SAR azimuth undersampling imaging method and system based on deep learning

Abstract

The invention discloses an SAR azimuth undersampling imaging method and system based on deep learning, and the method comprises the steps: obtaining an SAR data set which comprises fully-sampled SAR images and echo data corresponding to each SAR image, and enabling the SAR data set to serve as the input of a deep expansion network; the method comprises the following steps: acquiring an SAR Doppler center frequency, a frequency modulation rate, a carrier frequency and a satellite equivalent speed, and designing an imaging operator by using a chirp scaling algorithm in SAR imaging; constructing a deep expansion network based on a Unet architecture, and performing image restoration on the echo signal; the deep expansion network is trained, a model weight file with the minimum loss is stored, and parameters in the weight file comprise parameters in a convolutional layer and a nonlinear activation function in a denoising device, learnable parameters in conjugate gradient descent and parameters in an undersampling mode; and loading a pre-trained weight file, performing reasoning by using the expanded network model, obtaining a deblurring imaging result, and obtaining an optimized undersampling strategy. The azimuth ambiguity suppression effect realized by the method is good.

Description

Technical Field

[0001] The present invention belongs to the technical field of synthetic aperture radar (SAR) signal processing, and particularly relates to a method and system for SAR azimuth undersampling imaging based on deep learning. Background Art

[0002] For a traditional synthetic aperture radar (hereinafter referred to as SAR) system, restricted by the minimum antenna area constraint, high azimuth resolution and wide range swath cannot be achieved simultaneously: According to the Nyquist sampling theorem, a higher pulse-repetition frequency (hereinafter referred to as PRF) is a necessary condition for obtaining high azimuth resolution, while a wide range swath requires a lower PRF to ensure the reception time window of the echo signal. In an actual system, azimuth undersampling will cause Doppler spectrum ambiguity and introduce azimuth ambiguity in the image. To achieve wide swath imaging, a non-uniform undersampling (i.e., variable PRF) system is designed. For example, Staggered SAR sampling, random dither sampling, and Poisson-disk sampling can avoid repetitive artifacts to a certain extent, spread the ambiguity, suppress the intensity of false targets, and ensure image quality.

[0003] In some application scenarios, such as maritime ship target detection and recognition, the target has typical sparsity. According to the compressive sensing theory, if the observation matrix meets certain conditions, high-resolution reconstruction of the image can also be achieved in an azimuth undersampling system that does not satisfy the Nyquist theorem. Therefore, some compressive sensing algorithms are used for downsampled SAR imaging. For example, the Iterative Shrinkage Thresholding Algorithm (hereinafter referred to as ISTA) directly processes the downsampled raw data through threshold screening and iteration.

[0004] In the above-mentioned prior art, whether it is Staggered sampling, random dither sampling or Poisson-disk sampling, only some general sampling criteria are considered when generating the sampling point positions. For example, the minimum distance constraint is used to avoid sampling point aggregation, and the sampling mode cannot be adjusted according to different imaging scenarios and target tasks. In the present invention, a deep learning method is introduced, and through a data-driven model, the sampling mode is adjusted for different imaging scenarios (such as wide large scenes, complex terrains, and dynamic targets). Compared with the preset mode of traditional downsampling methods, this method is more adaptable and flexible.

[0005] Traditional downsampling imaging methods represented by Staggered SAR need to be interpolated to uniform sampling through interpolation and resampling algorithms, which may introduce errors or noise in this step. Additionally, a deblurring algorithm needs to be introduced for processing. The purposes of different steps conflict with each other, and this step-by-step processing method may lead to information loss or poor imaging quality due to inconsistent objectives. The deep learning method in the present invention integrates multiple steps such as sampling pattern design, reconstruction, imaging, and deblurring into the same network, realizes end-to-end training and inference, globally optimizes the network with the final imaging quality as the goal, more effectively utilizes information, and ensures imaging quality.

[0006] In the above-mentioned prior art, when the traditional compressive sensing algorithm is applied to downsampling SAR imaging, multiple hyperparameters (such as the update threshold ρ, etc.) need to be preset and manually adjusted within a certain range to achieve the best imaging effect. This method has high requirements for the tuning strategy and accuracy, and the required time cost is relatively large. Moreover, the observation matrix of SAR imaging is large, and the memory requirement is high when processing the original data and the observation matrix simultaneously. In addition, the basic SAR imaging network has a large number of iterations and a slow inference speed, which cannot meet the timeliness requirements of imaging. Summary of the Invention

[0007] The purpose of the present invention is to provide a SAR azimuth undersampling imaging method and system based on deep learning.

[0008] The technical solution for realizing the present invention is: a SAR azimuth undersampling imaging method based on deep learning, including the following steps:

[0009] Step 1: Obtain a SAR dataset, including full-sampled SAR images and the echo data corresponding to each SAR image, as the input of the deep unfolding network;

[0010] Step 2: Obtain the SAR Doppler center frequency, chirp rate, carrier frequency, and satellite equivalent velocity, and design an imaging operator using the chirp scaling algorithm in SAR imaging;

[0011] Step 3: Construct a deep unfolding network based on the Unet architecture to restore the echo signal into an image;

[0012] Step 4: Train the deep unfolding network, save the model weight file with the minimum loss, and the parameters in the weight file include the parameters in the convolutional layer and non-linear activation function of the denoiser, the learnable parameters in conjugate gradient descent, and the parameters of the undersampling pattern;

[0013] Step 5: Load the pre-trained weight file, use the unfolding network model for inference, obtain the deblurred imaging result, and obtain the optimized undersampling strategy.

[0014] Further, step 2: Obtain radar parameters and platform parameters, and design an imaging operator based on the chirp scaling algorithm to correct the signal range migration on different range gates, and achieve range and azimuth compression. The imaging operator is expressed as:

[0015]

[0016] In the formula, Y is the echo received by the radar, F r and F a represent the range Fourier transform and the azimuth Fourier transform respectively; and represent the inverse range Fourier transform and the inverse azimuth Fourier transform respectively; Θ sc represents the range migration correction operator; Θ rc and Θ ac represent the range and azimuth compression operators respectively;

[0017] Derive its inverse imaging operator from the imaging operator, which is expressed as:

[0018]

[0019] where X represents the radar image, and * represents the conjugate transpose.

[0020] Further, step 3: Construct a deep unfolding network based on the U-Net architecture to perform image restoration on the echo signal. The specific method is as follows:

[0021] Define the input echo signal as S, and the output imaging result as σ. The process of image restoration is as follows:

[0022]

[0023] where D Φ (σ) represents a denoiser. The denoiser adopts the U-Net architecture, consists of an encoder and a decoder, and is directly connected to the initial input. It extracts features at different scales, trains the parameters in each convolutional layer and non-linear activation function, and realizes the suppression of azimuth ambiguity caused by undersampling;

[0024] In the iterative process, let z n = D Φ (σ), and write the process of image restoration in the form of the alternating multiplier method:

[0025] z n+1 = D Φ (σ n )

[0026] σ n+1 = (I CS G CS + I) -1[z n+1 +S - G CS (σ n )]

[0027] Meanwhile, the inverse matrix in the S update process is implemented using the conjugate gradient algorithm. For the following equivalent problem:

[0028] (I CS G CS +I)σ n+1 = z n+1 +S - G CS (σ n )

[0029] Given z n+1 +S - G CS (σ n ) and the matrix I CS G CS +I, solve it through the conjugate gradient method, and combine the denoising process and the conjugate gradient solution process to obtain the layer structure of the unfolded network.

[0030] Furthermore, step 4: Train the deep unfolded network and save the model weight file with the minimum loss. The parameters in the weight file include the parameters in the convolutional layer and the non - linear activation function of the denoiser, the learnable parameters in the conjugate gradient descent, and the parameters of the undersampling pattern. The loss function is:

[0031]

[0032] The loss function used is a composite structure, consisting of the inter - layer loss L1 and the overall loss L2. The inter - layer loss L1 targets the difference between each intermediate layer and the output layer in the network, and takes the two - norm of the difference between the result x K of the output layer and the result x i of the i - th intermediate layer as the loss; while the overall loss L2 takes the two - norm of the difference between the output result x K of the network and the labeled result x label as the loss. In the loss function Loss, and calculate the loss for the j - th image in the dataset and add the two losses according to the weight of γ:1.

[0033] A SAR azimuth undersampling imaging system based on deep learning implements the above - mentioned SAR azimuth undersampling imaging method based on deep learning to achieve SAR azimuth undersampling imaging based on deep learning, and executes steps 1 - 5 in five modules respectively.

[0034] A computer device includes a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, the SAR azimuth undersampling imaging method based on deep learning is implemented to achieve SAR azimuth undersampling imaging based on deep learning.

[0035] A computer-readable storage medium stores a computer program. When the computer program is executed by a processor, the SAR azimuth undersampling imaging method based on deep learning is implemented to achieve SAR azimuth undersampling imaging based on deep learning.

[0036] Compared with the prior art, the significant advantages of the present invention are as follows: 1) By using a deep unfolding network to learn the azimuth undersampling pattern in SAR imaging, azimuth ambiguity can be suppressed under undersampling conditions, and a high-quality result close to the real image can be restored. This strategy can simultaneously achieve a wide swath in the range direction and high resolution in the azimuth direction. 2) Using a deep unfolding network to replace the iterative process of the sparse imaging algorithm, the optimal sparse imaging hyperparameters are trained by data-driven methods, which can reduce the number of iterations, effectively suppress azimuth ambiguity under undersampling conditions, and restore a higher-quality image. 3) A method based on a matched-filter imaging operator instead of the SAR observation matrix is proposed, which effectively reduces the memory overhead and realizes fast SAR imaging. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a schematic diagram of the imaging operator.

[0038] Figure 2 It is a schematic diagram of the inverse imaging operator.

[0039] Figure 3 It is a schematic diagram of the denoiser module.

[0040] Figure 4 It is a schematic diagram of the unfolding network structure.

[0041] Figure 5 It is a technical flow chart of the present invention.

[0042] Figure 6 It is a comparison chart of imaging results using other methods and the method of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0043] In order to make the objectives, technical solutions, and advantages of the present application clearer, the present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0044] The present invention uses deep learning methods for SAR imaging signal processing methods, designs an unfolding network to optimize undersampled SAR imaging, can train optimal hyperparameters based on data, and saves time costs. Using the layer modules of the unfolding network to replace the iterative process of traditional sparse reconstruction algorithms and combining training can achieve a better imaging effect while reducing the number of iterations. A SAR azimuth undersampling imaging method and system based on deep learning, whose basic idea is to use a matched filtering algorithm to construct an imaging operator and replace a huge observation matrix with a one-dimensional decoupled imaging operator. On the other hand, use deep learning methods to construct an unfolding network, design the iterative process of the original traditional algorithm as the layer module of the unfolding network, and at the same time use the azimuth undersampling mode as a trainable parameter of the unfolding network to enhance the joint ability of sampling mode learning and ambiguity suppression. After completing the azimuth undersampling strategy learning, the optimized undersampling strategy can be applied to the azimuth sampling process of SAR to achieve SAR imaging with a wide swath and low azimuth ambiguity.

[0045] I. Network training part:

[0046] Step 1: Obtain a SAR dataset, which contains full-sampled SAR images and the echo data corresponding to each SAR image. Organize this data as the input of the deep unfolding network.

[0047] Step 2: Obtain the SAR Doppler center frequency, chirp rate, carrier frequency, and satellite equivalent velocity, and use the chirp scaling algorithm in SAR imaging to design an imaging operator. The constructed imaging operator can be expressed as:

[0048]

[0049] In the formula, F r and F a respectively represent the range and azimuth Fourier transforms; and respectively represent the inverse range and azimuth Fourier transforms; Θ sc represents the range migration correction operator; Θ rc and Θ ac respectively represent the range and azimuth compression operators. It should be noted that these operators are all designed based on specific radar parameters, and Θ sc , Θ rc and Θ ac are all related to the azimuth sampling mode. Initialize the sampling mode as a learnable parameter and incorporate it into the imaging operator. The schematic diagram of the imaging operator is as shown in Figure 1 .

[0050] The inverse imaging operator can be derived from the imaging operator. The latter is the conjugate transpose of the former and can be expressed as:

[0051]

[0052] Among them, * represents conjugate transpose. For example, represents the conjugate transpose of Θ. The schematic diagram of the inverse imaging operator is as ac shown. Figure 2 shown.

[0053] Step 3: Construct the deep unfolding network for SAR imaging. Define the echo signal input to the network as S, and the imaging result output as σ. The process of image restoration is as follows:

[0054]

[0055] where D Φ (σ) represents a denoiser. In order to remove the blur and noise of σ during the restoration process, our denoiser is designed as a U-Net architecture. This model consists of an encoder and a decoder, and is directly connected to the initial input, which can extract features at different scales, extract features at different scales, and eliminate the blur noise of σ caused by undersampling. The learnable parameters in the network include the weights of each convolutional layer and the parameters in the non-linear activation function. These parameters are continuously optimized through backpropagation during the training process to enhance the denoising ability of the model. The schematic diagram of the denoiser module network is as Figure 3 shown.

[0056] During the iteration process, let z n = D Φ (σ), then the process of image restoration can be written in the form of the alternating direction method of multipliers:

[0057] z n+1 = D Φ (σ n )

[0058] σ n+1 = (I CS G CS + I) -1 [z n+1 + S - G CS (σ n )]

[0059] Meanwhile, the inverse matrix in the σ update process can be implemented using the conjugate gradient algorithm, which can be denoted by the symbol C Φ represent.

[0060] For the following equivalent problem:

[0061] (I CS G CS + I)σ n+1 = z n+1 + S - GCS (σ n )

[0062] Given \(z\) n +S - G CS (σ n ) and the matrix \(I\) CS G CS +I, it can be solved by the conjugate gradient method. By integrating the denoising process and the conjugate gradient solving process, the layer structure of the unfolding network can be obtained. The schematic diagram of the layer structure is as shown in Figure 4 shown.

[0063] Step 4: Input the SAR echo into the depth unfolding network and conduct multiple rounds of training. Save the model weight file with the minimum loss. The parameters in the weight file include the parameters of the convolutional layer and the non - linear activation function in the denoiser, the learnable parameters in the conjugate gradient descent, and the parameters of the undersampling pattern. During the training process, compare the SAR real image in the dataset with the model prediction image. The loss function is:

[0064]

[0065] The loss function used is a composite structure, consisting of the inter - layer loss \(L1\) and the overall loss \(L2\). The inter - layer loss \(L1\) targets the difference between each intermediate layer and the output layer in the network. Take the Euclidean norm of the difference between the result \(x\) K of the output layer and the result \(x\) i of the \(i\) - th intermediate layer as the loss; while the overall loss \(L2\) takes the Euclidean norm of the difference between the output result \(x\) K of the network and the labeled result \(x\) label as the loss. In the loss function \(Loss\), and calculate the loss for the \(j\) - th image in the dataset and add the two losses according to the weight of \(\gamma:1\).

[0066] Step 5: After training, save the model weight file with the minimum loss. The parameters in the weight file include the parameters of the convolutional layer and the non - linear activation function in the denoiser, the learnable parameters in the conjugate gradient descent, and the parameters of the undersampling pattern. The weight file will initialize the model in the inference imaging part for de - blurring imaging and undersampling pattern learning.

[0067] II. Inference Imaging Part:

[0068] Step 1: Obtain the SAR echo data and determine the constants such as the radar parameters and platform parameters of the radar from which the data is sourced;

[0069] Step 2: Construct the imaging operator according to the parameters obtained in Step 1, construct an unfolding network model with the same structure as that in the first part, and load the pre - trained weight file for the model;

[0070] Step 3: Input the acquired SAR echo data, perform inference using the unfolding network model, obtain the defocused imaging result of the model, and obtain the optimized non-uniform undersampling strategy, that is, the azimuth time corresponding to each sample in the azimuth direction;

[0071] Step 4: Optimize the undersampling scheme of the radar according to the undersampling strategy generated by the model, and design the transmission time of each azimuth signal.

[0072] The present invention also proposes a SAR azimuth undersampling imaging system based on deep learning, implements the SAR azimuth undersampling imaging method based on deep learning, and realizes the SAR azimuth undersampling imaging based on deep learning, including:

[0073] SAR Echo Data Analysis Module: Read the single-channel SAR raw echo, and extract auxiliary parameters such as satellite orbit, attitude, GPS, and SAR payload parameters;

[0074] Imaging Operator and Inverse Imaging Operator Generation Module: Obtain the SAR Doppler center frequency, chirp rate, carrier frequency, and satellite equivalent velocity, generate the imaging operator and inverse imaging operator using the chirp scaling algorithm in SAR imaging, apply them to the compressive sensing iteration process in the imaging unfolding network, and use the inverse imaging operator to replace the SAR observation matrix with a huge number of parameters;

[0075] Unfolding Network Module: Construct a deep learning network model for SAR imaging, adopt a network structure for azimuth ambiguity suppression, where each layer of the network corresponds to each iteration step in the imaging algorithm, and simulate the imaging iteration process through the forward propagation of the input echo in the network. The network structure is specially designed, and the undersampling mode is added as a learnable parameter to learn the undersampling mode in a data-driven manner;

[0076] Network Training Module: Responsible for loading the acquired SAR echo data set and performing multiple rounds of training on the unfolding network model. During the training process, compare the real image with the model prediction image, and optimize the network parameters and undersampling mode through the loss function;

[0077] Network Inference Module: Load the weight file of the model, input the acquired SAR echo data for image inference, output a high-quality image after azimuth ambiguity suppression, and obtain the optimized undersampling strategy.

[0078] A computer device includes a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, it implements the SAR azimuth undersampling imaging method based on deep learning and realizes the SAR azimuth undersampling imaging based on deep learning

[0079] A computer-readable storage medium stores a computer program thereon. When the computer program is executed by a processor, it implements a SAR azimuth undersampling imaging method based on deep learning to achieve SAR azimuth undersampling imaging based on deep learning.

[0080] Embodiment

[0081] To illustrate the effectiveness of the solution of the present invention, it is verified based on the open-source SAR dataset SRSDD 1.0.

[0082] Regarding the difference between the reconstructed image and the real image, we will measure it with two metrics, namely Structural Similarity (hereinafter referred to as SSIM) and Peak Signal-to-noise Ratio (hereinafter referred to as PSNR). SSIM measures the similarity of the local structures of two images in the spatial domain, while PSNR calculates the ratio between the image signal and the noise. The calculation formulas of the two metrics are as follows:

[0083]

[0084] where x and y are local image patches of two images, μ x and μ y are the means (brightness information) of the two images respectively, and are the variances (contrast information) of the two images respectively, and σ xy is the covariance (structural information) of images x and y, and C1 and C2 are constants used to avoid the denominator being zero.

[0085]

[0086] where is the maximum value of the pixel values in the image. For common 8-bit images, and MSE is the Mean Squared Error, which is used to measure the difference between the original image and the compressed image.

[0087] To compare the influence of different undersampling modes on azimuth ambiguity suppression, we compare the method of the present invention with traditional undersampling modes, such as Staggered SAR sampling, random dither sampling, and Poisson-disk sampling. The traditional undersampling modes all use the ISTA method in sparse imaging for imaging. The comparison metrics are SSIM and the PSNR after reconstruction (after ambiguity suppression). The comparison results are shown in Table 1, and the imaging results are shown in the figure.

[0088] It can be seen that the present invention is superior to the traditional undersampling mode in all three indicators, indicating that the azimuth ambiguity suppression effect achieved by this method is good; at the same time, the PSNR improved after reconstruction by undersampling with this method is higher, indicating that the undersampling mode obtained by this method is better, and the resulting ambiguity is easy to eliminate.

[0089] Table 1 Results of Different Undersampling Modes

[0090]

[0091]

[0092] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0093] The above-described embodiments merely represent several implementation manners of the present application. The description is relatively specific and detailed, but it should not be construed as a limitation on the scope of the present application. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present application, several modifications and improvements can still be made, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the appended claims.

Claims

1. A SAR azimuth undersampling imaging method based on deep learning, characterized in that, It includes the following steps: Step 1: Obtain the SAR dataset, including the full-sampled SAR images and the echo data corresponding to each SAR image, as the input of the deep unfolding network; Step 2: Obtain the SAR Doppler center frequency, chirp rate, carrier frequency, and satellite equivalent velocity, and design the imaging operator using the chirp scaling algorithm in SAR imaging; Step 3: Construct a deep unfolding network based on the Unet architecture to perform image restoration on the echo signal; Step 4: Train the deep unfolding network and save the model weight file with the minimum loss. The parameters in the weight file include the parameters in the convolutional layer and the non-linear activation function in the denoiser, the learnable parameters in the conjugate gradient descent, and the parameters of the undersampling pattern; Step 5: Load the pre-trained weight file, use the unfolding network model for inference, obtain the deblurred imaging result, and obtain the optimized undersampling strategy.

2. The SAR azimuth undersampling imaging method based on deep learning according to claim 1, wherein Step 2: Obtain the SAR Doppler center frequency, chirp rate, carrier frequency, and satellite equivalent velocity, and design the imaging operator using the chirp scaling algorithm in SAR imaging, where the imaging operator is expressed as: Where Y is the echo received by the radar, F r and F a represent the range - direction and azimuth - direction Fourier transforms respectively; and represent the inverse range - direction and inverse azimuth - direction Fourier transforms respectively; Θ sc represents the range migration correction operator; Θ rc and Θ ac represent the range and azimuth compression operators respectively; Derive its inverse imaging operator from the imaging operator, which is expressed as: Where, X represents the radar image, and * represents the conjugate transpose.

3. The SAR azimuth undersampling imaging method based on deep learning according to claim 2, wherein Step 3: Construct a deep unfolding network based on the U-Net architecture to perform image restoration on the echo signal. The specific method is as follows: Define the input echo signal as S, and the output imaging result as σ. The process of image restoration is as follows: Among them, D Φ (σ) represents a denoiser. The denoiser adopts a U-Net architecture, consists of an encoder and a decoder, and is directly connected to the initial input, extracts features at different scales, trains the parameters in each convolutional layer and non-linear activation function, and realizes the suppression of azimuth ambiguity caused by undersampling; During the iteration process, let z n = D Φ (σ), and write the process of image restoration in the form of the alternating direction method of multipliers: z n+1 = D Φ (σ n ) σ n+1 =(I CS G CS +I) -1 [z n+1 +S - G CS (σ n )] Meanwhile, the inverse matrix in the σ update process is implemented using the conjugate gradient algorithm for the following equivalent problem: (I CS G CS +I)σ n+1 =z n+1 +S-G CS (σ n ) Given z n+1 +S-G CS (σ n ) and matrix I CS G CS +I, solve by the conjugate gradient method, and integrate the denoising process and the conjugate gradient solving process, then the layer structure of the unfolding network can be obtained.

4. The method for SAR azimuth undersampling imaging based on deep learning according to claim 2, wherein Step 4: Train the deep unfolding network and save the model weight file with the minimum loss. The parameters in the weight file include the parameters in the convolutional layer and the non-linear activation function in the denoiser, the learnable parameters in the conjugate gradient descent, and the parameters of the undersampling pattern. The loss function is: The loss function used is a composite structure, consisting of an inter-layer loss L1 and an overall loss L2. The inter-layer loss L1 targets the difference between each intermediate layer and the output layer in the network, taking the second norm of the difference between the result x of the output layer K and the result x i of the i-th intermediate layer as the loss; while the overall loss L2 takes the second norm of the difference between the output result x K of the network and the labeled result x label as the loss. In the loss function Loss, and calculate the loss for the j-th image in the dataset and add the two losses according to the weight ratio of γ:

1.

5. A SAR azimuth undersampling imaging system based on deep learning, characterized in that, Implement the deep learning-based SAR azimuth undersampling imaging method according to any one of claims 1-4 to achieve deep learning-based SAR azimuth undersampling imaging, and execute steps 1 to 5 in five modules respectively.

6. A computer device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, it implements the deep learning-based SAR azimuth undersampling imaging method according to any one of claims 1-4 to achieve deep learning-based SAR azimuth undersampling imaging.

7. A computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it implements the deep learning-based SAR azimuth undersampling imaging method according to any one of claims 1-4 to achieve deep learning-based SAR azimuth undersampling imaging.

Images