. The solution of the compressed sensing problem is transformed into the optimization problem of Equation (2 - 1): 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; The solution process to use the half - quadratic splitting method to construct the optimization problem of the sparse coefficient vector is: To simplify the gradient calculation, scale the original objective function to obtain the objective function in standard form: 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; The half - quadratic splitting method introduces an auxiliary variable u to equivalently transform the objective function in standard form into an objective function with an auxiliary variable: wherein represents optimizing z and u to find the values of z and u that minimize the objective function introducing the auxiliary variable ; subject to the equality constraint u = z to ensure that z and u are equal at the optimal solution Further, use the quadratic penalty function for the objective function introducing the auxiliary variable Relax the constraints, convert the equality constraint u = z into a soft constraint, and obtain the objective function after the relaxation constraint: In the formula, μ is the penalty - term hyperparameter; the half - quadratic splitting method alternately optimizes z and u in the iteration to approximate the optimal solution of the objective function after relaxation constraints. The iterative alternating optimization process is expressed as: z k is the sparse coefficient vector obtained in the k-th iteration, and u k is the auxiliary variable obtained in the k-th iteration; Among them, represents optimizing z to find the value of z that minimizes the objective function ; represents optimizing u to find the value of u that minimizes the objective function ; k and k - 1 represent the number of iterations. Solve according to the normal equation for to obtain z k : where the normal equation is: (Φ * (Φ + μI)z k =Φ * s + μu k-1 (2 - 7) where Φ * denotes the conjugate transpose of Φ, and I is the identity matrix; Solve for u by the soft threshold iteration algorithm k : u k = S ρ (u k-1 + tΦ * (z k - Φu k-1 )) (2 - 8) Among them, t and S ρ (·) are the step size hyperparameter and the soft threshold function respectively. The soft threshold function for complex numbers is expressed as: S ρ (v) = sign(v) max(|v| - ρ, 0), (2-9) where v is a complex number, ρ is the threshold hyperparameter, and |v| represents the modulus of the complex number v; Solve the problem of SAR target scattering center parameter extraction by the half - quadratic splitting method to obtain the sparse coefficient vector z k and the auxiliary variable u k , z k is the sparse coefficient vector obtained in the k - th iteration, and u k is the auxiliary variable obtained in the k - th iteration.

6. A fast extraction method for SAR target scattering center parameters based on deep unfolding according to claim 1, characterized in that, The steps for constructing a prior-embedded deep unfolding network in the solution process of the optimization problem for constructing a sparse coefficient vector based on the half-quadratic splitting method are as follows: Step 3.1: Construct a prior-embedded deep unfolding network; For the problem of SAR target scattering center parameter extraction, based on the deep unfolding method and the half-quadratic splitting method, combined with the image-domain dictionary to provide the SAR target scattering center position information, a prior-embedded deep unfolding network based on the half-quadratic splitting method is constructed; The prior embedded depth unfolding network includes N identical stages, and the N identical stages are cascaded; the hyperparameters of each stage include μ d , ρ d and t d ; the range of d is [1, N]; the input of the prior embedded depth unfolding network is the radar echo signal in the image domain, and the output is the sparse coefficient vector z N and the auxiliary variable u N ; According to the solution process of the optimization problem for constructing a sparse coefficient vector using the half-quadratic splitting method described in Step 2, the prior-embedded deep unfolding network in the d-th stage is expressed as: where μ d , ρ d and t d are learnable parameters of the d-th stage; z d is the sparse coefficient vector of the d-th stage of the prior embedding depth unfolding network, and u d is the auxiliary variable of the d-th stage of the prior embedding depth unfolding network; d represents the d-th stage of the prior embedding depth unfolding network, and d - 1 represents the (d - 1)-th stage of the prior embedding depth unfolding network; Step 3.2: Construct the loss function of the prior-embedded deep unfolding network; During the training process of the prior embedding depth unfolding network, the input SAR image is converted into a one-dimensional vector through a vectorization operation to obtain the radar echo signal s in the image domain, and s is used as the input of the prior embedding depth unfolding network; the prior embedding depth unfolding network can gradually extract the SAR target scattering center information; the sparse coefficient vector z in the Nth stage N and the image domain dictionary Φ are multiplied through matrix multiplication to obtain the reconstructed map vector s reconstruct , s reconstruct = Φz N ; Combined with the constraint conditions of the half-quadratic splitting method, the loss function of the prior-embedded deep unfolding network includes residual loss, regularization term loss, penalty term loss, and total loss function; Residual loss L residual is as follows: L residual = ||s - s reconstruct ||2 (3 - 3) Residual loss L residual Ensure the consistency between the reconstructed graph vector s reconstruct and the radar echo signal s in the image domain; Regular term loss L regular is as follows: L regular = λ r ||u N ||1 (3 - 4) where λ r is a hyperparameter for constraining the sparsity of the auxiliary variable u N in the N-th stage, and the regularization term loss L regular ensures the sparsity of the auxiliary variable u N in the N-th stage; Penalty term loss L penalty is as follows: L penalty = λ p ||z N - u N ||2 (3 - 5) where λ p is the auxiliary variable u for constraining the Nth stage N and the sparse coefficient vector z of the Nth stage N is the hyperparameter for consistency, and the penalty loss L penalty ensures the consistency between the auxiliary variable u of the Nth stage N and the sparse coefficient vector z of the Nth stage N ; The total loss function is L total : L total = L residual + L regular + L penalty (3 - 6) That is, the total loss function is the sum of the residual loss, regularization term loss, and penalty term loss.

7. A fast extraction method for SAR target scattering center parameters based on deep unfolding according to claim 1, characterized in that The steps for extracting SAR target scattering center parameters using the prior-embedded deep unfolding network are: Step 4.1: Train the prior-embedded deep unfolding network; Step 4.1.1: Data preprocessing: The training set images are cropped to obtain input images of 80×80 pixels, and the input images are L2-normalized; The normalized input images are converted into one-dimensional vectors through vectorization operations to obtain the radar echo signal s in the image domain; Step 4.1.2: Train the prior-embedded deep unfolding network: The training set images are preprocessed to obtain the radar echo signal s in the image domain, and s is used as the input of the prior-embedded deep unfolding network; the d-th stage of the prior-embedded deep unfolding network is: where z d is the sparse coefficient vector of the d-th stage of the prior embedded depth unfolding network, u d is the auxiliary variable of the d-th stage of the prior embedded depth unfolding network, μ d , ρ d and t d are the learnable parameters of the d-th stage; after N stages, the sparse coefficient vector z N and the auxiliary variable u N of the N-th stage are obtained; z N and the image domain dictionary Φ are used to obtain the reconstructed image vector s reconstruct through matrix multiplication operation, s reconstruct = Φz N ; the difference between the reconstructed image vector s reconstruct and the radar echo signal s in the image domain is constrained by L residual , and the sparsity of u regular is constrained by L N , and the consistency between z penalty and u N is maintained by L N , which is specifically expressed as follows: L residual = ||s - s reconstruct ||2(4 - 3) L regular = λ r ||u N ||1 (4-4) L penalty = λ p ||z N - u N ||2 (4 - 5) L total = L residual + L regular + L penalty (4 - 6) Total loss function L total Composed of L residual , L regular and L penalty When the total loss function L total tends to be stable in successive iterations, that is, the loss value no longer decreases, it is considered that the prior embedding depth unfolding network converges; save the learnable parameters of each stage of the prior embedding depth unfolding network at this time for subsequent SAR target scattering center parameter extraction; Step 4.2: Extract SAR target scattering center parameters; Load the learnable parameters of each stage saved on the prior-embedded deep unfolding network; The test set images are input into the model after the data preprocessing in step 4.1.1 to obtain the sparse coefficient vector z at the Nth stage N ; According to z N The SAR target scattering center parameters are obtained by inversion: x K , y K , A K , α K , where K is the number of SAR target scattering centers; Among them, x K represents a vector containing the range coordinates of K SAR target scattering centers, and x K = [x1, x2, …, x i , … x K , where x i is the range coordinate of the i-th SAR target scattering center; y K represents a vector containing the azimuth coordinates of K SAR target scattering centers, and y K = [y1, y2, …, y i , … y K , where y i is the azimuth coordinate of the i-th SAR target scattering center; A K represents a vector containing the echo amplitudes of K SAR target scattering centers, and A K = [A1, A2, …, A i , … A K , where A i is the echo amplitude of the i-th SAR target scattering center; α K represents a vector containing the frequency-dependent factors of K SAR target scattering centers, and α K = [α1, α2, …, α i , …, α K , where α i is the frequency-dependent factor of the i-th SAR target scattering center; To obtain the SAR target scattering center parameter set θ of the i-th SAR target scattering center i , first determine the index value of the i-th SAR target scattering center in z N , map the index value to an 80×80 grid to obtain the pixel position of the i-th SAR target scattering center; then, based on the initial sampling value of the pixel position, obtain the range coordinate x i and the azimuth coordinate y i of the i-th SAR target scattering center; take the absolute value of the value corresponding to the index value in z N to obtain the echo amplitude A i of the i-th SAR target scattering center; calculate the phase angle of the value corresponding to the index value in z N , where the unit of the phase angle is radians; Select elements sequentially from the set of frequency-dependent factors {-1, -0.5, 0, 0.5, 1}, and use the value with the smallest absolute value of the difference between the selected element and the phase angle as the frequency-dependent factor α of the i-th SAR target scattering center. i ; x i 、y i 、A i 、α i are the parameters of the i-th SAR target scattering center.

8. A fast extraction method for SAR target scattering center parameters based on deep unfolding according to claim 3, characterized in that The set of frequency-dependent factors is {-1, -0.5, 0, 0.5, 1}.

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 fast extraction method for SAR target scattering center parameters based on deep unfolding according to any one of claims 1-8.

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