Sparse ISAR high-resolution imaging method based on depth unfolding

Abstract

The application discloses a kind of sparse ISAR high-resolution imaging networks based on depth development, mainly solve the problem that prior art is not robust to echo signal-to-noise ratio and defect rate, high spatial complexity and low efficiency.Its implementation scheme includes: the establishment of echo defect condition under sparse observation model;According to the sparse observation model Y under echo defect condition, the objective function conforming to L1 norm optimization criterion is constructed;Based on 2D-ISTA iterative algorithm, a sparse ISAR high-resolution imaging network is constructed;Scattering point is used to generate training set, and the training set is used to train the sparse ISAR high-resolution imaging network;The measured data is input into the trained imaging network, and the objective function is solved by network forward propagation, to obtain the final ISAR imaging result.The application significantly improves the robustness of the network to echo signal-to-noise ratio and defect rate, while reducing the time and spatial complexity, and can be used for ship-borne, airborne ISAR system to extract important information.

Description

Technical Field

[0001] This invention belongs to the field of radar remote sensing technology, and further relates to an ISAR high-resolution imaging method that can be used in shipborne and airborne ISAR systems to extract important information about the shape, structure and attitude of targets. Background Technology

[0002] Inverse synthetic aperture radar (ISAR) enables long-range, high-resolution imaging of non-cooperative targets, thus playing a crucial role in space situational awareness. Under complex observation conditions such as low signal-to-noise ratio and echo loss, while focused imaging can be achieved through sparse signal reconstruction methods, these methods involve multiple iterations and complex steps such as matrix inversion. Furthermore, multiple hyperparameters dependent on target and echo characteristics typically need to be manually set, making it difficult to find optimal solutions in practice and consuming considerable time.

[0003] Model-driven high-resolution ISAR imaging based on deep unfolded networks expands the iterative steps of sparse signal reconstruction methods into a neural network, transforming manually tuned parameters into learnable parameters for the network. This allows for optimal imaging performance to be achieved through network training. Since different network layers have different parameter values, this approach offers greater flexibility and faster convergence. While various high-resolution ISAR imaging methods using deep unfolded networks have been proposed, they still face challenges such as instability with echo loss rates and signal-to-noise ratios (SNR). This necessitates separate network training for different echo loss rates and SNRs, significantly increasing time and space complexity.

[0004] Patent application CN202010501764.4 discloses a "SA-ISAR imaging method for targets with micro-motion components based on low-rank and sparse joint constraints," which is completed in three parts. First, a one-dimensional range image sequence of the target with micro-motion components after translational compensation is modeled. Then, the sparse aperture ISAR imaging problem of the target with micro-motion components is modeled. Finally, a linear ADMM is used to solve the sparse aperture ISAR imaging problem of the target with micro-motion components. Although this method can obtain well-focused ISAR images in complex observation environments, it involves multiple iterations and has high complexity in steps such as matrix inversion. In addition, it usually requires manually setting multiple hyperparameters that depend on the target and echo characteristics, which is difficult to find the optimal solution in practice and is time-consuming.

[0005] Patent application CN202111464674.3 discloses a "structured sparse aperture ISAR imaging method based on C-ADMMN," which is completed in three parts. First, the sparse aperture ISAR echo signal is modeled. Then, a C-ADMMN forward propagation model is constructed, including a reconstruction layer, a noise reduction layer, and a multiplier update layer. Finally, C-ADMMN is used to solve the structured sparse aperture ISAR imaging problem and obtain the final imaging result. Although this method improves ISAR imaging performance and shortens imaging time, it has the following problems: 1) It lacks robustness to different signal-to-noise ratios, requiring separate training of the imaging network according to different signal-to-noise ratios, thus resulting in high time and space complexity; 2) It lacks robustness to different echo loss rates, requiring separate training of the imaging network according to different echo loss rates, further increasing time and space complexity. Summary of the Invention

[0006] The purpose of this invention is to address the shortcomings of the prior art by proposing a depth-deployed ISAR high-resolution imaging method to improve the network's robustness to echo signal-to-noise ratio and defect rate, while reducing time and space complexity.

[0007] The technical approach of this invention is to expand the imaging network using a traditional iterative algorithm and design a controllable near-end mapping module to construct a sparse ISAR high-resolution imaging network based on depth expansion. The implementation steps include the following:

[0008] (1) Establish a sparse observation model under the condition of echo loss:

[0009] Y = Φ1XΦ2 + E

[0010] in, For echo signal, For ISAR images, For the complex field distance dictionary, For complex field Doppler dictionaries, For the complex domain noise matrix, M and N represent the number of sampling points and the total number of pulses, respectively, and U and V represent the length and width of the image, respectively. When there are sparse observations in the frequency band or azimuth, M < U and N < V.

[0011] (2) Based on the sparse observation model Y under the condition of echo loss, construct an objective function that conforms to the L1 norm optimization criterion:

[0012]

[0013] Where y = Vect(Y), x = Vect(X), and Vect(·) represents the vectorization operation. Represents the observation matrix. T This indicates the transpose operation. Represents the Kronecker product;

[0014] (3) Construct a sparse ISAR high-resolution imaging network based on depth unfolding:

[0015] 3a) The iterative algorithm is expanded into an imaging network including gradient descent layers and proximal mapping layers;

[0016] 3b) Construct a controllable proximal mapping module that includes a proximal mapping unit and a controllable unit;

[0017] 3c) Embed the controllable proximal mapping module into the proximal mapping layer of the imaging network, and integrate it with the high-frequency feature extractor. Residual Reconstructor The gradient descent layer is connected sequentially, and then the output of the gradient descent layer is connected to the output of the residual reconstructor in a skip connection to form a controllable proximal mapping layer.

[0018] 3d) The gradient descent layer and the controllable near-end mapping layer are connected in sequence to obtain the nth sub-network. Then, multiple sub-networks are cascaded to obtain a sparse ISAR high-resolution imaging network.

[0019] (4) Generate training set:

[0020] 4a) Using randomly distributed scattering points with amplitudes following a Gaussian distribution as training labels, different echo loss rates and signal-to-noise ratios are set to obtain different ISAR scenes, thereby generating original images under different scenes;

[0021] 4b) Combine the original image and the labeled image into image pairs to generate n image pairs as the training set, where n ≥ 600;

[0022] (5) Training the sparse ISAR high-resolution imaging network:

[0023] 5a) Use normalized mean square error (NMSE) as the loss function for network training. Each time, select data of batch size from the training set and input it into the sparse ISAR high-resolution imaging network to calculate the loss value l in each batch. Update the network parameters through the stochastic gradient descent algorithm until all data in the training set has been selected. Sum the loss values ​​obtained from all batches and take the average to obtain the loss after one training pass.

[0024] 5b) Repeat step 5a) until the network converges to obtain the trained sparse ISAR high-resolution imaging network.

[0025] (6) Input the measured Yak-42 data into the trained imaging network, and obtain the final ISAR imaging result through forward propagation of the network.

[0026] Compared with the prior art, the present invention has the following advantages:

[0027] First, this invention constructs a near-end mapping unit based on a residual network, which uses a convolutional neural network to extract noise features and further suppresses noise components in the image through skip connections, thereby improving the robustness of the sparse ISAR high-resolution imaging network to echo signal-to-noise ratio and reducing time and space complexity.

[0028] Secondly, this invention constructs a controllable unit and adds it to the near-end mapping module to obtain a controllable near-end mapping module. It uses a conditional vector containing echo defect information as input to generate a controllable vector and modulates the output of the last convolutional layer in the residual network. This enables the network to dynamically adjust the network parameters for different echo defect rates during the imaging process, thereby improving the robustness of the sparse ISAR high-resolution imaging network to echo defect rates and further reducing time and space complexity. Attached Figure Description

[0029] Figure 1 This is a flowchart illustrating the implementation of the present invention;

[0030] Figure 2 This is a diagram of the sparse ISAR high-resolution imaging network structure based on depth unfolding constructed in this invention.

[0031] Figure 3 This is a comparison chart of the ISAR imaging effects of the present invention and existing technologies. Detailed Implementation

[0032] The embodiments and effects of the present invention will be further described in detail below with reference to the accompanying drawings. The embodiments are only used to illustrate the implementation scheme of the present invention and do not constitute any limitation on the present invention. Obviously, those skilled in the art can make various modifications and changes in form and details without departing from the principle and structure of the present invention after understanding the content and principle of the present invention. However, these modifications and changes based on the idea of ​​the present invention are still within the protection scope of the present invention.

[0033] refer to Figure 1 The implementation steps of this embodiment include the following:

[0034] Step 1: Establish a sparse observation model under the condition of echo loss.

[0035] 1.1) Assuming the radar transmits a linear frequency modulated pulse signal, and the target is represented by Q scattering points, obtain the echo signal of the p-th target scattering point in the range-time-azimuth-time domain.

[0036]

[0037] Among them, f c T is the carrier frequency. pγ is the pulse width, t is the modulation frequency, and t is the pulse width. n =nT represents the slow time, where T is the pulse repetition interval, and n = 1, 2, ..., N represents the number of pulses; Represents fast time; rect(·) represents the unit rectangular function. R p (t n ) represents the distance between the p-th scattering point and the radar, A p Let a represent the back reflection coefficient at the p-th scattering point. a (t n ) is an azimuth window function and T a For the observation time, exp(·) denotes the exponential operation with the natural constant e as the base, and j denotes the imaginary unit symbol;

[0038] 1.2) For echo signals By performing line frequency modulation processing, the echo s of the p-th scattering point in the range-frequency-slow-time domain is obtained. p (f,t n ):

[0039]

[0040] in, Where R is the distance frequency, B is the bandwidth; ps Let R be the instantaneous slant distance between the scattering point p and the reference point s. According to the turntable model, the instantaneous slant distance is expressed as: R ps (θ)≈x p sinθ+y p cosθ≈x p θ+y p , (x p ,y p ) represents the coordinates of the p-th scattering point of the target, θ = ωt n ω represents the angular velocity of the ISAR target rotation;

[0041] Because ISAR imaging accumulation time is short, the target's relative rotation angle ω to the radar is small during the imaging accumulation time, therefore sin(ωt) n )≈ωt n =θ、cos(ωt) n )≈1, so R ps Substitute (θ) into s p (f,t n From this, we can obtain:

[0042]

[0043] 1.3) Given the frequency interval Δf and the pulse repetition interval T, discretize the range and azimuth directions as f = mΔf and t, respectively. n=nT, then s p (f,t n This can be further transformed into the discrete form s. p (m,n):

[0044]

[0045] Where m = 1, 2, ..., M, n = 1, 2, ..., N, M and N represent the number of sampling points and the total number of pulses, respectively;

[0046] 1.4) Let the ISAR image size be U×V, and the elements in the image be i. p (u,v), u∈[1,U], v∈[1,V), echo signal s p (m,n) and image i p The transformation relationship between (u,v) is expressed as follows:

[0047]

[0048] Where d1 is the range loss vector, representing the vector of length M obtained after random downsampling of the original vector of length U under sparse observation conditions. 1m Let d1 be the m-th element; d2 is the azimuth loss vector, representing the vector of length N obtained by randomly downsampling the original vector of length V under sparse observation conditions. 2n It is the nth element in d2;

[0049] 1.5) Order Let Φ1 be a dictionary of complex field distances, and the complex field element in the m-th row and u-th column is: For a complex field Doppler dictionary, the complex field element in the nth row and vth column of Φ2 is: The sparse observation model Y under the condition of echo loss is obtained:

[0050] Y = Φ1XΦ2 + E

[0051] in, For ISAR images, For echo signal, For a complex domain noise matrix, when there are sparse observations in the frequency band or azimuth, M < U, N < V;

[0052] In this embodiment, the size of the ISAR image is set to, but is not limited to, U=128, V=128.

[0053] Step 2: Based on the sparse observation model Y under the condition of echo loss, construct an objective function that conforms to the L1 norm optimization criterion.

[0054] 2.1) Perform a vectorization operation Vect(·) on the sparse observation model under the condition of echo loss, so that y = Vect(Y), x = Vect(X), e = Vect(E), to obtain the vectorized sparse observation model y:

[0055] y = Φ0x + e

[0056] in, For the complex field distance dictionary, For complex field Doppler dictionaries,

[0057] T represents the transpose operation. Represents the Kronecker product;

[0058] 2.2) Construct an objective function that conforms to the L1 norm optimization criterion based on the vectorized sparse observation model.

[0059]

[0060] in, The Euclidean norm of a vector. Let x represent the ISAR scene to be solved, λ represent the regularization coefficient, and the sparsity of x is constrained by the L1 norm.

[0061] Step 3: Construct an ISAR imaging network based on depth unfolding.

[0062] refer to Figure 2 The implementation of this step includes the following:

[0063] 3.1) The 2D-ISTA iterative algorithm is expanded into an imaging network including gradient descent layers and proximal mapping layers:

[0064] The 2D-ISTA algorithm is an algorithm for solving convex optimization problems, and its process is as follows:

[0065] Input echo signal Y, complex domain distance dictionary Φ1 and complex domain Doppler dictionary Φ2, initialization parameters: iteration step size ρ, regularization coefficient λ, and initial imaging result X. (0) And the auxiliary variable R in the first iteration (1) ;

[0066] According to the iteration steps and X (k) =S soft (R (k) ,α) for imaging result X (k) Perform iterative updates until the iteration stopping condition is met. Stop the iteration when the time is right, and obtain the final imaging result X. (N) ;

[0067] Where ε is a small value, usually taken as ε = 1 × 10 -6 k represents the number of iterations in 2D-ISTA, ρ represents the iteration step size, and S soft (R (k) ,α (k) ) represents the soft threshold shrinkage function, defined as S soft (R (k) ,α (k) ) = sgn(R (k) )max{|R (k) |-α (k) ,0}, where α represents the shrinkage threshold of the iteration.

[0068] This example uses the 2D-ISTA algorithm to expand into an imaging network, which is then used to solve the objective function constructed in step two that conforms to the L1 norm optimization criterion. The implementation steps include the following:

[0069] 3.1.1) Extract N iterations from the 2D-ISTA iterative algorithm, and extract the auxiliary variable R contained in the nth iteration. (n) Reconstruction result X (n) These correspond to two different network layers: gradient descent layer and proximal mapping layer.

[0070] 3.1.2) The gradient descent layer and the proximal mapping layer are connected sequentially to obtain the nth sub-network. Multiple sub-networks are repeatedly cascaded to obtain the ISTA unfolded imaging network.

[0071] 3.2) Construct a controllable proximal mapping module that includes a proximal mapping unit and a controllable unit;

[0072] 3.2.1) Design a near-end mapping unit based on residual networks:

[0073] This unit comprises two convolutional modules c1 and c2 and a skip connection. The first convolutional module c1 consists of a cascaded convolutional layer with a kernel size of 3×3 and 32 kernel channels, and a ReLU activation layer. The second convolutional module c2 consists of a convolutional layer with a kernel size of 3×3 and 32 kernel channels. The output of each convolutional module is represented as follows: x is the input to the near-end mapping unit;

[0074] The output of the entire proximal mapping unit is represented as z = relu(y² + x), where relu(·) represents the ReLU activation function;

[0075] 3.2.2) Design of controllable units:

[0076] The controllable unit consists of a fully connected layer W CU The implementation takes a conditional vector z containing echo loss information as input and generates a controllable vector of dimension C.

[0077]

[0078] 3.2.3) The controllable unit is embedded into the proximal mapping unit to obtain a controllable proximal mapping module. Its output F (n) for:

[0079]

[0080] Among them, G (n) It is the output of the previous module, z is Input, and These represent controllable proximal mapping modules. The first and last convolutional layers in the model have a vector dimension C = 32 in this embodiment;

[0081] 3.3) Embed the controllable proximal mapping module into the proximal mapping layer of the imaging network, and integrate it with the high-frequency feature extractor. Residual Reconstructor The gradient descent layer's output is then sequentially connected to the residual reconstructor's output, forming a controllable proximal mapping layer. This high-frequency feature extractor... and residual reconstructor Structural parameters, and the output X of the entire controllable proximal mapping layer. (n) They are as follows:

[0082] The high-frequency feature extractor It consists of convolutional layers with a kernel size of 3×3 and a kernel channel number of 32;

[0083] The residual reconstructor It consists of convolutional layers with a kernel size of 3×3×32 and a kernel channel number of 1;

[0084] The output X (n) for

[0085]

[0086] in, and S represents the soft threshold shrinkage function. soft Controllable proximal mapping modules before and after (·); This is a high-frequency feature extractor for the nth layer of the network. For the residual reconstructor of the nth layer of the network, α (n) The learnable shrinkage threshold of the nth layer of the network;

[0087] 3.4) The gradient descent layer and the controllable near-end mapping layer are sequentially connected to obtain the nth sub-network. Multiple sub-networks are then cascaded to obtain the sparse ISAR high-resolution imaging network, the structure of which is as follows:

[0088] Network input → Layer 1 gradient descent layer, controllable proximal mapping layer → … → Layer n gradient descent layer, controllable proximal mapping layer → … → Layer N gradient descent layer, controllable proximal mapping layer → Network output.

[0089] The learnable parameters in a network are represented by Θ:

[0090]

[0091] Where, ρ (n) For gradient descent layer R (n) The iteration step size in the middle, For high-frequency feature extractor parameters, For the residual reconstructor parameters, α (n) The shrinkage threshold, W represents the parameters of two convolutional layers in the controllable proximal mapping module. CU Here are the parameters of the fully connected layer, and N is the total number of stages in the network. These parameters can all be learned through the neural network.

[0092] In this embodiment, the iteration step size ρ (n) and regularization parameter α (n) They were initialized to 1.0 and 0.01 respectively, parameters Random initialization is then used, and the number of network layers is set, but not limited to, N=9.

[0093] Step 4: Generate the training set.

[0094] 4.1) Use scattering points whose positions are randomly distributed and whose amplitudes follow a Gaussian distribution as training labels X;

[0095] 4.2) Substitute the labeled image X into the sparse observation model Y = Φ1XΦ2 + E to obtain echo data with varying degrees of loss and added random signal-to-noise ratio noise, and then perform initialization calculations. Obtain the original image And use it as network input data;

[0096] 4.3) Combine the original image and the labeled image into image pairs to construct a sample size of N. b Image pairs As a training set;

[0097] In this embodiment, the training set image size is set to, but is not limited to, 128×128; the echo defect rate is set to, but is not limited to, 25%–75%; the echo signal-to-noise ratio is set to, but is not limited to, 0–20dB; and the number of training set samples N. bLet's assume, but not be limited to, 800.

[0098] Step 5: Train the sparse ISAR high-resolution imaging network.

[0099] 5.1) Select data of batch size from the training set each time and calculate the loss value for each batch. The network parameters are updated using the stochastic gradient descent algorithm until all data in the training set has been selected.

[0100] 5.1.1) Each time, select data of batch size from the training set and input it into the sparse ISAR high-resolution imaging network to calculate the loss value in each batch.

[0101]

[0102] in, Let N be the F-norm. batch The number of samples in each batch. X represents the reconstructed image output by the imaging network, and X represents the input label image;

[0103] 5.1.2) The gradient of the loss function with respect to arbitrary parameters in the sparse ISAR high-resolution imaging network is calculated using the complex domain backpropagation algorithm. Based on the gradient obtained from the solution Update the network parameters of the sparse ISAR high-resolution imaging network to obtain the network parameters Θ′ for the current training phase:

[0104]

[0105] Where Θ0 represents the network parameters during the training phase of the sparse ISAR high-resolution imaging network, and lr represents the learning rate during training.

[0106] 5.2) Repeat step 5.1) until the network converges and the final trained network parameters are obtained, thus completing the training of the sparse ISAR high-resolution imaging network.

[0107] In this embodiment, the batch size for each training session is set to 1, and the Adam optimizer with a learning rate of 0.005 is used for training.

[0108] Step 6: Obtain ISAR target imaging results.

[0109] The measured Yak-42 aircraft data is input into the trained imaging network, and the final ISAR imaging result is obtained through forward propagation of the network.

[0110] The numbering of the above steps is for the purpose of more clearly describing the implementation scheme of the present invention, and the order of the numbers is not limited.

[0111] The effects of this invention can be further illustrated by the following simulation experiments:

[0112] I. Simulation Experiment Conditions

[0113] The software platform for the simulation experiment of this invention is Windows 10 operating system and PyTorch 3.7, and the hardware configuration is: Core i5-9300H CPU and NVIDIA GeForce 1650 GPU.

[0114] The simulation experiment of this invention uses point simulation data with randomly distributed positions and amplitudes following a Gaussian distribution. The image size in the training set is 128×128, and the number of images is 800.

[0115] II. Simulation Content and Result Analysis

[0116] Under the aforementioned simulation conditions, the present invention and the existing "Structured Sparse Aperture ISAR Imaging Method Based on C-ADMMN" were used to image the measured ISAR data. In the existing technology, the imaging network is trained separately for each fixed ISAR scenario and then used to image the measured data for that corresponding scenario; that is, one network corresponds to one test scenario, obtaining a well-focused ISAR image. In contrast, the imaging network in the present invention, after training, can obtain well-focused ISAR images for measured data in different ISAR scenarios; that is, one network corresponds to multiple test scenarios, and the imaging results are as follows: Figure 3 As shown. Wherein:

[0117] Figure 3 (a) The imaging results obtained from measured Yak-42 aircraft data using existing technology under conditions of 25% echo loss rate and 5dB echo signal-to-noise ratio.

[0118] Figure 3 (b) shows the imaging results obtained from measured Yak-42 aircraft data using existing technology under conditions of 25% echo loss rate and 10dB echo signal-to-noise ratio.

[0119] Figure 3 (c) This is the imaging result obtained by the present invention from measured Yak-42 aircraft data under the conditions of 25% echo loss rate and 5dB echo signal-to-noise ratio.

[0120] Figure 3 (d) shows the imaging results obtained by the present invention from measured Yak-42 aircraft data under the conditions of 25% echo loss rate and 10dB echo signal-to-noise ratio.

[0121] Figure 3(e) shows the imaging results obtained from measured Yak-42 aircraft data using existing technology under conditions of 50% echo loss rate and 5dB echo signal-to-noise ratio.

[0122] Figure 3 (f) shows the imaging results obtained from measured Yak-42 aircraft data using existing technology under conditions of 50% echo loss rate and 10dB echo signal-to-noise ratio.

[0123] Figure 3 (g) shows the imaging results obtained by the present invention from measured Yak-42 aircraft data under the conditions of 50% echo loss rate and 5dB echo signal-to-noise ratio.

[0124] Figure 3 (h) is the imaging result obtained by the present invention on the measured Yak-42 aircraft data under the conditions of 50% echo loss rate and 10dB echo signal-to-noise ratio.

[0125] from Figure 3 As can be seen, under different echo loss rates and echo signal-to-noise ratios, the imaging results obtained by the present invention retain more information in the aircraft image, especially the nose information of the aircraft, compared with the existing technology, and the imaging quality is better.

[0126] For the above imaging results, the normalized mean square error and peak signal-to-noise ratio (PSNR) were calculated respectively, and the results are shown in Table 1.

[0127] Table 1 Comparison of Evaluation Indicators for Measured Data Imaging Results

[0128]

[0129] The evaluation metrics, normalized mean square error and peak signal-to-noise ratio, in Table 1 are defined as follows:

[0130] The normalized mean square error is a measurement method based on energy normalization. A smaller value indicates better image quality, and it is defined as:

[0131]

[0132] Where g(i,j) represents each pixel of the original image. To process each pixel of the image, M and N are the length and width of the image;

[0133] Peak signal-to-noise ratio (PSNR) is an objective standard for measuring the level of image distortion or noise. The higher the PSNR between two images, the more similar they are. A common benchmark is 30 dB. Images with a PSNR below 30 dB show more significant degradation. PSNR is defined as follows:

[0134]

[0135] in, This represents the mean square error between the original M×N monochrome image and the processed image, where MAX represents the maximum value of the image color.

[0136] As can be seen from the comparison in Table 1, the imaging network obtained by the present invention, after training, has a smaller normalized mean square error and a higher peak signal-to-noise ratio under different echo loss rates and echo signal-to-noise ratios, indicating that the imaging quality of the present invention is better than that of the existing technology.

[0137] In summary, the imaging results and imaging evaluation indicators of this invention are superior to existing schemes under different echo loss rates and echo signal-to-noise ratios, verifying the advantages of this invention in improving the robustness of the network to echo signal-to-noise ratio and loss rate, and reducing time and space complexity.

Claims

1. A sparse ISAR high-resolution imaging method based on depth unfolding, characterized in that, The method comprises the following steps: (1) establishing a sparse observation model under echo missing condition: ； wherein, is the echo signal, is the ISAR image, is a complex-valued range dictionary, is a complex-valued Doppler dictionary, is a complex-valued noise matrix, and denote the number of samples and the total number of pulses, respectively, and denote the length and width of the image, respectively, when there is a case of sparse observation in the frequency band or the azimuth, , ; (2) Sparse observation model according to echo defect , construct the objective function conforming to the L1 norm optimization criterion: ； wherein , , denotes a vectorization operation, denotes an observation matrix, denotes a transposition operation, denotes a Kronecker product; denotes a regularization coefficient; (3) constructing a sparse ISAR high-resolution imaging network based on depth unfolding: 3a) unfolding the iterative algorithm into an imaging network comprising a gradient descent layer and a proximal mapping layer; 3b) constructing a controllable proximal mapping module comprising a proximal mapping unit and a controllable unit; 3c) embedding the controllable near-end mapping module into a near-end mapping layer in the imaging network, and connecting the high-frequency feature extractor , the residual reconstructor in sequence, and then connecting the output of the gradient descent layer and the output of the residual reconstructor in a skip connection to form the controllable near-end mapping layer; 3d) connecting the gradient descent layer and the controllable near-end mapping layer in sequence to obtain the first sub-network, and cascading the plurality of sub-networks to obtain the sparse ISAR high-resolution imaging network; (4) generating a training set: 4a) taking scattering points with random position distribution and amplitude obeying Gaussian distribution as training labels, setting different echo missing rates and signal-to-noise ratios to obtain different ISAR scenes, and then generating original images under different scenes; 4b) composing the original image and the label image into an image pair, generating an image pair as a training set, ; (5) training the sparse ISAR high-resolution imaging network: 5a) using normalized mean square error (NMSE) as the loss function of network training, selecting data of batch size from the training set each time, inputting into the sparse ISAR high-resolution imaging network to calculate the loss value in each batch updating the network parameters through the stochastic gradient descent algorithm until the data in the training set are all selected, summing up the loss values obtained by all batches and taking the average to obtain the loss after one training of the network; 5b) repeating step 5a) until the network converges, and obtaining the trained sparse ISAR high-resolution imaging network; (6) inputting the measured data into the trained imaging network, and obtaining the final ISAR imaging result through network forward propagation.

2. The method of claim 1, wherein, In step (1), the sparse observation model under echo missing condition is established, and the implementation steps include the following: 1a) Assuming that the radar transmits a linear frequency modulated pulse signal, the target is represented by a number of scattering points, the return signal of the th target scattering point in the range fast-time-azimuth slow-time domain is given by ​ ； in, For carrier frequency, The pulse width. To adjust the frequency, Indicates slow time. The pulse repetition interval, Indicates the number of pulses; Indicates a fast time; Represents the unit rectangle function , Indicates the first The distance between each scattering point and the radar. Indicates the first Back reflection coefficient at each scattering point It is an azimuth window function and , For observation time, Represented by natural constant Index-based operations. Symbol for the imaginary unit; 1b) performing dechirping on the echo signal to obtain the echo of the first scattering point in the range-frequency-slow-time domain : ； wherein, is the distance frequency, is the bandwidth; is the scattering point to the reference point the instantaneous slant range between the scattering point and the reference point, expressed according to the rotation model as: , denotes the coordinates of the target's thscattering point, , denotes the ISAR target rotation angular velocity; since the ISAR imaging accumulation time is short, the target's rotation angle relative to the radar in the imaging accumulation time is small, so , ; Substituting into one obtains: ； 1c) Given frequency interval and pulse repetition interval , the range and azimuth are discretized as and respectively, where , , and denote the number of sampling points and the total number of pulses respectively; then can be further transformed into discrete form : ； 1d) Let the ISAR image size be , and the elements in the image be , , ; the echo signal is expressed as follows by Fourier transform in the range direction and the azimuth direction. ； wherein, is a distance direction missing vector, representing a vector with original length after random down-sampling, and the length of the vector is , wherein is the th element in ; is an azimuth direction missing vector, representing a vector with original length after random down-sampling, and the length of the vector is , wherein is the th element in ; 1e) Let be the complex-valued range dictionary, be the complex-valued Doppler dictionary, be the complex-valued range dictionary, be the complex-valued Doppler dictionary, ; be the complex-valued range dictionary, be the complex-valued Doppler dictionary, be the complex-valued range dictionary, be the complex-valued Doppler dictionary, , we obtain the sparse observation model under echo dropout : ； wherein is an ISAR image, is an echo signal, is a complex domain noise matrix.

3. The method of claim 1, wherein, The step (2) according to the sparse observation model under the echo defect condition , the target function meeting the L1 norm optimization criterion is constructed, and the implementation step comprises the following: 2a) Vectorization of the sparse observation model in case of echo lacunae , such that , , the vectorized sparse observation model is obtained : ； wherein , is a complex-valued range dictionary, is a complex-valued Doppler dictionary, denotes a transpose operation, denotes a Kronecker product; 2b) Constructing an objective function that fits the L1 norm optimization criterion from the vectorized sparse observation model : ； wherein, denotes the Euclidean norm of a vector, denotes the ISAR scene to be solved, denotes a regularization coefficient, the sparsity of is constrained by the L1 norm.

4. The method of claim 1, wherein, In step 3a), the iterative algorithm is unfolded into an imaging network comprising a gradient descent layer and a proximal mapping layer, and the implementation steps include the following: 3a1) intercepting the 2D-ISTA iterative algorithm at the second iteration, where the first auxiliary variables involved in the second iteration reconstruction result correspond to two different network layers, gradient descent layer and proximal mapping layer, where: ， ， is an echo signal, is an iteration step size for the gth iteration, is a complex domain range dictionary, is a complex domain Doppler dictionary; denotes a soft threshold shrinkage function defined as , is a shrinkage threshold for the gth iteration; ; 3a2) sequentially connecting the gradient descent layer and the proximal mapping layer to obtain the first sub-networks, repeating cascading the plurality of sub-networks to obtain an ISTA unfolding imaging network.

5. The method of claim 4, wherein, In step 3b), a controllable proximal mapping module comprising a proximal mapping unit and a controllable unit is constructed, including the following steps: 3b1) designing a proximal mapping unit based on a residual network: The unit includes two convolution modules , and a skip connection, wherein: the first convolution module is composed of a convolution layer and a ReLU activation layer; the second convolution module is composed of a convolution layer; the output of each convolution module is represented as , , which is the input of the near-end mapping unit; The output of the entire proximal mapping unit is denoted as where denotes the ReLU activation function; 3b2) designing a controllable unit: The controllable unit is a fully connected layer The implementation has an input of a conditional vector containing echo dropout information and generates a controllable vector of dimension C : ； 3b3) embedding the controllable unit into the near-end mapping unit, resulting in a controllable near-end mapping module , whose output is: ； in, It is the output of the front-end module. yes Input, and These represent controllable proximal mapping modules. The first and last convolutional layers in the process.

6. The method of claim 5, wherein, In step 3c), the high-frequency characteristics of the controllable proximal mapping layer are constructed, including the following steps: Feature extractor And residual reconstructor Structural parameters, and output of the entire controllable near-end mapping layer Respectively as follows: The high-frequency feature extractor consists of a convolution layer with a convolution kernel size of , a convolution kernel channel number of ; The residual reconstructor consists of a convolution layer with a convolution kernel size of , a convolution kernel channel number of ; The output To ； wherein, and are soft threshold shrinkage functions controllable pre-mapping modules at the front and back; is a network first stage controllable pre-mapping layer high-frequency feature extractor, is a network first stage controllable pre-mapping layer residual reconstructor, is a network first stage controllable pre-mapping layer learnable shrinkage threshold.

7. The method of claim 6, wherein, In step 3d), the sparse ISAR high-resolution imaging network obtained has the following structure: Network input → Stage 1 gradient descent layer, controllable proximal mapping layer → … → Stage 2 gradient descent layer, controllable proximal mapping layer → … → Stage 2 gradient descent layer, controllable proximal mapping layer → Network output.

8. The method of claim 1, wherein, The loss value in each batch is calculated in step 5a) The network parameters are updated by a stochastic gradient descent algorithm, and the implementation steps include the following: 5a1) Select data of batch size from the training set each time, input into the sparse ISAR high-resolution imaging network to calculate the loss value in each batch : ； wherein, is norm, is the number of samples in each batch, denotes the reconstructed image output by the imaging network, denotes the ISAR image; 5a2) apply the complex domain back propagation algorithm to calculate the gradient of the loss function with respect to any parameter in the sparse ISAR high resolution imaging network , update the network parameters of the sparse ISAR high resolution imaging network according to the solved gradient , obtain the network parameters of the current training stage : ； wherein, is the network parameter of the sparse ISAR high-resolution imaging network in the training phase, represents the learning rate during training.

Images