A Synthetic Aperture Radar Autofocusing Method Based on Invariant Risk Minimization

Abstract

This invention discloses a synthetic aperture radar (SAR) autofocusing method based on invariant risk minimization, belonging to the field of radar imaging technology. It is used for SAR autofocusing, including acquiring SAR images; constructing a SAR autofocusing framework, including a random error generation module, a phase error prediction model, a self-supervised constraint module, and a refocusing imaging module; the random error generation module generates the defocused SAR image; the phase error prediction model outputs the corresponding predicted azimuth phase error parameters; the self-supervised constraint module constructs the overall objective function; and the refocusing imaging module outputs the refocused SAR image. This invention significantly enhances the model's ability to extract and represent the physical characteristics of phase errors through redundant representation and feature fusion in both time and frequency domains; and by introducing invariant risk minimization constraints, it establishes a robust causal regression mapping, significantly improving the model's generalization robustness in heterogeneous scenarios.

Description

Technical Field

[0001] This invention discloses a synthetic aperture radar autofocusing method based on minimizing invariant risk, belonging to the field of radar imaging technology. Background Technology

[0002] In recent years, deep learning methods have begun to be applied in the field of SAR refocusing. AFnet and PAFnet models have achieved high focusing quality while maintaining real-time performance. A data-driven SAR image autofocusing method utilizes an encoder-decoder architecture to directly learn the defocusing mechanism from the input SAR image, thereby achieving efficient refocusing. A model based on Restormer and convolutional neural networks estimates error coefficients; the Restormer feature extraction network predicts low-order error coefficients, while the convolutional neural network feature extraction network predicts high-order error coefficients to achieve autofocus. An autofocusing method based on ensemble learning combines multiple CELMs to further improve estimation accuracy, thereby achieving high-speed and accurate error compensation. The above methods have proven that learning-based algorithms outperform traditional methods in autofocusing performance. However, existing learning-based autofocusing methods are generally based on the assumption that the training and test sets are independent and identically distributed. In complex and variable real-world application scenarios, due to differences in imaging parameters and environment, data domain offset is common, which greatly challenges the model's generalization ability, leading to a significant decrease in its focusing performance in the distributed offset domain. The fundamental reason for this performance degradation lies in the model's difficulty in establishing a robust, cross-environmental invariant relationship between image defocus features and azimuth error parameters under different imaging environments. Therefore, effectively improving the robustness and generalization ability of learning-based self-focusing methods in scenarios with significant distributed offsets has become a pressing bottleneck problem that needs to be addressed. Summary of the Invention

[0003] The purpose of this invention is to provide a synthetic aperture radar autofocusing method based on minimizing invariant risk, so as to solve the problem that the learning-based autofocusing method in the prior art has insufficient generalization ability in cross-domain scenarios.

[0004] A synthetic aperture radar autofocusing method based on invariant risk minimization includes: Acquire synthetic aperture radar images; A synthetic aperture radar autofocusing framework is constructed, including a random error generation module, a phase error prediction model, a self-supervised constraint module, and a refocusing imaging module; The random error generation module transforms the synthetic aperture radar image into the range-Doppler frequency domain via Fourier transform, injects random azimuth phase error into the frequency domain, and returns it to the image domain via inverse Fourier transform to obtain the defocused synthetic aperture radar image. The defocused synthetic aperture radar image is input into the phase error prediction model, which outputs the corresponding predicted azimuth phase error parameters. The overall objective function is calculated using the self-supervised constraint module, and the phase error prediction model is updated to complete the neural network training. The phase error prediction model includes a feature encoder and a predictor; the self-supervised constraint module includes invariant risk minimization constraint, image entropy loss and learning strategy, and the overall objective function is constructed based on the invariant risk minimization constraint, image entropy loss and learning strategy. The refocusing imaging module transforms the defocused synthetic aperture radar image into the range-Doppler frequency domain via Fourier transform, compensates for the corresponding predicted azimuth phase error parameters in the frequency domain, and returns it to the image domain via inverse Fourier transform to obtain the refocused synthetic aperture radar image.

[0005] A time-frequency alternating Mamba-CNN model is constructed as the feature encoder for the phase error prediction model, including a time-domain branch, a frequency-domain branch, and a time-frequency interaction module; The temporal branch uses a CNN, with a synthetic aperture radar image as input. , , For the complex field, we first separate the real and imaginary parts: ; In the formula, For real part diagram, This is a diagram of the imaginary part. It is the symbol for imaginary numbers. For height, Width; Will and Each input is a separate convolutional block for feature extraction, yielding the real part features. and the characteristics of the imaginary part , ,right and Channel-dimensional fusion is performed to obtain temporal complex features. : ; In the formula, It is the field of real numbers.

[0006] The frequency domain branch uses Mamba, and the input frequency domain plot is... , , for Obtained through two-dimensional fast Fourier transform, for Perform amplitude and phase decomposition: ; In the formula, This is an amplitude graph. , For phase diagram, ; Will and Inputting separate Mamba blocks yields amplitude characteristics. and phase characteristics , ,right and By performing complex combinations, frequency domain features are obtained. : .

[0007] Will and Input to the time-frequency interaction module to extract intermediate features in the time domain. and intermediate features in the frequency domain : ; ; In the formula, For convolutional blocks, For Mamba blocks; right Perform FFT to obtain forward transformation features , ;Will , and The enhanced frequency domain features are obtained by averaging the amplitude and phase values ​​respectively. , ;right Perform IFFT to obtain the inverse transformation features. , ,Will , and The features are concatenated and fused along the channel dimension, and then further enhanced by convolutional blocks to obtain enhanced temporal features. , , Number of channels; Will and The predictor is input and outputs the corresponding predicted azimuth phase error parameters; the predictor is a linear projection layer.

[0008] By introducing an invariant risk minimization constraint, each synthetic aperture radar image is treated as an independent environment. Multiple environments combined The model prediction function is Minimize loss due to invariant risk for: ; In the formula, For the environment Experience risks in These are the invariant constraint weights.

[0009] Introducing image entropy constraints : ; In the formula, The normalized grayscale histogram probability of the compensated amplitude image.

[0010] Learning strategies include introducing balance constraints. : ; ; In the formula, The weight truncation threshold prevents excessive entropy loss due to excessive weights. It is a tiny constant used to prevent division by zero errors. For the number of training rounds, For dynamic scaling factor, This serves as the lower bound for the scaling factor. and They are respectively The growth rate and curvature control parameters.

[0011] based on , and Construct the overall objective function : .

[0012] Compared with existing technologies, this invention has the following advantages: It captures long-range non-stationary features caused by azimuth phase error by leveraging Mamba's powerful linear sequence modeling capabilities in the frequency domain, and extracts local spatial structure information of the scatterer in the time domain using CNN. Through redundant representation and feature fusion in both time and frequency domains, the model's ability to extract and represent the physical features of phase error is significantly enhanced. By treating azimuth error estimation as a regression estimate and introducing IRM to optimize the model, a robust causal regression mapping is effectively established, significantly improving the model's generalization robustness in heterogeneous scenarios such as cross-band and cross-polarity scenarios. A dynamic balancing optimization strategy is designed to ensure that the model significantly improves image focus sharpness while maintaining the physical realism of the reconstructed image. Attached Figure Description

[0013] Figure 1 This is a schematic diagram of the technical process of the present invention;

[0014] Figure 2 These are the prediction error curves for each model under the first set of cross-band distributed migrations;

[0015] Figure 3 These are the prediction error curves for each model under the first group of non-cross-band distributed migrations;

[0016] Figure 4 These are the prediction error curves for each model under the second group of cross-band distribution migrations;

[0017] Figure 5 These are the prediction error curves for each model under the second group of non-cross-band distributed migrations;

[0018] Figure 6 These are the prediction error curves for each model under the third group of cross-band distribution migrations;

[0019] Figure 7 These are the prediction error curves for each model under the third group of non-cross-band distributed migrations;

[0020] Figure 8 These are the prediction error curves for each model under the first set of cross-platform distributed offsets;

[0021] Figure 9 These are the prediction error curves for each model under the second set of cross-platform distribution offsets. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention are described clearly and completely below. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0023] A synthetic aperture radar autofocusing method based on invariant risk minimization includes: Acquire synthetic aperture radar images; A synthetic aperture radar autofocusing framework is constructed, including a random error generation module, a phase error prediction model, a self-supervised constraint module, and a refocusing imaging module; The random error generation module transforms the synthetic aperture radar image into the range-Doppler frequency domain via Fourier transform, injects random azimuth phase error into the frequency domain, and returns it to the image domain via inverse Fourier transform to obtain the defocused synthetic aperture radar image. The defocused synthetic aperture radar image is input into the phase error prediction model, which outputs the corresponding predicted azimuth phase error parameters. The overall objective function is calculated using the self-supervised constraint module, and the phase error prediction model is updated to complete the neural network training. The phase error prediction model includes a feature encoder and a predictor; the self-supervised constraint module includes invariant risk minimization constraint, image entropy loss and learning strategy, and the overall objective function is constructed based on the invariant risk minimization constraint, image entropy loss and learning strategy. The refocusing imaging module transforms the defocused synthetic aperture radar image into the range-Doppler frequency domain via Fourier transform, compensates for the corresponding predicted azimuth phase error parameters in the frequency domain, and returns it to the image domain via inverse Fourier transform to obtain the refocused synthetic aperture radar image.

[0024] A time-frequency alternating Mamba-CNN model is constructed as the feature encoder for the phase error prediction model, including a time-domain branch, a frequency-domain branch, and a time-frequency interaction module; The temporal branch uses a CNN, with a synthetic aperture radar image as input. , , For the complex field, we first separate the real and imaginary parts: ; In the formula, For real part diagram, This is a diagram of the imaginary part. It is the symbol for imaginary numbers. For height, Width; Will and Each input is a separate convolutional block for feature extraction, yielding the real part features. and the characteristics of the imaginary part , ,right and Channel-dimensional fusion is performed to obtain temporal complex features. : ; In the formula, It is the field of real numbers.

[0025] The frequency domain branch uses Mamba, and the input frequency domain plot is... , , for Obtained through two-dimensional fast Fourier transform, for Perform amplitude and phase decomposition: ; In the formula, This is an amplitude graph. , For phase diagram, ; Will and Inputting separate Mamba blocks yields amplitude characteristics. and phase characteristics , ,right and By performing complex combinations, frequency domain features are obtained. : .

[0026] Will and Input to the time-frequency interaction module to extract intermediate features in the time domain. and intermediate features in the frequency domain : ; ; In the formula, For convolutional blocks, For Mamba blocks; right Perform FFT to obtain forward transformation features , ;Will , and The enhanced frequency domain features are obtained by averaging the amplitude and phase values ​​respectively. , ;right Perform IFFT to obtain the inverse transformation features. , ,Will , and The features are concatenated and fused along the channel dimension, and then further enhanced by convolutional blocks to obtain enhanced temporal features. , , Number of channels; Will and The predictor is input and outputs the corresponding predicted azimuth phase error parameters; the predictor is a linear projection layer.

[0027] By introducing an invariant risk minimization constraint, each synthetic aperture radar image is treated as an independent environment. Multiple environments combined The model prediction function is Minimize loss due to invariant risk for: ; In the formula, For the environment Experience risks in These are the invariant constraint weights.

[0028] Introducing image entropy constraints : ; In the formula, The normalized grayscale histogram probability of the compensated amplitude image.

[0029] Learning strategies include introducing balance constraints. : ; ; In the formula, The weight truncation threshold prevents excessive entropy loss due to excessive weights. It is a tiny constant used to prevent division by zero errors. For the number of training rounds, For dynamic scaling factor, This serves as the lower bound for the scaling factor. and They are respectively The growth rate and curvature control parameters.

[0030] based on , and Construct the overall objective function : .

[0031] The azimuth phase error calculation of this invention includes the following: During SAR imaging, azimuth phase errors often occur in SAR images due to factors such as system instability, platform motion errors, and imperfect electromagnetic propagation effects. Let the carrier frequency be... slow time Quick time The frequency modulation of the transmitted signal is The estimated slant distance of the platform is The error slant distance is The true slope distance is The echo after carrier frequency modulation can be obtained as follows: ; In the formula, At the speed of light, It is an exponential function. It is the symbol for imaginary numbers; Using the range-Doppler algorithm as the imaging method, after range compression, matched filtering, and RCMC of the echo signal, the following can be obtained: ; in, It is the Doppler frequency. It is distance frequency. It is an error-free image in the distance-Doppler domain. The azimuth error can be expanded into a polynomial form: ; in, This is the azimuth error coefficient. Indicates the order of error. The order of the maximum error. This refers to the azimuth tuning frequency. Coefficients of different orders will have different effects on the image. It exhibits a constant phase. This manifests as a directional translation. At higher levels, this manifests as defocusing.

[0032] The invariant risk minimization constraint of this invention includes constraining the model to learn only by relying on invariant risks that are stable across environments, thereby helping the model establish robust and non-degenerate causal cues. Let the given training environment be... Each environmental sample Characterizing the encoder Predictor Environmental risks This can be expressed as: ; in, Let be the sample loss function. For sample pairs, For the environment The following data distribution It is a composite function. As expected, For the environment The goal of IRM is to minimize risk across all environments while ensuring that the direction of its optimal solution remains consistent. ; In the formula, Let be any predictor variable; Limited by; This constraint enables the model to maintain a consistent APE mapping relationship across multiple scenario data, thereby achieving cross-scenario generalization.

[0033] The state-space model of this invention and Mamba include, assuming an input signal Hidden state Output signal The SSM can be expressed by the following linear ordinary differential equation (ODE): ; ; in, Here is the state transition matrix. For the input projection matrix, To output the projection matrix, For the skip link matrix, For continuous time variables, The time derivative of the hidden state; To apply SSM to deep learning scenarios, zero-order preserved discretization is used, with a sampling rate of [missing value]. The ODE is converted into the following discrete form: ; ; in, For the first Step stealth state, For the first Step output, The discrete time step index represents the discretized state transition matrix. Discretized input projection matrix Discretized output projection matrix Discretized jump connection matrix Building upon SSM, Mamba uses time-varying parameters for input dependencies instead of those in ODE. To achieve non-stationary long sequences; Mamba generates gated features from the current local context at each time step and adjusts the system matrix accordingly, then performs linear recursion in the ZOH discrete form. Let the input sequence be... The gating unit is The parameter is then obtained from the following formula: ; in These are the gated convolution parameters. It is an input sequence fragment. This is a convolution operation.

[0034] The proof process for minimizing the invariant risk of this invention includes assuming that the model is composed of a representation encoder. Predictor composition, Used to process high-dimensional observation data Mapping to latent feature space To facilitate the analysis of closed-form solutions for gradients, the final decoding part of the network is simplified into a linear projection layer for extracting features. Mid-regression phase error : ; In the formula, For input data, For feature vectors, For linear regression head, This is the output of the feature encoder; Simultaneously, assuming that the error is determined only by APE error features and ground texture environment features, the features are explicitly decomposed into two subspaces, with phase error being an inherently related invariant feature. Environmental characteristics determined by the texture of landforms In an ideal situation, Phase error with the true value Irrelevant, that is : ; In any environment In this process, using the minimum mean square error strategy, the linear regression head can be obtained. The optimal solution is: ; in, For the environment Expectations; ; ; In the formula, for The autocovariance matrix, for The autocovariance matrix, , for and The cross-covariance matrix, for and The cross-covariance vector, for and The cross-covariance vector, It is the transpose symbol; Therefore, the environment The optimal regression under these conditions can be written as: ; In the formula, For the environment The optimal regression head is... for The corresponding part, for The corresponding part; The above formula shows that, Simultaneously dependent on At the same time, due to Follow change, As scene statistics change, different terrain texture environments during training will lead to... Inevitable changes, leading to solutions If it exists right Therefore, its first-order necessary condition is: ; In the formula, For risk The gradient; By introducing IRMv2 (Invariant Risk Minimization Version 2), at fixed points Gradient penalty : ; In the formula, It is the Frobenius norm. For constant risk penalty weights, For experience risk and; exist Under the given conditions, the gradient of the linear regression head is: ; Therefore, the IRMv2 penalty will drive each environment to meet approximately consistent conditions: ; because With environmental changes, its relationship with Related items Different Inconsistencies lead to different optimal regression heads for each environment. They are different, thus failing to satisfy the global optimum. At the same time, it cannot satisfy Therefore, during the optimization process, the IRM penalty item will be forced. Reduce The regression contribution made The estimation mainly depends on invariant features .set up .

[0035] The following description, in conjunction with the accompanying drawings and embodiments, further illustrates the process of this invention. Figure 1 As shown, prepare all error-free original images. Individual, constitutive features Then inject all of them into each error-free image. The random errors are multiplied element by element, the first one... The first image Random error is denoted as Generate a defocused image, including Each out-of-focus scene Error images, totaling A set of error images is generated. These images are then fed into a model for training, which includes Mamba and CNN, and outputs the prediction error. An Empirical Risk Minimization (ERM) loss is constructed by combining the random error and the prediction error. This involves directly comparing the model's estimated error value with the original generated error value and feeding this comparison back into the model for constraint. The prediction error is combined with Invariant Risk Minimization (IRM) to... Learn relevant features of each scenario and leverage environmental risks. The expression is used to obtain invariant features, and the IRM Loss is calculated and returned to the model for constraint. This method enables the model to learn the differences between different scenes. The prediction error is multiplied element-wise with the defocused image to obtain the focused image. The image entropy is calculated on the focused image and returned to the model for constraint. The loss values ​​generated by these three parts are used to correct the model through gradient optimization.

[0036] Embodiment 1 of this invention covers various typical SAR imaging scenarios, and after segmentation processing, a total of 9416 original images are obtained, all with a uniform size. Pixels. Includes C, L, P, S, and X bands, with spatial resolution ranging from 0.1m to 8m, encompassing fully polarimetric data. The imaging platform includes both airborne and spaceborne systems. To verify the model's cross-band, cross-polarimetric, and cross-platform performance, the dataset is shown in Table 1: Table 1 Experimental Dataset ; Given the randomness of phase errors, a single test result cannot fully reflect the robustness of the algorithm. Therefore, a Monte Carlo simulation evaluation method is used in the testing, and each image in the test set is tested independently. Second-rate( Random error injection is used, and the error coefficients are resampled randomly for each injection. The final evaluation metric is taken from this. The average value of several independent trials. This evaluation protocol not only assesses the average performance of the algorithm, but also effectively eliminates random fluctuations under specific error parameters, thus more objectively verifying the stability of the proposed method under different phase error distributions.

[0037] To comprehensively and quantitatively evaluate algorithm performance, this embodiment employs four image evaluation metrics. Image entropy and contrast are no-reference metrics used to measure the focus quality of SAR images; peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) are full-reference metrics used to evaluate the fidelity of the reconstructed image relative to the ground truth. Based on the minimum entropy criterion, image entropy characterizes the sparsity of energy; a lower entropy value indicates better focus. Contrast quantifies the statistical difference between the target and the background; a higher value indicates clearer texture. Image intensity is defined as... The normalized power distribution is The two are defined as follows: ; ; In the formula, Image entropy, For contrast, Standard deviation, The mean; In the full-reference evaluation, PSNR measures pixel-level reconstruction accuracy based on mean squared error (MSE), while SSIM measures perceptual similarity based on three dimensions: brightness, contrast, and structure. and Let the ground truth and the reconstructed image be represented, respectively, and their definitions be: ; ; In the formula, For reference image, Mean square error, Peak signal-to-noise ratio; To evaluate the image, For reference image, The mean, For variance, , It is the stability constant. For structural similarity.

[0038] During the training phase, all C-band data were removed from the training set to verify whether the model, when exposed to samples from other bands, learned the inherent physical laws of phase error rather than the overfitting characteristics of specific bands. Several mainstream autofocusing algorithms were selected for comparative experiments. Among traditional autofocusing algorithms, the PGA-LUMV (Phase Gradient Autofocusing-Minimum Unbiased Variance) method was chosen as the comparison method. Among deep learning-based autofocusing algorithms, RestormerCNN (Restormer Convolutional Neural Network), FocusNet (Focusing Network), ECELM (Extreme Learning Machine), AFNet (Autofocusing Network), and PAFNet (Phase Autofocusing Network) were selected as comparison methods. The experimental results of each model under cross-band distribution migration are shown in Table 2. Table 2 Experimental results of various models under cross-band distributed migration. ; The results are shown in Table 2. In non-cross-band experiments, all algorithms effectively improved defocus. However, DPMCnet (the basic model of this invention without the invariant risk minimization constraint) and ID-DPMCnet (the model of this invention) outperformed other models in all metrics. This is attributed to the time-frequency hybrid feature extraction architecture adopted by DPMCnet, whose powerful representation capabilities can more accurately decouple complex phase contamination and achieve higher-dimensional phase feature representation in the feature space. Meanwhile, in cross-band experiments, all models showed performance degradation when facing domain offset. Among them, ID-DPMCnet led the comparison algorithms by an absolute advantage in all metrics, and its performance degradation in OOD scenarios was minimal. This is because the introduction of IRM allows the model to discard spurious correlation textures that only exist in specific band datasets and instead capture causal phase features that still hold true in cross-domain environments. This consistent modeling of the physical mechanism enables the model to learn causally, allowing it to achieve robust phase compensation even when faced with unseen band interference. C in Train indicates whether complex numbers were used during the training process, Defocus is the defocused image, and Original is the original image.

[0039] Figures 2 to 7The diagram shows the error curves estimated by all the learned autofocus algorithms. It can be seen that the proposed method has higher accuracy than other models in non-cross-domain experiments. However, in cross-domain experiments, other models exhibited varying degrees of estimation errors, while the proposed method maintained stable performance. These experimental results demonstrate the advantages of DPMCnet in phase error feature extraction and representation, and illustrate that existing methods often overfit the distribution characteristics of specific bands in the training domain data, leading to performance degradation when facing unknown band data. The proposed method successfully learns the invariant characteristics of azimuth error across different bands, thus exhibiting strong robustness and effectiveness in complex cross-domain scenarios. In the diagram, Ground Truth represents the true value, and RCM represents range migration correction.

[0040] In Embodiment 2 of this invention, the model is trained on an airborne SAR dataset and inference evaluation is performed on spaceborne SAR data with significantly different parameter distributions. The experimental results of each model under cross-band distribution migration are shown in Table 3. Table 3 Experimental results indicators for each model under cross-band distributed migration ; The results are shown in Table 3. The PGA algorithm only slightly improves the image entropy value, and even slightly decreases the structural restoration. The RestormerCNN model overfits to the specific statistical distribution of the training domain. When faced with unseen plateau parameters, its extracted features almost completely fail, instead introducing secondary distortion, leading to a severe degradation in image quality. FocusNet exhibits another ill-conditioned representation, with its entropy index even lower than the original undistorted image, but its image similarity and peak signal-to-noise ratio do not improve. In contrast, PAFnet, AFnet, and ECELM do not show ill-conditioned degradation. Among them, ID-DPMCnet significantly outperforms the other comparative models. The difference between DPMCnet and ID-DPMCnet indicates that IRM effectively improves the model's OOD capability.

[0041] Figure 8 and Figure 9The phase error estimation curves of various models in cross-platform scenarios are presented. From the two sets of experimental results, it is clear that the error curves estimated by some models deviate significantly from the true values, even showing the opposite trend. This edge estimation failure directly leads to residual phase blurring during imaging, explaining why these models perform poorly on quantitative metrics. While some models can fit the general trend, they exhibit severe oscillations or drifts at local details. ID-DPMCnet, however, maintains extremely high consistency with the true values ​​across the entire aperture range. Whether at the beginning of drastic phase error fluctuations or at the aperture edges, its estimation residuals remain at a low level, intuitively demonstrating ID-DPMCnet's powerful feature representation capabilities. Furthermore, there is a very significant performance difference between DPMCnet and ID-DPMCnet, indicating that the IRM strategy enables the model to learn causal invariant features that still hold true in OOD environments, greatly improving the model's robustness in OOD scenarios.

[0042] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A synthetic aperture radar self-focusing method based on invariable risk minimization, characterized in that, include: Acquire synthetic aperture radar images; A synthetic aperture radar autofocusing framework is constructed, including a random error generation module, a phase error prediction model, a self-supervised constraint module, and a refocusing imaging module; The random error generation module transforms the synthetic aperture radar image into the range-Doppler frequency domain via Fourier transform, injects random azimuth phase error into the frequency domain, and returns it to the image domain via inverse Fourier transform to obtain the defocused synthetic aperture radar image. The defocused synthetic aperture radar image is input into the phase error prediction model, which outputs the corresponding predicted azimuth phase error parameters. The overall objective function is calculated using the self-supervised constraint module, and the phase error prediction model is updated to complete the neural network training. The phase error prediction model includes a feature encoder and a predictor; the self-supervised constraint module includes invariant risk minimization constraint, image entropy loss and learning strategy, and the overall objective function is constructed based on the invariant risk minimization constraint, image entropy loss and learning strategy. The refocusing imaging module transforms the defocused synthetic aperture radar image into the range-Doppler frequency domain via Fourier transform, compensates for the corresponding predicted azimuth phase error parameters in the frequency domain, and returns it to the image domain via inverse Fourier transform to obtain the refocused synthetic aperture radar image.

2. The SAR self-focusing method based on invariable risk minimization according to claim 1, characterized in that, A time-frequency alternating Mamba-CNN model is constructed as the feature encoder for the phase error prediction model, including a time-domain branch, a frequency-domain branch, and a time-frequency interaction module; The time domain branch adopts CNN, and an input is a synthetic aperture radar image , , is a complex domain, and first, real and imaginary parts are separated: ； wherein is a real part plot, is an imaginary part plot, is an imaginary sign, is a height, is a width; Will and input independent convolutional blocks for feature extraction, respectively, to obtain real part features and imaginary part features , , the channel dimension fusion is performed on and to obtain time domain complex number features : ； In the formula, It is the field of real numbers.

3. The synthetic aperture radar autofocusing method based on invariant risk minimization according to claim 2, characterized in that, The frequency domain branch uses Mamba, and the input frequency domain plot is... , , for Obtained through two-dimensional fast Fourier transform, for Perform amplitude and phase decomposition: ； In the formula, This is an amplitude graph. , For phase diagram, ; Will and Inputting separate Mamba blocks yields amplitude characteristics. and phase characteristics , ,right and By performing complex combinations, frequency domain features are obtained. : 。 4. The synthetic aperture radar autofocusing method based on invariant risk minimization according to claim 3, characterized in that, Will and Input to the time-frequency interaction module to extract intermediate features in the time domain. and intermediate features in the frequency domain : ； ； In the formula, For convolutional blocks, For Mamba blocks; right Perform FFT to obtain forward transformation features , ;Will , and The enhanced frequency domain features are obtained by averaging the amplitude and phase values ​​respectively. , ;right Perform IFFT to obtain the inverse transformation features. , ,Will , and The features are concatenated and fused along the channel dimension, and then further enhanced by convolutional blocks to obtain enhanced temporal features. , , Number of channels; Will and The predictor is input and outputs the corresponding predicted azimuth phase error parameters; the predictor is a linear projection layer.

5. A synthetic aperture radar autofocusing method based on invariant risk minimization according to claim 4, characterized in that, By introducing an invariant risk minimization constraint, each synthetic aperture radar image is treated as an independent environment. Multiple environments combined The model prediction function is Minimize loss due to invariant risk for: ； In the formula, For the environment Experience risks in These are the invariant constraint weights.

6. A synthetic aperture radar autofocusing method based on invariant risk minimization according to claim 5, characterized in that, Introducing image entropy constraints : ； In the formula, The normalized grayscale histogram probability of the compensated amplitude image.

7. A synthetic aperture radar autofocusing method based on invariant risk minimization according to claim 6, characterized in that, Learning strategies include introducing balance constraints. : ； ； In the formula, The weight truncation threshold prevents excessive entropy loss due to excessive weights. It is a tiny constant used to prevent division by zero errors. For the number of training rounds, For dynamic scaling factor, This serves as the lower bound for the scaling factor. and They are respectively The growth rate and curvature control parameters.

8. A synthetic aperture radar autofocusing method based on invariant risk minimization according to claim 7, characterized in that, based on , and Construct the overall objective function : 。

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