SAR moving target self-focusing imaging method based on multi-frame correlation learning

Abstract

The invention provides an SAR moving target self-focusing imaging method based on multi-frame correlation learning, and relates to the technical field of synthetic aperture radar imaging, and the method comprises the steps: building an observation model of a moving target echo signal according to an SAR working process and moving target motion characteristics; establishing an SAR moving target sparse reconstruction and self-focusing imaging model; constructing an iterative solution process of the SAR moving target sparse reconstruction and self-focusing imaging model by using an alternating direction multiplier method; constructing an SAR moving target self-focusing imaging network by deeply expanding the iterative solution process and combining with a moving target motion compensation module based on multi-frame correlation learning; and training the SAR moving target self-focusing imaging network through back propagation, and optimizing parameters of the SAR moving target self-focusing imaging network to obtain a final SAR moving target self-focusing imaging network. According to the method, the focusing imaging performance of the moving target can be ensured under the condition of signal sparse sampling, and the method has applicability to a complex moving target motion scene.

Description

Technical Field

[0001] This invention relates to the field of synthetic aperture radar imaging technology, and more specifically to a SAR moving target autofocusing imaging method based on multi-frame correlation learning. Background Technology

[0002] Synthetic Aperture Radar (SAR) achieves high-resolution scene imaging by processing echo signals, but moving targets can cause image defocusing or shifting due to unknown motion parameters. Especially under sparse signal sampling conditions, traditional methods struggle to simultaneously guarantee the accuracy of motion parameter estimation and image quality, severely limiting their practical application value.

[0003] Current moving target focusing imaging methods are mainly divided into two categories. One is the transformation-based method (such as Keystone transform), which relies on the Nyquist sampling rate, cannot adapt to sparse sampling scenarios, and has poor adaptability to complex motion. The other is the optimization-based method, which models the imaging as a sparse reconstruction problem, but the manually built model is difficult to accurately represent the real scene, and the iterative solution process has high computational complexity.

[0004] Therefore, how to effectively ensure the focusing imaging performance of moving targets and its applicability to complex motion scenes under the condition of sparse signal sampling has become an urgent problem to be solved. Summary of the Invention

[0005] To address the problems in related technologies, this invention provides a SAR moving target autofocusing imaging method based on multi-frame correlation learning.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A SAR moving target autofocusing imaging method based on multi-frame correlation learning includes the following steps: Step S1: Establish an observation model for the moving target echo signal based on the SAR working process and the motion characteristics of the moving target; Step S2: Based on the observation model and combined with the sparsity characteristics of SAR moving target images, establish a SAR moving target sparse reconstruction and autofocusing imaging model; Step S3: Using the alternating direction multiplier method, construct the iterative solution process for the SAR moving target sparse reconstruction and autofocusing imaging model; Step S4: By deeply expanding the iterative solution process and combining it with the moving target motion compensation module based on multi-frame correlation learning, a SAR moving target autofocusing imaging network is constructed. Step S5: Train the SAR moving target autofocusing imaging network through backpropagation, optimize its parameters, and obtain the final SAR moving target autofocusing imaging network.

[0007] Optionally, step S1 specifically includes: Step S1-1: Based on the SAR geometry and the motion characteristics of the moving target, establish the slant range expression for the moving target: In the formula, Indicates the instantaneous slant range of a moving target. Indicates location and time. Indicates the SAR platform's velocity. This indicates the distance from the moving target to the center of the radar beam along the azimuth direction. This indicates the reference slant range between the SAR platform and the moving target along the center of the radar beam. This indicates the angle between the radar beam center and the range direction. This indicates the velocity of a moving target along the azimuth direction. This indicates the velocity of a moving target along the range direction; Step S1-2: Establish a SAR moving target echo signal model based on the slant range expression: In the formula, This represents the echo signal of a moving target. Represents the range and azimuth envelope functions. The imaginary unit is the complex value. Indicates the carrier frequency. Indicates instantaneous slant distance. Represents the speed of light. Indicates the signal frequency modulation; Step S1-3: Based on the SAR moving target echo signal model, represent the echo signal in vector form and establish a SAR moving target vector observation model represented in vector form: In the formula, Represents the echo data of SAR moving targets. Represents the signal downsampling matrix. This represents the observation matrix determined by the SAR moving target echo signal model. Represents the motion parameters of a moving target. This represents the scattering coefficient of the scene observed from a moving target. Indicates observation noise; Steps S1-4: Based on the Omega-K imaging algorithm and combined with the SAR moving target vector observation model, establish a SAR moving target observation model represented in matrix form: In the formula, This represents the echo signal of a SAR moving target. Representation and downsampling matrix The corresponding downsampling operator, This represents the Hadamard product along the azimuth and range directions. This represents an image of a SAR moving target observation scene. Represents the observation noise in matrix form. This represents the echo generation operator constructed according to the Omega-K algorithm, and... In the formula, Denotes the conjugate matrix of the distance-to-Fourier transform matrix. This indicates stolt interpolation. This represents the distance-to-Fourier transform matrix. This represents the azimuth-to-Fourier transform matrix. Represents matrix dot product. This represents the conjugate matrix of the motion compensation matrix for the moving target in the Omega-K algorithm. This represents the conjugate matrix of the compression matrix in the Omega-K algorithm. This represents the conjugate matrix of the azimuth Fourier transform matrix.

[0008] Optionally, in step S2, the established SAR moving target sparse reconstruction and autofocusing imaging model is as follows: In the formula, Indicates about , The multi-objective optimization problem Indicates taking The square of the Frobenius norm, The regularization coefficient is . Indicates taking The L1 norm.

[0009] Optionally, step S3 specifically includes: Step S3-1: Based on the correspondence between the vector and matrix forms of the SAR moving target observation model, the SAR moving target sparse reconstruction and autofocusing imaging model is rewritten as follows: Step S3-2: Solve iteratively using the alternating direction multiplier method: In the formula, This represents the value of x in the (t+1)th iteration. This means finding x that minimizes the expression. Indicates the speed of the moving target as The observation matrix at that time Indicates the t-th iteration The solution value, express The value obtained in the (t+1)th iteration. This means finding the minimum value of the expression. .

[0010] Optionally, step S3-2 specifically includes: Step S3-2-1: Initialization , And set the regularization coefficient. Maximum number of iterations T, current number of iterations t=0; Step S3-2-2: When t≤T, solve using the complex-value iterative soft thresholding algorithm. : In the formula, This represents a complex-valued soft threshold function with a weighting factor of β. This represents the solution value of x in the t-th iteration. This represents the weight coefficient for the (t+1)th iteration. Represents the observation matrix The inverse matrix, express The transpose; then with corresponding The solution is: In the formula, This indicates that the algorithm is constructed based on the Omega-K algorithm. The inverse operator of , and, In the formula, This represents the motion compensation matrix for the moving target in the Omega-K algorithm. This represents the compression matrix in the Omega-K algorithm; Step S3-2-3: Based on the spatiotemporal correlation of SAR moving targets, estimate the correlation through correlation extraction and nonlinear fitting. ,Right now, In the formula, Represents a nonlinear fitting function. This represents the correlation extraction function; Step S3-2-4: Let the iteration number t = t + 1, and repeat steps S3-2-2 and S3-2-3 until the iteration stopping condition is met.

[0011] Optionally, step S4 specifically includes: Step S4-1: Construct the first network module, based on The computational expression is used to design the network layer, and the input is... and Output ; Step S4-2: Construct the second network module: Attention-based relevance extraction network, input Output the correlation of moving targets ; Based on a fully connected network module, the correlation of the input moving target is analyzed. Output ; Step S4-3: Repeat Steps S4-1 to S4-2 are repeated, and the output of the last step S4-2 is input into step S4-1 to complete the construction of the SAR moving target sparse reconstruction and autofocus imaging model. This indicates the number of network iteration modules formed by steps S4-1 to S4-2.

[0012] Optionally, the parameters of the attention-based relevance extraction network include: The feature dimension is 128 or 256, the number of attention heads is 8 to 16, and the weight coefficient is 0.4 to 0.6. The spatial convolution kernel size is 3 to 5, the number of channels is 3 to 6, the stride is 1 to 2, and the padding is 2 to 10. The temporal convolution kernel size is 3 to 5, the number of channels is 3 to 6, the stride is 1 to 2, and the padding is 2 to 10.

[0013] Optionally, the parameters of the fully connected network module include: The input layer feature dimension is 256 or 512, the intermediate layer feature dimension is 128 or 256, and the output feature dimension is 256 or 512.

[0014] Optionally, the number of network iteration modules is 4 to 8, and the update step size is 0.4 to 0.6.

[0015] Optionally, in step S5, SAR moving target sparse reconstruction and autofocus imaging model training are performed through backpropagation. During the backpropagation process, the Adam optimizer is used to update and optimize the network parameters to obtain the final SAR moving target autofocus imaging network.

[0016] Beneficial effects: 1. Through the above technical solution, firstly, the method of the present invention can ensure focusing performance under sparse sampling conditions. Specifically, the method of the present invention, by constructing a SAR moving target autofocusing imaging network architecture and optimizing network parameters, can effectively suppress moving target defocus and offset and maintain imaging quality even under sparse signal sampling conditions (e.g., 30%-70% sampling rate).

[0017] Second, the method of the present invention is well applicable to complex motion scenarios. Specifically, the method of the present invention utilizes a motion compensation module based on multi-frame correlation learning, which can overcome the limitations of traditional single-frame data processing and significantly enhance the adaptability to complex motions of moving targets (e.g., variable speed motion in the azimuth / range directions).

[0018] Third, the method of this invention can optimize end-to-end imaging efficiency. Specifically, the method of this invention avoids manual modeling and complex iterative calculations through deep expansion iterative solution process and network training, thereby improving imaging efficiency and meeting the needs of practical engineering applications.

[0019] 2. Other beneficial effects or advantages of the present invention will be described in detail in the specific embodiments. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] in: Figure 1 A flowchart illustrating the steps of a SAR moving target autofocusing imaging method based on multi-frame correlation learning, provided as an exemplary embodiment of the present invention; Figure 2 A schematic diagram of the structure of a SAR moving target sparse reconstruction and autofocusing imaging network provided as an exemplary embodiment of the present invention; Figure 3 A schematic diagram of a SAR moving target motion parameter estimation network layer based on multi-frame correlation learning, provided as an exemplary embodiment of the present invention; Figure 4 A schematic diagram of a SAR system provided as an exemplary embodiment of the present invention; Figure 5 A comparison diagram of motion target simulation imaging results with a data sampling rate of 70% is provided as an exemplary embodiment of the present invention, wherein a is the original scene and b is the result of the method of the present invention; Figure 6 A comparison diagram of motion target simulation imaging results with a data sampling rate of 30% is provided as an exemplary embodiment of the present invention, wherein a is the original scene and b is the result of the method of the present invention; Figure 7 A comparison of simulated imaging results of moving targets on ships with a data sampling rate of 70% is provided as an exemplary embodiment of the present invention, wherein a is the original scene and b is the result of the method of the present invention; Figure 8 The image shows a comparison of simulated imaging results of moving targets on ships at a data sampling rate of 30% as an exemplary embodiment of the present invention. In the image, a represents the original scene and b represents the result of the method of the present invention. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0023] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0024] Furthermore, the terms "comprising" and "having," and any variations thereof, used in the description of this invention are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units is not limited to the listed steps or units, but may optionally include other steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or devices. It should also be noted that in embodiments of this invention, the words "exemplary" or "for example" are used to indicate examples, illustrations, or descriptions. Any embodiment or design described as "exemplary" or "for example" in embodiments of this invention should not be construed as preferred or advantageous over other embodiments or designs. Specifically, the use of the words "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0025] To facilitate a clearer and more accurate understanding of the technical solutions of this invention by those skilled in the art, the existing related technologies and their technical problems will be described in more detail below.

[0026] Synthetic Aperture Radar (SAR) is an active microwave sensor that transmits, receives, and processes microwave signals to obtain high-resolution electromagnetic scattering images of the observed scene. SAR has the advantages of being available in all weather conditions and can penetrate obstacles such as clouds, rain, and fog to detect targets. SAR has significant application value in target monitoring, traffic control, and target reconnaissance.

[0027] SAR imaging requires utilizing the relative positional relationship between the target and the radar platform to deduce the target's backscattering coefficient from the echo signal, thereby achieving focused imaging. Therefore, accurately obtaining the positional relationship between the target and the radar is crucial for achieving high-precision focused imaging. However, the motion parameters of moving targets are unknown and difficult to estimate accurately, especially under sparse signal sampling conditions. When motion parameters cannot be fully compensated, the moving target will appear defocused or shifted in the SAR image, making focused imaging of moving targets in sparsely sampled SAR challenging.

[0028] To achieve focused imaging of moving targets, it is necessary to estimate and compensate for the motion parameters of the moving targets during the imaging process. Typical moving target imaging methods include transform-based methods and optimization-based methods. Transform-based methods utilize transforms such as Keystone and time-frequency analysis to project the echo signal into the transform domain, and estimate and compensate for the motion parameters of the moving targets in the transform domain. This type of method is currently the most widely used in moving target imaging. However, transform-based methods usually require the echo data to meet the Nyquist sampling rate, making them unsuitable for sparse sampling situations. Furthermore, these methods employ a fixed processing mode, making them less adaptable to complex and dynamic scenes. Optimization-based methods typically utilize compressed sensing theory to model moving target imaging as a sparse reconstruction optimization problem, using the motion parameters of the moving targets as variables to be optimized. This type of method usually achieves focused imaging of moving targets through iterative solutions of SAR image sparse reconstruction and motion parameter estimation. However, due to the complexity of moving target motion scenes, manually established optimization models are difficult to accurately represent the real scene, and the iterative solution process also makes this type of method computationally complex, resulting in low imaging efficiency.

[0029] In recent years, SAR learning imaging technology based on deep networks has been extensively studied. Deep network-based moving target focusing imaging methods are mainly divided into two categories: post-imaging refocusing and end-to-end focusing imaging. Post-imaging refocusing methods use deep networks such as convolutional neural networks to process defocused moving target images to obtain focused moving target images. For example, research in "CV-GMTINet: GMTI Using a Deep Complex-Valued Convolutional Neural Network for MultichannelSAR-GMTI System" shows that complex-valued convolutional neural networks can effectively improve the focusing performance of defocused SAR moving target images. End-to-end focusing imaging utilizes the fitting and learning capabilities of deep networks to directly reconstruct moving target images from echo data. For example, research in "Omega-KA-Net: A SAR ground moving target imaging network based on trainable Omega-K algorithm and sparse optimization" shows that using a deep imaging network based on parameterized Omega-K can achieve moving target focusing imaging under sparse sampling conditions.

[0030] The above research demonstrates the advantages and potential of deep learning-based moving target focusing imaging. However, existing learning-based moving target focusing imaging methods only use single-frame SAR data to estimate and compensate for the motion parameters of moving targets, while ignoring the spatiotemporal correlation of moving targets between multiple frames of SAR data. This limits the applicability of existing methods to complex moving target motion scenarios.

[0031] Therefore, how to effectively ensure the focusing imaging performance of moving targets and its applicability to complex motion scenes under the condition of sparse signal sampling has become an urgent problem to be solved.

[0032] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings.

[0033] like Figure 1 As shown, this embodiment provides a SAR moving target autofocusing imaging method based on multi-frame correlation learning, including the following steps: Step S1: Establish an observation model for the moving target echo signal based on the SAR working process and the motion characteristics of the moving target; Step S2: Based on the observation model and combined with the sparsity characteristics of SAR moving target images, establish a SAR moving target sparse reconstruction and autofocusing imaging model; Step S3: Using the alternating direction multiplier method, construct the iterative solution process for the SAR moving target sparse reconstruction and autofocusing imaging model; Step S4: Construct a SAR moving target autofocusing imaging network by performing a deep expansion iterative solution process and combining it with a moving target motion compensation module based on multi-frame correlation learning; Step S5: Train the SAR moving target autofocusing imaging network through backpropagation, optimize its parameters, and obtain the final SAR moving target autofocusing imaging network.

[0034] Through the above technical solution, firstly, the method of the present invention can ensure focusing performance under sparse sampling conditions. Specifically, the method of the present invention, by constructing a SAR moving target autofocusing imaging network architecture and optimizing network parameters, can effectively suppress moving target defocus and shift and maintain imaging quality even under sparse signal sampling conditions (e.g., 30%-70% sampling rate).

[0035] Second, the method of the present invention is well applicable to complex motion scenarios. Specifically, the method of the present invention utilizes a motion compensation module based on multi-frame correlation learning, which can overcome the limitations of traditional single-frame data processing and significantly enhance the adaptability to complex motions of moving targets (e.g., variable speed motion in the azimuth / range directions).

[0036] Third, the method of this invention can optimize end-to-end imaging efficiency. Specifically, the method of this invention improves imaging efficiency and meets the needs of practical engineering applications by using a deep expansion iterative solution process and network training to avoid manual parameter tuning and complex iterative calculations.

[0037] In one embodiment of the present invention, step S1 may specifically include: Step S1-1: Based on the SAR geometry and the motion characteristics of the moving target, establish the slant range expression for the moving target: In the formula, Indicates the instantaneous slant range of a moving target. The azimuth time represents the positional time, and v represents the SAR platform's velocity. This indicates the distance from the moving target to the center of the radar beam along the azimuth direction. This indicates the reference slant range between the SAR platform and the moving target along the center of the radar beam. This indicates the angle between the radar beam center and the range direction. This indicates the velocity of a moving target along the azimuth direction. This indicates the velocity of a moving target along the range direction; Step S1-2: Establish a SAR moving target echo signal model based on the slant range expression: In the formula, This represents the echo signal of a moving target. Represents the range and azimuth envelope functions. The imaginary unit is the complex value. Indicates the carrier frequency. Indicates instantaneous slant distance. Represents the speed of light. Indicates signal modulation frequency Step S1-3: Based on the SAR moving target echo signal model, represent the echo signal in vector form and establish a SAR moving target vector observation model represented in vector form: In the formula, Represents the echo data of SAR moving targets. Represents the signal downsampling matrix. This represents the observation matrix determined by the SAR moving target echo signal model. Represents the motion parameters of a moving target. This represents the scattering coefficient of the scene observed from a moving target. Indicates observation noise; Steps S1-4: Based on the Omega-K imaging algorithm and combined with the SAR moving target vector observation model, establish a SAR moving target observation model represented in matrix form: In the formula, This represents the echo signal of a SAR moving target. Representation and downsampling matrix The corresponding downsampling operator, This represents the Hadamard product along the azimuth and range directions. This represents an image of a SAR moving target observation scene. Represents the observation noise in matrix form. This represents the echo generation operator constructed according to the Omega-K algorithm, and... In the formula, Denotes the conjugate matrix of the distance-to-Fourier transform matrix. This indicates stolt interpolation. This represents the distance-to-Fourier transform matrix. This represents the azimuth-to-Fourier transform matrix. Represents matrix dot product. This represents the conjugate matrix of the motion compensation matrix for the moving target in the Omega-K algorithm. This represents the conjugate matrix of the compression matrix in the Omega-K algorithm. This represents the conjugate matrix of the azimuth Fourier transform matrix.

[0038] Thus, through this implementation method, firstly, an accurate geometric relationship representation of the moving target can be established. Specifically, through the slant range expression in step S1-1, the dynamic geometric relationship between the moving target and the SAR platform is fully quantified (including the platform velocity v and the distance of the moving target along the azimuth direction). Reference slope distance Beam angle and the velocity components in the azimuth and range directions of the target. and In this way, this formula can provide a physical basis for subsequent signal modeling, ensuring that the influence of motion parameters on the echo phase is accurately modeled, thereby facilitating the solution of moving target defocusing problems.

[0039] Second, it can construct a highly adaptable moving target echo signal model. Specifically, the SAR moving target echo signal model in steps S1-2 is constructed using carrier frequencies. Frequency modulation and slant distance The coupling can accurately characterize the time-varying phase and frequency modulation characteristics of the moving target echo. In this way, the target motion and signal distortion can be directly correlated, providing a mathematical basis for the subsequent separation of motion parameters under sparse sampling conditions.

[0040] Third, it can construct vectorized observation models compatible with sparse sampling. Specifically, the SAR moving target vector observation model represented in vector form in steps S1-3 is downsampled using a matrix... An explicit signal undersampling mechanism is introduced, enabling the model to directly adapt to sparse sampling scenarios. Simultaneously, the observation matrix... motion parameters Embedded into the system response, echo data is established. Scattering coefficient of moving target The explicit mapping provides a mathematical framework for the sparse optimization problem of subsequent moving target focusing imaging.

[0041] Fourth, it enables matrix-based modeling to improve computational efficiency. Specifically, the SAR moving target observation model represented in matrix form in steps S1-4 is decomposed using the Omega-K algorithm (including Stolt interpolation and motion compensation). and Fourier transform and This method transforms the echo generation process into two-dimensional matrix operations to avoid point-by-point calculations, thereby significantly improving the efficiency of subsequent iterative solutions, especially suitable for large-scale scene imaging. The echo generation operator... The definition integrates motion compensation with imaging processing (Fourier transform, interpolation, compression) into a single operator, which helps ensure the end-to-end optimizability of motion parameters in the imaging process, so as to provide a differentiable mathematical structure for subsequent parameter estimation.

[0042] Overall, this implementation method, through a progressive design of geometric modeling → signal modeling → vectorization → matrixization, constructs a moving target observation model that combines physical accuracy, sparse sampling compatibility, and computational efficiency. It not only provides a rigorous mathematical foundation for moving target imaging under sparse sampling but also improves processing efficiency through matrix operations. Furthermore, it supports the joint optimization of subsequent motion compensation and imaging through embedded motion parameter design.

[0043] In one embodiment of the present invention, in step S2, the established SAR moving target sparse reconstruction and autofocusing imaging model is as follows: In the formula, Indicates about , The multi-objective optimization problem Indicates taking The square of the Frobenius norm, The regularization coefficient is . Indicates taking The L1 norm.

[0044] This implementation unifies motion parameter estimation and scene imaging into a multi-objective optimization problem through a joint optimization framework, whereby the sparsity constraint ( From the perspective of data consistency constraints, it can force the sparsity of moving target images, adapt to signal undersampling conditions, and suppress noise interference. For this purpose, it can ensure the matching between the reconstructed image and the original echo data. This solves the problem that traditional methods cannot balance motion compensation and image quality under sparse sampling.

[0045] In one embodiment of the present invention, step S3 may specifically include: Step S3-1: Based on the correspondence between the vector and matrix forms of the SAR moving target observation model, the SAR moving target sparse reconstruction and autofocusing imaging model is rewritten as follows: Step S3-2: Solve iteratively using the alternating direction multiplier method: In the formula, This represents the value of x in the (t+1)th iteration. This means finding x that minimizes the expression. Indicates the speed of the moving target as The observation matrix at that time Indicates the t-th iteration The solution value, express The value obtained in the (t+1)th iteration. This means finding the minimum value of the expression. .

[0046] This implementation decomposes the optimization problem using the Alternating Directional Multiplier Method (ADMM), which not only decouples the complex coupled problem into two independent sub-problems—image reconstruction and motion parameter estimation—but also provides an feasible iterative structure for subsequent depth unfolding. This overcomes the difficulties of manually setting solution parameters and the high computational cost of iterative solutions.

[0047] In one embodiment of the present invention, step S3-2 may specifically include: Step S3-2-1: Initialization , And set the regularization coefficient. Maximum number of iterations T, current number of iterations t=0; Step S3-2-2: When t≤T, solve using the complex-value iterative soft thresholding algorithm. : In the formula, This represents a complex-valued soft threshold function with a weighting factor of β. This represents the solution value of x in the t-th iteration. This represents the weight coefficient for the (t+1)th iteration. Represents the observation matrix The inverse matrix, express The transpose; then with corresponding The solution is: In the formula, This indicates that the algorithm is constructed based on the Omega-K algorithm. The inverse operator of , and, In the formula, This indicates stolt interpolation. This represents the motion compensation matrix for the moving target in the Omega-K algorithm. This represents the compression matrix in the Omega-K algorithm; Step S3-2-3: Based on the spatiotemporal correlation of SAR moving targets, estimate the correlation through correlation extraction and nonlinear fitting. ,Right now, In the formula, Represents a nonlinear fitting function. This represents the correlation extraction function; Step S3-2-4: Let the iteration number t = t + 1, and repeat steps S3-2-2 and S3-2-3 until the iteration stopping condition is met.

[0048] This implementation details the iterative solution process, employing a complex-valued iterative soft-thresholding algorithm for image reconstruction to efficiently solve sparse-constrained problems. Simultaneously, it estimates motion parameters through correlation extraction and nonlinear fitting, utilizing the spatiotemporal correlation of the moving target to avoid complex mathematical derivations. This effectively improves iterative efficiency and robustness.

[0049] In one embodiment of the present invention, step S4 may specifically include: Step S4-1: Construct the first network module, based on The computational expression is used to design the network layer, and the input is... and Output ; Step S4-2: Construct the second network module: Attention-based relevance extraction network, input Output the correlation of moving targets ; Based on a fully connected network module, the correlation of the input moving target is analyzed. Output ; Step S4-3: Repeat Steps S4-1 to S4-2 are repeated, and the output of the last step S4-2 is input into step S4-1 to complete the construction of the SAR moving target sparse reconstruction and autofocus imaging model. This indicates the number of network iteration modules formed by steps S4-1 to S4-2.

[0050] This implementation constructs a trainable deep unfolded network, wherein the first network module is for implementing... The solution layer; the attention-based correlation extraction network in the second network module is used to output the correlation. The fully connected network module is used for output. The iterative architecture is as follows: The loop-connected modules approximate the optimization process. In this way, the mathematical iteration can be transformed into a learnable network, preserving physical interpretability and improving solution performance and computational efficiency.

[0051] In one embodiment of the present invention, the parameters of the attention-based relevance extraction network of the present invention may include: The feature dimension is 128 or 256, the number of attention heads is 8 to 16, and the weight coefficient is 0.4 to 0.6. The spatial convolution kernel size is 3 to 5, the number of channels is 3 to 6, the stride is 1 to 2, and the padding is 2 to 10. The temporal convolution kernel size is 3 to 5, the number of channels is 3 to 6, the stride is 1 to 2, and the padding is 2 to 10.

[0052] This implementation limits the parameters of the attention-based correlation extraction network to balance computational complexity with the ability to capture multi-frame correlations.

[0053] In one embodiment of the present invention, the parameters of the fully connected network module of the present invention include: The input layer feature dimension is 256 or 512, the intermediate layer feature dimension is 128 or 256, and the output feature dimension is 256 or 512.

[0054] This implementation limits the parameters of the fully connected network module. It prevents overfitting and improves generalization through dimensionality reduction design, while ensuring dimensionality compatibility of motion parameters by matching inputs and outputs.

[0055] In one embodiment of the present invention, the number of network iteration modules is 4 to 8, and the update step size is 0.4 to 0.6.

[0056] This implementation limits the number of network iteration modules and the update step size to control the computational load (6 iterations balance imaging quality and real-time performance). At the same time, a fixed step size is used to avoid training divergence and ensure convergence.

[0057] In one embodiment of the present invention, in step S5, SAR moving target sparse reconstruction and autofocus imaging model training are performed through backpropagation. During the backpropagation process, the Adam optimizer is used to update and optimize the network parameters to obtain the final SAR moving target autofocus imaging network.

[0058] This implementation method is limited to using the Adam optimizer for network training to accelerate convergence, avoid local optima, and achieve efficient end-to-end training.

[0059] The method of the present invention will be described below with reference to an exemplary embodiment.

[0060] In this embodiment, the network structure is as follows: Figure 2 and Figure 3 As shown, Figure 4 The diagram below shows the geometric configuration of the SAR system in this embodiment. The basic parameters are shown in Table 1.

[0061] Table 1 SAR System Parameters In this embodiment, a simulated SAR moving target is used as the original scene. The network training dataset and test dataset are generated by combining the system parameters in Table 1. The specific process is as follows: A0. Generate the original scene. According to the moving target motion parameters in Table 1, randomly generate SAR images of point moving targets and ship moving targets, and use these images as the original scene for generating echo data. A. Generate echo data: Based on the system parameters and the original scene of the moving target in Table 1, simulation parameters were set and echoes were generated. The generated echoes were demodulated to obtain the demodulated baseband echo data: in, For SAR moving target observation scenarios, For The backscattering coefficient of a moving target at that location. These represent the range and azimuth window functions, respectively; in this embodiment, a rectangular window is used. This indicates the modulation frequency of a linear frequency modulated signal. The moment when the target is crossed by the beam center. The time frame for synthesizing the aperture of the point target. Let distance and time be the variables, and the number of discrete points is... , For the azimuth-time variable, the number of discrete points is: , Let be the slant range of the moving target, and its calculation formula is: B. Set the parameters for the SAR moving target focusing imaging network: Figure 2 Number of iterative modules in the network Set it to 6.

[0062] C. Set the SAR imaging network training parameters: The training dataset has 3000 samples, the validation dataset has 200 samples, the test dataset has 200 samples, the batch size for network training is 50, the total number of epochs is 100, the learning rate is set to 0.0001, and the Adam optimizer is used.

[0063] D. Training the SAR moving target focusing imaging network using backpropagation: The SAR moving target focusing imaging network was trained using the network training parameters and dataset set above. The network training platform was configured as follows: Intel Xeon Gold 6128 CPU and NVIDIA Tesla P100 GPU (16GB VRAM).

[0064] E. Network Testing: The trained imaging network is tested using a test dataset. The echo data from the training dataset is fed into the trained network, the network outputs the SAR moving target imaging results, and the corresponding performance indicators are calculated.

[0065] The test results of the motion target simulation data under different data sampling rates are shown in Table 2 below. Figure 5 , Figure 6 As shown in Table 3, the test results of the ship moving target simulation data are as follows: Figure 7 , Figure 8 As shown.

[0066] The calculation formulas for the evaluation metrics Peak Signal-to-Noise Ratio (PSNR), Structural Similarity (SSIM), and Image Entropy (ENT) are as follows: In the formula, This represents the output of the moving target focusing imaging network. This indicates the original scene it corresponds to. This represents the total number of pixels in the SAR image. , They represent and The mean, , They represent and variance The parameter for SSIM is set to 0.01. The parameters of SSIM are calculated, with a value of 0.03, where M and N represent the image. The number of pixels in the mid-range and azimuth directions. X represents the total energy of the SAR image, and P represents the probability of each pixel value appearing in X.

[0067] Table 2 Performance Indicators of Moving Target Test Results Table 3 Performance Indicators of Ship Moving Target Test Results This invention establishes a SAR moving target focusing imaging network for sparse signal sampling conditions. The established SAR moving target focusing imaging model based on sparse reconstruction can solve the SAR moving target imaging problem under sparse sampling. Furthermore, it solves the SAR moving target focusing imaging problem model through a deep unfolded network, extracts multi-frame correlations of moving targets using attention convolutional neural network layers, and estimates moving target motion parameters through fully connected network layers. This improves the proposed method's moving target focusing imaging performance under sparse sampling conditions and its applicability to complex motion scenes, meeting practical application requirements. Simulation results for different moving targets show that the method of this invention has the characteristics of low data sampling requirements and excellent imaging performance.

[0068] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A SAR moving target autofocusing imaging method based on multi-frame correlation learning, characterized in that, The steps include: Step S1: Establish an observation model for the moving target echo signal based on the SAR working process and the motion characteristics of the moving target; Step S2: Based on the observation model and combined with the sparsity characteristics of SAR moving target images, establish a SAR moving target sparse reconstruction and autofocusing imaging model; Step S3: Using the alternating direction multiplier method, construct the iterative solution process for the SAR moving target sparse reconstruction and autofocusing imaging model; Step S4: By deeply expanding the iterative solution process and combining it with the moving target motion compensation module based on multi-frame correlation learning, a SAR moving target autofocusing imaging network is constructed. Step S5: Train the SAR moving target autofocusing imaging network through backpropagation, optimize its parameters, and obtain the final SAR moving target autofocusing imaging network.

2. The SAR moving target autofocusing imaging method based on multi-frame correlation learning according to claim 1, characterized in that, Step S1 specifically includes: Step S1-1: Based on the SAR geometry and the motion characteristics of the moving target, establish the slant range expression for the moving target: In the formula, Indicates the instantaneous slant range of a moving target. Indicates location and time. Indicates the SAR platform's velocity. This indicates the distance from the moving target to the center of the radar beam along the azimuth direction. This indicates the reference slant range between the SAR platform and the moving target along the center of the radar beam. This indicates the angle between the radar beam center and the range direction. This indicates the velocity of a moving target along the azimuth direction. This indicates the velocity of a moving target along the range direction; Step S1-2: Establish a SAR moving target echo signal model based on the slant range expression: Where, This represents the echo signal of a moving target. Represents the range and azimuth envelope functions. The imaginary unit is the complex value. Indicates the carrier frequency. Indicates instantaneous slant distance. Represents the speed of light. Indicates the signal frequency modulation; Step S1-3: Based on the SAR moving target echo signal model, represent the echo signal in vector form and establish a SAR moving target vector observation model represented in vector form: Where, Represents the echo data of SAR moving targets. Represents the signal downsampling matrix. This represents the observation matrix determined by the SAR moving target echo signal model. Represents the motion parameters of a moving target. This represents the scattering coefficient of the scene observed from a moving target. Indicates observation noise; Steps S1-4: Based on the Omega-K imaging algorithm and combined with the SAR moving target vector observation model, establish a SAR moving target observation model represented in matrix form: Where, This represents the echo signal of a SAR moving target. Representation and downsampling matrix The corresponding downsampling operator, This represents the Hadamard product along the azimuth and range directions. This represents an image of a SAR moving target observation scene. Represents the observation noise in matrix form. This represents the echo generation operator constructed according to the Omega-K algorithm, and... In the formula, Denotes the conjugate matrix of the distance-to-Fourier transform matrix. This indicates stolt interpolation. This represents the distance-to-Fourier transform matrix. This represents the azimuth-to-Fourier transform matrix. Represents matrix dot product. This represents the conjugate matrix of the motion compensation matrix for the moving target in the Omega-K algorithm. This represents the conjugate matrix of the compression matrix in the Omega-K algorithm. This represents the conjugate matrix of the azimuth Fourier transform matrix.

3. The SAR moving target autofocusing imaging method based on multi-frame correlation learning according to claim 2, characterized in that, In step S2, the established SAR moving target sparse reconstruction and autofocus imaging model is as follows: Where, Indicates about , The multi-objective optimization problem Indicates taking The square of the Frobenius norm, The regularization coefficient is . Indicates taking The L1 norm.

4. The SAR moving target autofocusing imaging method based on multi-frame correlation learning according to claim 3, characterized in that, Step S3 specifically includes: Step S3-1: Based on the correspondence between the vector and matrix forms of the SAR moving target observation model, the SAR moving target sparse reconstruction and autofocusing imaging model is rewritten as follows: Step S3-2: Solve iteratively using the alternating direction multiplier method: Where, This represents the value of x in the (t+1)th iteration. This means finding x that minimizes the expression. Indicates the speed of the moving target as The observation matrix at that time, Indicates the t-th iteration The solution value, express The value obtained in the (t+1)th iteration. This means finding the minimum value of the expression. .

5. The SAR moving target autofocusing imaging method based on multi-frame correlation learning according to claim 4, characterized in that, Step S3-2 specifically includes: Step S3-2-1: Initialization , And set the regularization coefficient. Maximum number of iterations T, current number of iterations t=0; Step S3-2-2: When t≤T, solve using the complex-value iterative soft thresholding algorithm. : In the formula, This represents a complex-valued soft threshold function with a weighting factor of β. This represents the solution value of x in the t-th iteration. This represents the weight coefficient for the (t+1)th iteration. Represents the observation matrix The inverse matrix, express The transpose; then with corresponding The solution is: Where, This indicates that the algorithm is constructed based on the Omega-K algorithm. The inverse operator of , and, In the formula, This represents the motion compensation matrix for the moving target in the Omega-K algorithm. This represents the compression matrix in the Omega-K algorithm; Step S3-2-3: Based on the spatiotemporal correlation of SAR moving targets, estimate the correlation through correlation extraction and nonlinear fitting. ,Right now, In the formula, Represents a nonlinear fitting function. This represents the correlation extraction function; Step S3-2-4: Let the iteration number t = t + 1, and repeat steps S3-2-2 and S3-2-3 until the iteration stopping condition is met.

6. The SAR moving target autofocusing imaging method based on multi-frame correlation learning according to claim 5, characterized in that, Step S4 specifically includes: Step S4-1: Construct the first network module, based on The computational expression is used to design the network layer, and the input is... and , output ; Step S4-2: Construct the second network module: Attention-based relevance extraction network, input Output the correlation of moving targets ; Based on a fully connected network module, the correlation of the input moving target is analyzed. Output ; Step S4-3: Repeat Steps S4-1 to S4-2 are repeated, and the output of the last step S4-2 is input into step S4-1 to complete the construction of the SAR moving target sparse reconstruction and autofocus imaging model. This indicates the number of network iteration modules formed by steps S4-1 to S4-2.

7. The SAR moving target autofocusing imaging method based on multi-frame correlation learning according to claim 6, characterized in that, The parameters of the attention-based relevance extraction network include: The feature dimension is 128 or 256, the number of attention heads is 8 to 16, and the weight coefficient is 0.4 to 0.

6. The spatial convolution kernel size is 3 to 5, the number of channels is 3 to 6, the stride is 1 to 2, and the padding is 2 to 10. The temporal convolution kernel size is 3 to 5, the number of channels is 3 to 6, the stride is 1 to 2, and the padding is 2 to 10.

8. The SAR moving target autofocusing imaging method based on multi-frame correlation learning according to claim 6, characterized in that, The parameters of the fully connected network module include: The input layer feature dimension is 256 or 512, the intermediate layer feature dimension is 128 or 256, and the output feature dimension is 256 or 512.

9. The SAR moving target autofocusing imaging method based on multi-frame correlation learning according to claim 6, characterized in that, The number of network iteration modules is 4 to 8, and the update step size is 0.4 to 0.

6.

10. The SAR moving target autofocusing imaging method based on multi-frame correlation learning according to claim 6, characterized in that, In step S5, SAR moving target sparse reconstruction and autofocus imaging model training are performed through backpropagation. During the backpropagation process, the Adam optimizer is used to update and optimize the network parameters to obtain the final SAR moving target autofocus imaging network.

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