A SAR image self-focusing method and system based on error coefficient optimization

Abstract

This invention discloses a SAR image autofocusing method and system based on error coefficient optimization. The method includes training a feature extraction module using defocused SAR image samples to establish a mapping relationship between the defocused SAR image and polynomial error coefficients. For the defocused SAR image to be processed, the trained feature extraction module is used to obtain polynomial error coefficients. The polynomial of the phase error vector is converted into an error matrix. The defocused SAR image is then subjected to a fast Fourier transform in the azimuth direction and multiplied with the error matrix. The result of this multiplication is then subjected to an inverse fast Fourier transform in the azimuth direction to obtain the focused SAR image. This invention aims to achieve a SAR autofocusing method with less manual intervention, higher computational efficiency, and better interpretability, thereby improving the quality and effect of SAR image autofocusing.

Description

Technical Field

[0001] This invention belongs to the field of remote sensing high-resolution imaging technology, specifically relating to a SAR image autofocusing method and system based on error coefficient optimization. Background Technology

[0002] SAR images are acquired using Synthetic Aperture Radar (SAR) technology. Unlike optical imaging, SAR imaging is essentially the result of SAR echo signal accumulation in the azimuth direction. It can utilize the movement of the radar platform to increase the effective observation aperture, thereby achieving a higher resolution in the azimuth direction than the physical antenna size. This synthetic aperture radar technology accumulates data from multiple observations by transmitting and receiving electromagnetic waves at different locations, and then compresses the data in the azimuth direction to form a high-resolution image. Figure 1 As shown, during the actual movement of the carrier aircraft, the actual trajectory deviates from the ideal trajectory due to airflow disturbances and irregular platform motion. This leads to phase errors during azimuth compression in SAR imaging, affecting SAR image quality and causing blurring. Eliminating motion errors generated during carrier aircraft movement is crucial for obtaining high-quality SAR images. Currently, SAR image motion compensation methods mainly include coarse compensation methods based on motion data and image autofocus methods based on echo data. Motion data-based compensation methods rely heavily on the measurement accuracy of the Inertial Navigation System (INS) and Global Positioning System (GPS), and can only compensate for larger motion errors. To obtain high-quality SAR images, it is necessary to estimate Doppler parameters from echo data and perform error compensation to achieve precise focusing of the SAR image.

[0003] like Figure 2As shown, SAR image autofocus methods can be divided into model-driven methods and data-driven methods. Model-driven SAR image autofocus methods can be further divided into phase-based and amplitude-based estimation methods. Phase-based estimation methods include the Phase Gradient Alignment (PGA) method and the Phase Difference Alignment (PDA) method. The performance of these methods is affected by the window size, they have weak compensation capabilities for high-frequency phase errors, and require strong scattering points in the image. Amplitude-based estimation methods mainly include two categories: View Displacement Alignment (MDA) and Metric-based optimization. The upper limit of the error order of sub-view-based SAR autofocus methods is limited by the size of the sub-aperture, and the estimation of phase errors is not accurate enough. Metric-based optimization methods are based on the classical image minimum entropy and maximum contrast theory, which can effectively compensate for phase errors of arbitrary frequencies. However, the optimization process requires repeated iterative calculations, which is time-consuming. Furthermore, the model parameter settings vary for SAR images with different degrees of defocusing, requiring significant manual intervention. In addition, the algorithm model does not consider environmental interference factors that may occur in real-world scenarios, resulting in poor application performance.

[0004] In recent years, with the rapid development of big data theory and computing power, data-driven technologies, represented by deep learning, have gradually emerged. This type of technology does not overly rely on prior theories, but rather on optimization techniques such as gradient backpropagation, relying on training models from large amounts of data. Its application scope is wider, and the models obtained through optimization with computing power support have stronger performance. Deep neural networks, through nested neural layers (or matrix-operation-based convolutional layers for images) and nonlinear activation functions, can establish a mapping model from input images to optimization metrics. By setting appropriate loss functions and training the model, adaptive learning of algorithm parameters can be achieved, thus avoiding the tedious steps of setting prior parameters and iterative trial and error in traditional algorithms. For example, Mason et al. proposed a synthetic aperture radar autofocusing imaging method based on recurrent neural networks, applying deep learning technology to the SAR imaging field for the first time. Wei Pu proposed a sparse autoencoder network (SAE-Net), where the encoder is designed for SAR imaging using the ADMM algorithm, while the decoder is used for reconstructing the mapping from imaging results to SAR echoes. Reconstruction loss and entropy loss guide the network training to generate focused SAR images. Liu Zhi proposed a non-iterative autofocus method based on deep learning and the minimum entropy criterion. Entropy is used as a loss function to guide the network in automatically learning autofocus rules, thereby achieving automatic focusing of SAR images. However, most current deep learning-based SAR autofocus methods directly establish a mapping relationship between the input image and the focused image, and then train the network to achieve the focusing effect. These methods cannot explain the cause of defocusing in SAR images, lack interpretability, and cannot calculate the specific phase error. Summary of the Invention

[0005] The technical problem to be solved by this invention is to provide a SAR image autofocusing method and system based on error coefficient optimization, which addresses the above-mentioned problems in the prior art. This invention aims to realize a SAR autofocusing method with less manual intervention, higher computational efficiency, and better interpretability, thereby improving the quality and effect of SAR image autofocusing.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0007] A SAR image autofocusing method based on error coefficient optimization includes the following steps:

[0008] S1, using defocused SAR image samples, train a feature extraction module to establish the defocused SAR image and polynomial error coefficients. ~ The mapping relationship between them, and the polynomial error coefficients ~ Phase error vector of defocused SAR image The polynomial is: ,in For order, This is the azimuth frequency vector;

[0009] S2, for the defocused SAR image to be processed Defocused SAR images The polynomial error coefficients are obtained after the trained feature extraction module. ~ The polynomial error coefficients ~ Using the phase error vector The polynomial is converted into an error matrix. Defocused SAR images After azimuth direction Fast Fourier Transform After and error matrix Multiply, and then perform an inverse fast Fourier transform in the azimuth direction on the result. Obtain focused SAR image .

[0010] Optionally, in step S2, the polynomial error coefficients are... ~ Convert to error matrix The function expression is:

[0011] ,

[0012] In the above formula, For diagonalization operation, The imaginary unit, Let be the phase error vector, and let be the phase error vector at this time. Polynomial error coefficients ~ and defocused SAR images azimuth frequency vector Using phase error vector The polynomial calculation is obtained.

[0013] Optionally, the polynomial error coefficients in step S1 ~ The feature extraction module trained in step S1 consists of two parts: low-order error coefficients and high-order error coefficients. It includes parallel global feature branches and local feature branches. The global feature branches extract global features of the defocused SAR image and map them to low-order error coefficients in the polynomial error coefficients. The local feature branches extract local features of the defocused SAR image and map them to high-order error coefficients in the polynomial error coefficients.

[0014] Optionally, the step of extracting global features from the defocused SAR image through a global feature branch and mapping them to low-order error coefficients in a polynomial error coefficient includes: inputting the defocused SAR image into a Restormer network to extract global features. f b global features f b Features f b The low-order error coefficients in the polynomial error coefficients are obtained by sequentially passing through a global pooling layer, a flattening layer, a random dropout layer, and a fully connected layer. The flattening layer consists of a fully connected layer and a LeakyReLU activation layer.

[0015] Optionally, the step of extracting local features of the defocused SAR image through local feature branches and mapping them to higher-order error coefficients in the polynomial error coefficients includes: inputting the defocused SAR image into a CNN network to extract local features. f a , local features f a After resizing, the polynomial error coefficients are obtained by passing the polynomial error coefficients through a global pooling layer, a flattening layer, a random dropout layer, and a fully connected layer. The flattening layer consists of a fully connected layer and a LeakyReLU activation layer.

[0016] Optionally, in step S1, a feature extraction module is trained using defocused SAR image samples to establish the defocused SAR image and polynomial error coefficients. ~ When determining the mapping relationship between them, this includes training the feature extraction module using the training dataset and updating the network parameters of the feature extraction module using a preset loss function, wherein the function expression of the preset loss function is:

[0017] ,

[0018] In the above formula, For loss function, and These represent the azimuth and range dimensions of the defocused SAR image, respectively. SAR amplitude image The element in the i-th row and j-th column, The power of the SAR echo signal. .

[0019] Optionally, when training the feature extraction module using the training dataset and updating the network parameters of the feature extraction module using a preset loss function, the optimizer used is the AdamW optimizer, and the function expression for updating the network parameters of the feature extraction module using the AdamW optimizer and the preset loss function is:

[0020] ,

[0021] ,

[0022] ,

[0023] In the above formula, and Let be the momentum at the t-th and t-1-th iterations, respectively. and These are the exponential decay rate of the gradient and the exponential decay rate of the squared gradient, respectively. Let be the gradient of the loss function at the t-th iteration. and The variances at the t-th and t-1-th iterations are respectively. Represents element-wise multiplication. and These are the network parameters of the feature extraction module RCM at iterations t+1 and t, respectively. For learning rate, This is a numerical stability term used to prevent the denominator from being zero. This is the weight decay term.

[0024] Furthermore, the present invention also provides a SAR image autofocusing system based on error coefficient optimization, comprising a microprocessor and a memory interconnected thereto, wherein the microprocessor is programmed or configured to execute the SAR image autofocusing method based on error coefficient optimization.

[0025] Furthermore, the present invention also provides a computer-readable storage medium storing a computer program or instructions that are programmed or configured to execute the error coefficient-optimized SAR image autofocusing method by a processor.

[0026] Furthermore, the present invention also provides a computer program product, including a computer program or instructions that are programmed or configured to execute the error coefficient-optimized SAR image autofocusing method via a processor.

[0027] Compared with existing technologies, the present invention has the following main advantages: The method of the present invention includes training a feature extraction module using defocused SAR image samples to establish a mapping relationship between the defocused SAR image and the polynomial error coefficients; for the defocused SAR image to be processed... Defocused SAR images The trained feature extraction module obtains polynomial error coefficients, which are then converted into an error matrix using the polynomial of the phase error vector. Defocused SAR images After azimuth direction Fast Fourier Transform After and error matrix Multiply, and then perform an inverse fast Fourier transform in the azimuth direction on the result. Obtain focused SAR image This invention realizes a SAR autofocusing method with less manual intervention, higher computational efficiency, and better interpretability, which can improve the quality and effect of SAR image autofocusing. Attached Figure Description

[0028] Figure 1 This is a schematic diagram of an existing airborne SAR imaging model.

[0029] Figure 2 Classify existing SAR image autofocusing methods.

[0030] Figure 3 This is a schematic diagram of the basic process of the method in an embodiment of the present invention.

[0031] Figure 4 This is a schematic diagram illustrating the principle of the method in an embodiment of the present invention.

[0032] Figure 5 This is a schematic diagram of the network structure of the feature extraction module in an embodiment of the present invention.

[0033] Figure 6 These are three original SAR defocused images selected in this embodiment of the invention.

[0034] Figure 7 This is a comparison of SAR focused images obtained by different methods in the embodiments of the present invention.

[0035] Figure 8 This is a comparison chart of qualitative index results from the ablation experiment in this embodiment of the invention. Detailed Implementation

[0036] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0037] like Figure 3 and Figure 4 As shown, the SAR image autofocusing method based on error coefficient optimization in this embodiment includes the following steps:

[0038] S1, using defocused SAR image samples, train a feature extraction module to establish the defocused SAR image and polynomial error coefficients. ~ The mapping relationship between them, and the polynomial error coefficients ~ Phase error vector of defocused SAR image The polynomial is: ,in For order, This is the azimuth frequency vector;

[0039] S2, for the defocused SAR image to be processed Defocused SAR images The polynomial error coefficients are obtained after the trained feature extraction module. ~ The polynomial error coefficients ~ Using the phase error vector The polynomial is converted into an error matrix. Defocused SAR images After azimuth direction Fast Fourier Transform After and error matrix Multiply, and then perform an inverse fast Fourier transform in the azimuth direction on the result. Obtain focused SAR image .

[0040] SAR image autofocusing methods based on MEA (Minimum Entropy Autofocus) estimate the azimuth phase error during SAR imaging through iterative optimization and compensate for it in the original image. The range phase error is generally small and negligible. Therefore, the estimation and compensation of the azimuth phase error is typically performed in the range-Doppler domain. For ease of study, let... Let be the complex matrix of the SAR defocused image in the range-Doppler domain. Then, the problem of azimuth phase error compensation for this image can be defined as follows:

[0041] ,

[0042] In the above formula, For the compensated SAR image The pixels at positions 'a' in the azimuth direction and 'r' in the range direction are represented in the SAR image, where 'a' and 'r' represent the indices in the azimuth and range directions, respectively. and Representing SAR images The number of points in the azimuth and distance directions, yes The corresponding phase error vector, SAR image Orientation in and distance The pixel of the position, The imaginary unit is used; the defocused SAR image is used. After azimuth direction Fast Fourier Transform After and error matrix Multiply, and then perform an inverse fast Fourier transform in the azimuth direction on the result. Obtain focused SAR image It can be represented as:

[0043] ,

[0044] In the above formula, It is composed of the phase error vector The transformed matrix for Diagonalization operation, and These are the azimuth-directed Fast Fourier Transform (FFT) and the inverse azimuth-directed FFT, respectively. From the above equation, it can be seen that for any input defocused SAR image... X If the corresponding phase error matrix can be calculated in this embodiment... This allows for compensation. Traditional MEA methods compensate for the phase error vector. Modeling can be performed based on actual physical factors. The error is modeled as a polynomial error or a sinusoidal error. In this embodiment, a polynomial error is used as an example, and its phase error vector can be modeled as follows:

[0045] ,

[0046] In the above formula, For the error vector coefficients, For order, The azimuth frequency vector is typically normalized to the range [-0.5, 0.5] or [-1, 1]. The constant and first-order terms are omitted in the polynomial above, primarily because the constant term does not affect the image entropy, while the first-order term only affects the Doppler center frequency, causing an azimuth shift in the image, but not affecting the image focus quality. In this embodiment, a seventh-order polynomial error is used as an example, and its expression is as follows:

[0047] .

[0048] In step S2 of this embodiment, the polynomial error coefficients are... ~ Convert to error matrix The function expression is:

[0049] ,

[0050] In the above formula, For diagonalization operation, The imaginary unit, Let be the phase error vector, and let be the phase error vector at this time. Polynomial error coefficients ~ and defocused SAR images azimuth frequency vector Using phase error vector The polynomial calculation is obtained.

[0051] The polynomial error coefficient in step S1 of this embodiment ~ The method consists of two parts: low-order error coefficients and high-order error coefficients, which can be specifically divided as needed. The feature extraction module trained in step S1 includes parallel global feature branches and local feature branches. The global feature branch extracts global features of the defocused SAR image and maps them to low-order error coefficients in the polynomial error coefficients. The local feature branch extracts local features of the defocused SAR image and maps them to high-order error coefficients in the polynomial error coefficients. Traditional metric-based SAR image autofocus methods continuously optimize SAR images by establishing a relationship between phase error and SAR image metrics to achieve autofocus. This method is relatively inefficient and somewhat blind. On the one hand, the network does not establish a relationship between the image itself and the metric values, resulting in significant blindness in network training; on the other hand, directly using phase error as the parameter to be optimized leads to a complex function mapping relationship and slow model convergence. Based on the shortcomings of traditional methods, this embodiment proposes a new SAR image autofocus method. This method starts from the image itself and predicts phase error by predicting error coefficients. Furthermore, this embodiment divides the error coefficients into high-order and low-order coefficients, making this method more favorable for model prediction of SAR image phase error. like Figure 4 This is an end-to-end network that starts from the original SAR image and generates the final focused SAR image. The network can be divided into three parts: feature extraction, parameter estimation, and autofocus compensation.

[0052] Based on the previously established seventh-order polynomial phase error expression, this embodiment also needs to predict the unknown error coefficients to obtain a set of coefficient values ​​that optimize the output image performance. In this embodiment, the phase error of the SAR image can be divided into low-order phase error and high-order phase error, which respectively affect the main lobe and side lobes of the SAR echo signal. This embodiment makes the following assumptions: low-order phase error mainly affects the basic shape and structure of the SAR image, causing large-scale blurring; while high-order phase error affects the details and texture of the image, leading to blurring or distortion of details. Based on this assumption, this embodiment considers the 2nd, 3rd, and 4th order polynomial errors in the proposed method as low-order phase errors, and the 5th, 6th, and 7th order polynomial errors as high-order phase errors. To obtain the predicted values ​​of the low-order and high-order phase error coefficients, this embodiment first extracts the global and local features of a SAR image, and then maps the extracted features to low-order and high-order error coefficients, respectively. Deep learning networks based on CNN and Transformer have significant advantages in extracting local and global features of SAR images. In this embodiment, the Transformer variant Restormer is used as the global feature extraction method. This is mainly because the Transformer requires calculating the relationship between each location of the self-attention layer and other locations during feature extraction, resulting in high computational cost and slow processing speed for high-resolution SAR images. Unlike the traditional Transformer, Restormer adopts multi-head attention and a feedforward network, replacing the traditional cross-spatial dimension self-attention layer in the Transformer with a cross-channel self-attention mechanism, thereby greatly reducing the computational complexity of the model.

[0053] like Figure 5 As shown, in this embodiment, extracting global features from the defocused SAR image through a global feature branch and mapping them to low-order error coefficients in a polynomial error coefficient includes: inputting the defocused SAR image into the Restormer network to extract global features. f b global features f b Features f bThe low-order error coefficients in the multinomial error coefficients are obtained by sequentially passing through a global pooling layer, a flattening layer, a random dropout layer, and a fully connected layer. The flattening layer consists of a fully connected layer and a LeakyReLU activation layer. The Restormer network is an existing network that combines the features of CNN and Transformer. It mainly includes an embedding layer, a Transformer encoder, an attention module, an upsampling layer, and activation function layers, and its output is the same size as the input. In order to maintain consistency with the output feature size of CNN feature extraction networks, this embodiment compresses the features extracted by the Restormer network in the distance direction, making its channel number 8 times the original, and then passes through a GAP layer, so that the output result size is also N×16×1×256.

[0054] like Figure 5 As shown, in this embodiment, extracting local features of the defocused SAR image through a local feature branch and mapping them to higher-order error coefficients in the polynomial error coefficients includes: inputting the defocused SAR image into a CNN network to extract local features. f a , local features f a After resizing, the polynomial error coefficients are obtained by sequentially passing the data through a global pooling layer, a flattening layer, a random dropout layer, and a fully connected layer. The flattening layer consists of a fully connected layer and a LeakyReLU activation layer. In this embodiment, let... The input samples are defocused SAR images, where N is the number of SAR image samples and the number of channels is 2. n a and n r These represent the dimensions of the SAR image in the azimuth and range directions, respectively, in this embodiment. n a and n r All values ​​are set to 256. For the CNN feature extraction network, its network structure mainly consists of an input layer, a convolutional layer, an instance normalization (IN) layer, a LeakyReLU activation layer, and a global average pooling (GAP) layer. The details of its network configuration and the output size of each layer are shown in Table 1.

[0055] Table 1 Input / Output Configuration Table for CNN Feature Extraction Network Layers

[0056]

[0057] After feature extraction from the defocused SAR image using a CNN and a Restormer network, a feature set of uniform scale is obtained. The extracted features then need to be converted into error coefficients. For the parameter estimation part, the network structure mainly consists of a flattening layer, a dropout layer, and a fully connected (FC) layer. The flattening layer is mainly used to flatten the result obtained from the global average pooling layer into a column vector, forming a 16×256 dimensional output. The dropout layer (p=0.5) is a regularization method, representing the random dropping of neurons with a probability of 0.5 to prevent overfitting during network training. Finally, a (16×256)×3 fully connected (FC) layer is passed, resulting in an N×3 column vector (N being the number of samples). The two N×3 vectors obtained from the parameter estimation of the features extracted by the CNN and Restormer networks can be represented as higher-order and lower-order error coefficients, respectively. The specific network layer configuration is shown in Table 2.

[0058] Table 2 Input / Output Configuration Table for Parameter Estimation Network Layer

[0059]

[0060] For any defocused SAR image of size 256×256 with 2 channels, such as Figure 5 The diagram shows the polynomial coefficient estimates obtained after feature extraction and parameter estimation.

[0061] After passing a feature extraction and parameter estimation network through a defocused SAR complex image to obtain estimated polynomial error coefficients, the defocused SAR image needs to be further compensated using these coefficient estimates to obtain the result of a single compensation. The optimal network structure is then continuously optimized by setting a loss function. Global and local features extracted from the Restormer branch and CNN branch, respectively, are processed by the network and mapped to lower-order terms of the polynomial error coefficients. ) and higher-order terms ( The phase error vector of the SAR image and the SAR image after autofocus compensation can be calculated separately. In step S1 of this embodiment, a feature extraction module is trained using defocused SAR image samples to establish the defocused SAR image and polynomial error coefficients. ~ When determining the mapping relationship between them, this includes training the feature extraction module using the training dataset and updating the network parameters of the feature extraction module using a preset loss function, wherein the function expression of the preset loss function is:

[0062] ,

[0063] In the above formula, For loss function, and These represent the azimuth and range dimensions of the defocused SAR image, respectively. SAR amplitude image The element in the i-th row and j-th column, The power of the SAR echo signal. .

[0064] Based on the calculated loss function, the polynomial error coefficients are adjusted and updated by the optimizer to finally obtain the optimal solution for the phase error vector. Commonly used optimizers for parameter optimization include the SGD optimizer, LBFGS optimizer, and Adam optimizer. The AdamW optimizer used in this embodiment adds a weight decay term to the Adam optimizer to better improve the model's generalization ability. Specifically, in this embodiment, when training the feature extraction module using the training dataset and updating the network parameters of the feature extraction module using a preset loss function, the optimizer used is the AdamW optimizer. The function expression for updating the network parameters of the feature extraction module using the preset loss function with the AdamW optimizer is as follows:

[0065] ,

[0066] ,

[0067] ,

[0068] In the above formula, and Let be the momentum at the t-th and t-1-th iterations, respectively. and These are the exponential decay rate of the gradient and the exponential decay rate of the squared gradient, respectively (usually set to 0.9 and 0.999). Let be the gradient of the loss function at the t-th iteration. and The variances at the t-th and t-1-th iterations are respectively. Represents element-wise multiplication. and These are the network parameters of the feature extraction module RCM at iterations t+1 and t, respectively. For learning rate, A numerical stability term used to prevent the denominator from being zero (usually set to 10). -8 ), Weight decay term (can be set to 10) -3 ).

[0069] To verify the SAR image autofocusing method based on error coefficient optimization in this embodiment, the data used in the experiment came from the Advanced Land Observing Satellite (ALOS) developed by the Earth Observation Research Center of a certain aerospace exploration bureau. This satellite is equipped with a phased array L-band synthetic aperture radar (PALSAR). PALSAR has three operating modes: high-resolution mode, scanning mode, and multi-polarization mode. In this embodiment, we used SAR images acquired in high-resolution mode, which has high resolution and high signal-to-noise ratio in the range direction, with a resolution better than 2m; in the azimuth direction, the azimuth resolution of SAR images in this mode is about 5m, and the ground resolution is about 7m. For ease of processing, we randomly cropped the original full-size SAR images, reducing them to 256×256 pixels, totaling 11,000 images. In this experiment, we allocated the training set to the test set at a ratio of 10:1. The relevant parameters of ALOS PALSAR are shown in Table 3.

[0070] Table 3 Parameters in ALOS PALSAR high-resolution mode

[0071]

[0072] For spaceborne SAR, phase errors are caused by many factors, such as orbital deviation, altitude changes, atmospheric effects, and parameter setting errors during the imaging process. These errors can all degrade image quality, causing SAR images to become defocused. This process can be modeled as the result of convolving the undefocused image with a blur filter. For the training and test sets in this embodiment, we simulate this process by randomly generating polynomial errors in the range Doppler domain for the undefocused image, thereby obtaining defocused SAR images. This is a common practice in the field of SAR imaging.

[0073] To verify whether the method proposed in this embodiment is effective for autofocusing of SAR images, this experiment proposes to use entropy and contrast as evaluation indicators of the experimental results. These indicators are briefly introduced below.

[0074] a. Entropy. In SAR autofocus imaging, image entropy can be used to measure the focusing quality of a SAR image. A smaller entropy value indicates a clearer and higher-quality SAR image after focusing. Its definition is as follows:

[0075] ,

[0076] In the above formula, Let be the image entropy, and the other parameters are the same as those of the loss function L.

[0077] b. Contrast Ratio. Similar to entropy, contrast ratio is also an indicator of SAR image sharpness. A higher contrast ratio indicates a sharper SAR image after focusing, and better image quality. There is no unified definition of contrast ratio; common definitions include the ratio of the mean square error of target energy to the mean target energy, and the ratio of the mean target energy to the square of the mean target amplitude. In this embodiment, we use the former definition, which is expressed as follows:

[0078] ,

[0079] In the above formula, For contrast, The amplitude representation of the input SAR defocused image X. This indicates the calculation of mathematical expectation.

[0080] In this embodiment, all method implementations were trained and tested on a high-performance workstation equipped with an Nvidia Tesla A100 GPU (80 GB RAM) and an AMD Ryzen Threadripper PRO 5995WX 64-core CPU. The deep learning framework used was PyTorch, with CUDA version 11.7. In the experiments, both the training and test sets were image data cropped to 256×256 pixels. The number of training epochs was set to 100, and the batch size was set to 8. The initial learning rate was set to 10. -3 The number of rounds is reduced by 50% every 20 rounds.

[0081] To verify the effectiveness of the proposed method in this embodiment, the autofocusing results obtained by the proposed method are compared with those obtained by the traditional MEA algorithm and the autofocusing method based on Bagging-ECELMs. Currently, research on deep learning-based SAR autofocusing methods is still relatively limited. The Bagging-ECELMs-based autofocusing method exhibits good autofocusing performance and is highly comparable. The following comparison will focus on both qualitative and quantitative indicators.

[0082] 1) Qualitative indicator results.

[0083] For ease of demonstration, the experiment selected three images from different scenarios in the test set as representative examples. For instance... Figure 6 The image shows three original SAR defocused images from the test set. As can be seen, there are some strong scattering points in the images, and the defocusing is more pronounced at these points. Some details, textures, and contours become blurred, severely affecting the overall imaging performance of the SAR image. The purpose of SAR image autofocusing methods is to eliminate defocusing in the image by compressing the SAR echo signal in the azimuth direction, thus making the image clearer.

[0084] like Figure 7 The figures show the comparison results of three original SAR defocused images from the test set, obtained through the MEA algorithm, the Bagging-ECELMs algorithm, and the method of this embodiment. It is clear from the figures that areas with higher scattering intensity are more prone to defocusing, and the degree of defocusing is more severe. The red boxes in the figures highlight some contours or textures in each image, while the yellow circles show the imaging information of strong scattering points. In the first row and third column, the strong scattering points are elongated in the azimuth direction due to severe defocusing; the yellow boxes are magnified views of the strong scattering point areas within the yellow circles. The comparison results show that the SAR images obtained by the three autofocusing methods are clearer and have improved resolution compared to the original SAR defocused images. Looking more closely, in the areas marked with red boxes in scenes 1 and 2, the SAR images obtained by the method of this embodiment have more distinct contours and clearer textures; while in scene 3, the magnified view marked with yellow boxes shows that the strong scattering points in the SAR image obtained by the method of this embodiment are more concentrated in the azimuth direction, resulting in better focusing. In summary, the method proposed in this embodiment can achieve autofocusing of SAR images, and compared with the traditional MEA method and the deep learning-based Bagging-ECELMs method, it has a better focusing effect on features such as elongated contours, textures, and strong scattering points.

[0085] To more objectively verify the effectiveness of the method in this embodiment, the experimental results were validated based on the entropy and contrast indices proposed above. Table 4 shows the quantitative index results of the original SAR defocused image, the SAR focused image obtained by the MEA method, the Bagging-ECELMs method, and the method in this embodiment in the test set. The bolded values ​​are the optimal values ​​for each index.

[0086] Table 4 Comparison of quantitative index results of SAR focused images obtained by different methods

[0087]

[0088] As shown in Table 4, the method in this embodiment performs best in both entropy and contrast metrics. The entropy index is reduced by 0.188 compared to the original image test set, while the contrast index is improved by 1.483. Experimental results demonstrate that the method in this embodiment can indeed improve the imaging quality of SAR images, and its autofocus performance is superior to both the MEA and Bagging-ECELMs methods.

[0089] To better verify the hypotheses proposed in this embodiment, an ablation experiment was conducted. The main purpose was to compare the method using the RCM module to predict both high-order and low-order error coefficients with the method using only a CNN network to predict error coefficients, to determine which method is more effective for SAR image autofocus. Regarding network settings, only the Restormer feature extraction network was replaced with a CNN feature extraction network, while other settings remained unchanged. Following the procedures in the comparative experiment, three SAR images from different scenes were selected from the test set for demonstration. The resulting SAR focused images are shown below. Figure 8 As shown in the figure, using only a CNN network to predict coefficients can achieve the effect of focusing SAR images. However, upon closer inspection, for the white texture and black outline within the red boxes in scenes 1 and 2, the SAR images obtained by our method have more obvious textures and clearer outlines; while for the local area of ​​the scattering point circled in yellow in scene 3, the focusing effect of both methods on strong scattering points is not significantly different, and both can achieve a good focusing effect. This also illustrates our hypothesis: low-order phase errors mainly affect the basic shape and structure of SAR images, causing large-scale blurring; while high-order phase errors affect the details and textures of the image, leading to detail blurring or distortion, which is reasonable.

[0090] In addition, from a quantitative perspective, Table 5 records a comparison of the quantitative indicators of SAR focused images obtained by using only the CNN network prediction error coefficient method and the SAR focused images obtained by the RCM module prediction error coefficient method proposed in this paper.

[0091] Table 5 Quantitative Indicators Results of Ablation Experiment

[0092]

[0093] As can be seen from 5, numerically, the method of this embodiment is optimal in terms of the two given indicators, contrast and entropy. Compared with the method using only CNN network, the entropy is 0.38 lower and the contrast is 0.435 higher, which further illustrates the effectiveness and rationality of the method of this embodiment.

[0094] In summary, this embodiment proposes a novel SAR image autofocusing method based on the traditional MEA SAR image autofocusing concept. This method starts with a feature extraction module designed from the SAR image itself to predict phase error coefficients. Leveraging the powerful feature extraction capabilities of neural networks such as CNN and Restormer, it extracts both detailed and global features of the SAR image. Secondly, this embodiment models the azimuth phase error as a polynomial phase error, dividing its coefficients into higher-order and lower-order error coefficients. The detailed and global features extracted from RCM are then mapped to the higher-order and lower-order error coefficients of the polynomial error, respectively. Next, the phase error of the input SAR image is calculated based on the predicted polynomial error coefficients, and the original SAR image is compensated. Finally, the network is continuously optimized and trained by an optimizer to output the optimal SAR image focusing result. In experimental verification, this embodiment's method is compared with traditional MEA methods and deep learning methods based on Bagging-ECELMs. Ablation experiments were also designed, and the experimental results demonstrate the effectiveness and advancement of this embodiment's method.

[0095] Furthermore, this embodiment also provides a SAR image autofocusing system based on error coefficient optimization, including a microprocessor and a memory interconnected, wherein the microprocessor is programmed or configured to execute the SAR image autofocusing method based on error coefficient optimization.

[0096] Furthermore, this embodiment also provides a computer-readable storage medium storing a computer program or instructions that are programmed or configured to execute the error coefficient-optimized SAR image autofocusing method by a processor.

[0097] Furthermore, this embodiment also provides a computer program product, including a computer program or instructions, which are programmed or configured to execute the error coefficient-optimized SAR image autofocusing method via a processor.

[0098] Those skilled in the art will understand that the technical solutions provided by the embodiments of this application may be in the form of a method, system, or computer program product. Therefore, this application may take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application may take the form of a computer program product embodied on one or more computer-readable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create an implementation for the process. Figure 1 One or more processes and / or boxes Figure 1 The computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable apparatus for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0099] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A SAR image autofocusing method based on error coefficient optimization, characterized in that, Includes the following steps: S1, using defocused SAR image samples, train a feature extraction module to establish the defocused SAR image and polynomial error coefficients. ~ The mapping relationship between them, and the polynomial error coefficients ~ Phase error vector of defocused SAR image The polynomial is: ,in For order, This is the azimuth frequency vector; S2, for the defocused SAR image to be processed Defocused SAR images The polynomial error coefficients are obtained after the trained feature extraction module. ~ The polynomial error coefficients ~ Using the phase error vector The polynomial is converted into an error matrix. Defocused SAR images After azimuth direction Fast Fourier Transform After and error matrix Multiply, and then perform an inverse fast Fourier transform in the azimuth direction on the result. Obtain focused SAR image ; Polynomial error coefficients in step S1 ~ It consists of two parts: low-order error coefficients and high-order error coefficients. The feature extraction module trained in step S1 includes parallel global feature branches and local feature branches. The global feature branches extract global features of the defocused SAR image and map them to low-order error coefficients in the polynomial error coefficients. The local feature branches extract local features of the defocused SAR image and map them to high-order error coefficients in the polynomial error coefficients. In step S1, a feature extraction module is trained using defocused SAR image samples to establish the defocused SAR image and polynomial error coefficients. ~ When determining the mapping relationship between them, this includes training the feature extraction module using the training dataset and updating the network parameters of the feature extraction module using a preset loss function, wherein the function expression of the preset loss function is: ， In the above formula, For loss function, and These represent the azimuth and range dimensions of the defocused SAR image, respectively. SAR amplitude image The element in the i-th row and j-th column, The power of the SAR echo signal. .

2. The SAR image autofocusing method based on error coefficient optimization according to claim 1, characterized in that, In step S2, the polynomial error coefficients are... ~ Convert to error matrix The function expression is: ， In the above formula, For diagonalization operation, The imaginary unit, Let be the phase error vector, and let be the phase error vector at this time. Polynomial error coefficients ~ and defocused SAR images azimuth frequency vector Using phase error vector The polynomial calculation is obtained.

3. The SAR image autofocusing method based on error coefficient optimization according to claim 1, characterized in that, The step of extracting global features from the defocused SAR image through a global feature branch and mapping them to low-order error coefficients in a polynomial error coefficient includes: inputting the defocused SAR image into the Restormer network to extract global features. f b global features f b Features f b The low-order error coefficients in the polynomial error coefficients are obtained by sequentially passing through a global pooling layer, a flattening layer, a random dropout layer, and a fully connected layer. The flattening layer consists of a fully connected layer and a LeakyReLU activation layer.

4. The SAR image autofocusing method based on error coefficient optimization according to claim 1, characterized in that, The step of extracting local features from the defocused SAR image through local feature branches and mapping them to higher-order error coefficients in the polynomial error coefficients includes: inputting the defocused SAR image into a CNN network to extract local features. f a , local features f a After resizing, the polynomial error coefficients are obtained by passing the polynomial error coefficients through a global pooling layer, a flattening layer, a random dropout layer, and a fully connected layer. The flattening layer consists of a fully connected layer and a LeakyReLU activation layer.

5. The SAR image autofocusing method based on error coefficient optimization according to claim 4, characterized in that, When training the feature extraction module using the training dataset and updating the network parameters of the feature extraction module using a preset loss function, the optimizer used is the AdamW optimizer, and the function expression for updating the network parameters of the feature extraction module using the AdamW optimizer and the preset loss function is as follows: ， ， ， In the above formula, and Let be the momentum at the t-th and t-1-th iterations, respectively. and These are the exponential decay rate of the gradient and the exponential decay rate of the squared gradient, respectively. Let be the gradient of the loss function at the t-th iteration. and The variances at the t-th and t-1-th iterations are respectively. Represents element-wise multiplication. and These are the network parameters of the feature extraction module RCM at iterations t+1 and t, respectively. For learning rate, This is a numerical stability term used to prevent the denominator from being zero. This is the weight decay term.

6. A SAR image autofocusing system based on error coefficient optimization, comprising a microprocessor and a memory interconnected, characterized in that, The microprocessor is programmed or configured to execute the SAR image autofocusing method based on error coefficient optimization as described in any one of claims 1 to 5.

7. A computer-readable storage medium storing a computer program or instructions, characterized in that, The computer program or instructions are programmed or configured to execute, via a processor, the SAR image autofocusing method based on error coefficient optimization as described in any one of claims 1 to 5.

8. A computer program product, comprising a computer program or instructions, characterized in that, The computer program or instructions are programmed or configured to execute, via a processor, the SAR image autofocusing method based on error coefficient optimization as described in any one of claims 1 to 5.

Images