ISAR robust imaging method based on sparse bayesian learning network

Abstract

The application discloses an ISAR robust imaging method based on a sparse Bayesian learning network, and mainly solves the problem that the prior art has poor imaging performance under a low signal-to-noise ratio condition and lacks robustness for echo imaging of different signal-to-noise ratios and defect rates. The implementation scheme is as follows: first, an ISAR sparse observation model under an echo defect condition is established, and a training set and a test set are constructed according to the observation model; then, a probability model is constructed according to the observation model, a 2D-IFGaPL algorithm is unfolded into a deep network according to the probability model, and a CNN is embedded into the deep network to form a main network; a super network is constructed to dynamically generate model parameters corresponding to echoes of different defect rates, and the model parameters are connected with the main network to form a sparse Bayesian learning network; and the training set is used to train the sparse Bayesian learning network, the test set is input into the trained network, and finally, an ISAR high-resolution imaging result is obtained. The application improves the imaging precision and robustness under a low signal-to-noise ratio condition, and can be used for ship-borne and aircraft-borne ISAR systems.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, and specifically relates to a robust ISAR imaging method that can be used in shipborne and airborne ISAR systems. Background Technology

[0002] Inverse Synthetic Aperture Radar (ISAR) is widely used in fields such as airborne target surveillance and space situational awareness, offering advantages such as all-weather, all-day operation, long range, and high-resolution imaging. Under ideal observation conditions such as high signal-to-noise ratio and complete echo, traditional Fourier analysis-based imaging methods, such as the range-Doppler RD algorithm, can obtain high-resolution focused images of stationary targets. However, in reality, the signal-to-noise ratio of the observed echoes from distant, weakly scattering targets is low and varies with the relative distance between the target and the radar during observation. Furthermore, interference suppression in adversarial environments and the switching of phased array radar operating modes lead to azimuth loss in the echoes, and the loss rate varies with radar resource allocation. These problems can cause a sharp decline in the performance of traditional imaging methods, or even their failure.

[0003] Leveraging the sparsity of ISAR images, ISAR imaging can be transformed into a sparse signal reconstruction problem, which can be solved using sparse signal reconstruction theory, including numerical optimization methods and sparse Bayesian learning methods. Numerical optimization methods struggle to determine optimal regularization parameters and exhibit significantly reduced imaging performance under low signal-to-noise ratio (SNR) conditions. Sparse Bayesian learning methods utilize prior information about the target and environment to construct statistical models, achieving high-resolution focused imaging in complex environments such as low SNR and echo defects. However, these methods often require numerous iterative steps, and their imaging performance is sensitive to hyperparameters, with hyperparameter tuning often being highly complex, resulting in time-consuming and inefficient algorithms. Existing ISAR imaging methods based on depth unfolding techniques unfold the iterative algorithm into a deep network and set the hyperparameters to be adjusted as learnable parameters, thus avoiding manual parameter tuning. However, due to the limited number of network parameters and the limited expressive power of the model, these methods can only be trained under fixed SNR and defect rates. When the echo SNR and defect rate change, the network often needs to be retrained, lacking robustness.

[0004] Patent document CN 117192548A discloses a high-resolution imaging method for sparse ISAR based on a deep unfolded network. This method first unfolds the 2D-ISTA algorithm into an imaging network consisting of a gradient descent layer and a near-end mapping layer. Then, a controllable near-end mapping module is embedded into the near-end mapping layer to construct a controllable near-end mapping layer. Finally, multiple gradient descent layers and controllable near-end mapping layers are cascaded to obtain the imaging network. While this method can achieve robust imaging within a certain signal-to-noise ratio and defect rate range, because it is based on a numerical optimization method, it cannot utilize prior information about the target and environment, resulting in poor imaging performance under low signal-to-noise ratio conditions.

[0005] Patent document CN 117706553A discloses an "ISAR Imaging Method Based on Sparse Bayesian Deep Unfolded Network." This method first unfolds a sparse Bayesian learning iterative algorithm into a deep network, and sets the adjustable parameters of the iterative algorithm as learnable parameters for the network. Then, it automatically updates the network parameters through end-to-end training. While this method can achieve good imaging results under low signal-to-noise ratio (SNR) conditions, it lacks robustness to different echo SNRs and defect rates. It requires separate training of the network under different SNR and defect rates, resulting in a large storage space requirement and long training time, leading to high cost and low imaging efficiency. Summary of the Invention

[0006] The purpose of this invention is to address the shortcomings of the prior art by proposing a robust ISAR imaging method based on a sparse Bayesian learning network, which reduces the training time of the network under different signal-to-noise ratios and loss rates, compresses storage space, and improves imaging robustness.

[0007] The technical approach of this invention is as follows: by unfolding the sparse Bayesian iterative algorithm into a finite-layer depth network with far fewer layers than the number of iterations required for convergence, the hyperparameters shared by each layer in the iterative algorithm and requiring fine-tuning are set as independent learnable parameters for each layer, thereby reducing the training time of the network and compressing storage space; by introducing a CNN into the image accuracy posterior estimation module of the unfolded network, the features of the intermediate image during the reconstruction process are learned, and by combining the unfolded network with the hypernetwork, the optimal parameters corresponding to echoes with different loss rates are generated, thereby improving the robustness of imaging.

[0008] Based on the above ideas, the implementation steps of the present invention include the following:

[0009] (1) Based on the distance dictionary A, the azimuth dictionary B, and the noise matrix N1, establish an ISAR sparse observation model under the condition of echo loss:

[0010] Y = AXB + N1

[0011] in, Represents the echo matrix. This represents an unknown ISAR image, where N represents the range dimension of the echo matrix, M represents the azimuth dimension of the echo matrix, P represents the range dimension of the ISAR image, and Q represents the azimuth dimension of the ISAR image.

[0012] (2) Constructing the training and testing sets:

[0013] 2a) Generate multiple sets of simulated label images where the positions and amplitudes of the scattering points follow different distributions;

[0014] 2b) Substitute the point simulation label image into the observation model to obtain the point simulation echo matrix Y1, and combine the simulation echo matrix with the point simulation label image to form a training set;

[0015] 2c) Use the echo data from the Yak-42 aircraft as the test set;

[0016] (3) Establish a probability model based on the ISAR sparse observation model:

[0017]

[0018] Where CN(Y) nm |A n· XB ·m ,α -1 ) indicates that the mean is A n· XB ·m The noise is a complex Gaussian distribution with precision α, and α follows a prior distribution p(α), X follows a conditional distribution p(X|Λ), and Y... nm A represents the element in the nth distance dimension and the mth azimuth dimension of the echo matrix. n· B represents the nth distance dimension in the distance dictionary. ·m Let m represent the m-th orientation dimension in the orientation dictionary, and Λ be the prior variance matrix of the image.

[0019] (4) Constructing a sparse Bayesian learning network:

[0020] 4a) Construct a deep network based on the probabilistic model and the iterative algorithm 2D-IFGaPL;

[0021] 4b) Construct a convolutional neural network (CNN) containing multiple convolutional modules and embed a deep network to obtain the main network;

[0022] 4c) Construct a supernetwork, connect the supernetwork to the main network to obtain a sparse Bayesian learning network, and select its loss function;

[0023] (5) Input the training set into the sparse Bayesian learning network and train it by backpropagation and gradient descent of the loss function to obtain the trained sparse Bayesian learning network.

[0024] (6) Input the test set into the trained sparse Bayesian learning network to obtain the final high-resolution ISAR imaging results.

[0025] Compared with the prior art, the present invention has the following advantages:

[0026] First, the sparse Bayesian learning network constructed in this invention makes full use of the prior information and statistical characteristics of the target and environment, thereby improving the imaging accuracy under low signal-to-noise ratio conditions.

[0027] Secondly, this invention introduces a convolutional neural network (CNN) into the image accuracy posterior expectation estimation module in the unfolded network to achieve robustness to the signal-to-noise ratio (SNR), and designs a super network to adaptively generate optimal hyperparameters corresponding to echoes with different defect rates to achieve robustness to the defect rate. It can achieve robust imaging of echoes with different SNRs and defect rates with only one training, thus improving imaging efficiency. Attached Figure Description

[0028] Figure 1 This is a flowchart illustrating the implementation of the present invention;

[0029] Figure 2 This is the network structure of the sparse Bayesian learning network constructed in this invention;

[0030] Figure 3 This is a comparison chart of the ISAR imaging performance of the present invention and existing technologies under different signal-to-noise ratios with a fixed defect rate.

[0031] Figure 4 This is a comparison chart of the ISAR imaging effects of the present invention and existing technologies under different defect rates with a fixed signal-to-noise ratio. Detailed Implementation

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

[0033] refer to Figure 1 This embodiment includes three main parts: model building, constructing a sparse Bayesian learning network, training the network, and obtaining the final imaging results.

[0034] Part 1: Model Building

[0035] Step 1: Establish an ISAR sparse observation model under echo loss conditions.

[0036] 1.1) Let the inverse synthetic aperture radar (ISAR) transmit a linearly frequency-modulated (LFM) signal. Then, the echo of the d-th scattering point after de-modulation of the LFM signal in the range-frequency-slow-time domain can be expressed as:

[0037]

[0038] Where d∈[1,D] represents the target scattering point index, σ d Let f be the back reflection coefficient at the d-th scattering point, c be the speed of light, B be the bandwidth, and f be the back reflection coefficient at the d-th scattering point. c For carrier frequency, f r For distance frequency, t m For slow time, ΔR d (t m ) represents the instantaneous slant distance from the d-th scattering point to the reference point, n1(t m () represents additive noise, and j is the imaginary unit. Represents a unit rectangle function;

[0039] 1.2) Based on the characteristic that a stable moving target has a small turning angle within a short imaging accumulation time, the instantaneous slant range ΔR is... d (t m Approximately expressed as:

[0040] ΔR d (t m ) = x d ωt m +y d <2>

[0041] Where x d and y d Let x and y represent the x and y coordinates of the d-th scattering point, respectively, and ω be the rotational angular frequency of the turntable model.

[0042] 1.3) will <2> Substitution <1> From the formula, we get:

[0043]

[0044] 1.4) Ignore steps <3> The distance element movement term in the formula yields the simplified distance frequency-slow time domain echo expression s. d '(f r ,t m ):

[0045]

[0046] 1.5) f r =nΔf and t m =mT Substitute <4> The discretized distance-frequency-slow-time domain echo can be expressed as follows:

[0047]

[0048] Where n∈[1,N] and m∈[1,M] represent the range and azimuth unit numbers respectively, Δf represents the range frequency interval, T represents the pulse repetition interval, N is the total number of echo range units in the discretized range frequency-slow time domain, and M is the total number of echo azimuth units in the discretized range frequency-slow time domain.

[0049] 1.6) To <5> Perform Fourier transforms on the range and azimuth directions to obtain the range-frequency-slow-time domain echo s after the Fourier transform. d '(m,n):

[0050]

[0051] Where i d(p,q) represents an element of the p-th range cell and the q-th azimuth cell in the ISAR image, where p∈[1,P] and q∈[1,Q] represent the range and azimuth cell indices, respectively. The ISAR image size is P×Q, where P is the dimension of the range direction of the ISAR image, Q is the dimension of the azimuth direction of the ISAR image, and c 1n Let c be the nth element in the distance-directed defect vector c1. 2m This is the m-th element in the azimuth defect vector c2;

[0052] 1.7) Let the expression for the distance between the complex field and the element in the complex field of the nth row and pth column of dictionary A be:

[0053]

[0054] in,

[0055] 1.8) Let the expression of the complex field element in the q-th row and m-th column of the complex field orientation dictionary B be:

[0056]

[0057] in,

[0058] 1.9) will <7> Mode, <8> Substitution <6> In the formula, <6> Transforming the equation into matrix form yields the observation model for ISAR images:

[0059] Y = AXB + N1.

[0060] In this embodiment, the size of the ISAR image is set, but not limited to, P=128, Q=128.

[0061] Step 2: Establish a probability model based on the ISAR sparse observation model.

[0062] 2.1) Let the noise precision α follow a prior distribution p(α):

[0063] p(α) = Gam(α|g,h),

[0064] Where Gam(α|g,h) indicates that the noise accuracy α follows a Gamma distribution, and g and h represent different hyperparameters of the prior distribution of the observation noise accuracy α;

[0065] 2.2) Suppose that the ISAR image X follows a conditional distribution p(X|Λ):

[0066]

[0067] Where L(X) pq |Λ pq ) represents X pqFollows a Laplace distribution, X pq Let Λ be an element of the p-th range dimension and the q-th azimuth dimension of the ISAR image, where P represents the range dimension of the ISAR image, Q represents the azimuth dimension of the ISAR image, and Λ is the azimuth dimension. pq Let p(Λ) be the element of the p-th distance dimension and q-th orientation dimension of the prior variance matrix of the image, and let p(Λ) be the element of its prior distribution. pq ) is represented as: p(Λ pq ) = Gam(Λ pq |1 / PQ,d), where 1 / PQ is the reciprocal of the product of the range and orientation dimensions of the ISAR image, and d is the observation Λ pq The hyperparameters of the prior distribution;

[0068] 2.3) Establish a probability model based on the prior distribution p(α) that the noise precision α follows and the conditional distribution p(X|Λ) that the ISAR image X follows:

[0069]

[0070] Where CN(Y) nm |A n· XB ·m ,α -1 ) indicates that the mean is A n· XB ·m The noise is a complex Gaussian distribution with precision α, and α follows a prior distribution p(α), X follows a conditional distribution p(X|Λ), and Y... nm A represents the element in the nth distance dimension and the mth azimuth dimension of the echo matrix. n· B represents the nth distance dimension in the distance dictionary. ·m Let m represent the m-th orientation dimension in the orientation dictionary, and Λ be the prior variance matrix of the image.

[0071] Step 3: Construct the training set and the test set.

[0072] 3.1) Generate multiple sets of simulated label images where the positions and amplitudes of the scattering points follow different distributions;

[0073] 3.2) Substitute the point simulation label image into the observation model Y=AXB+N1 to obtain the point simulation echo matrix after different degrees of defects and the addition of random signal-to-noise ratio noise, and combine the simulation echo matrix with the point simulation label image to form a training set;

[0074] 3.3) Use the echo data of the Yak-42 aircraft as the test set;

[0075] In this embodiment, the training set image size is set to, but is not limited to, 128×128, the echo defect rate range is set to, but is not limited to, 25% to 75%, the echo signal-to-noise ratio range is set to, but is not limited to, 1 to 11 dB, and the number of point simulation label images is set to, but is not limited to, 800.

[0076] Part Two: Constructing a Sparse Bayesian Learning Network.

[0077] Reference Figure 2 The implementation of this part includes the following:

[0078] Step 4: Construct a deep network based on the probability model and the iterative algorithm 2D-IFGaPL.

[0079] 4.1) Scaling the lower bound function of the Expected Maximum EM algorithm yields the iterative algorithm 2D-IFGaPL;

[0080] 4.2) Based on the probability model, the update expressions for multiple variables in the k1th iteration of the iterative algorithm 2D-IFGaPL are obtained:

[0081] 4.2.1) Obtain the update expression for the posterior expectation of the ISAR image in the k1th iteration using the iterative algorithm 2D-IFGaPL. for:

[0082]

[0083] in Let k be the posterior expectation of the noise accuracy in the (k1-1)th iteration. Let be the matrix representation of the auxiliary variables in the (k1-1)th iteration. Let be the posterior expectation matrix of the image accuracy in the (k1-1)th iteration. Let L1 be the posterior expectation of the ISAR image in the (k1-1)th iteration, L1 be the Lipschitz parameter in the k1th iteration, A be the distance dictionary, and B be the orientation dictionary. H This indicates taking the conjugate transpose of matrix A, B H This indicates taking the conjugate transpose of matrix B, where Y is the echo matrix and I is the identity matrix. This symbol represents element-wise division.

[0084] 4.2.2) Update expression based on the posterior expectation of the ISAR image The update expression in matrix form of the auxiliary variables is obtained in the k1th iteration. for:

[0085]

[0086] 4.2.3) Update expression based on the posterior expectation of the ISAR image Obtain the posterior expectation of the noise accuracy in the k1th iteration. The update expression is:

[0087]

[0088] in express The square of the norm, Let N be the posterior expectation of the ISAR image in the k1th iteration, where N represents the range dimension of the echo matrix, M represents the azimuth dimension of the echo matrix, and g and h represent two different hyperparameters of the prior distribution of the observation noise accuracy α.

[0089] 4.2.4) Update expression based on the posterior expectation of the ISAR image The posterior expectation matrix of image accuracy in the k1th iteration is obtained. element in row p and column q The update expression is:

[0090]

[0091] in for The 1 / PQ-3 order modified Bessel function of the second kind, for The 1 / PQ-2 order modified Bessel function of the second kind, Let d1 be the element of the p-th distance dimension and q-th azimuth dimension of the posterior expectation of the ISAR image in the k1-th iteration, where d1 is the observation. The hyperparameters of the prior distribution;

[0092] 4.3) Construct a deep network based on the update expression of multiple variables in the k1th iteration:

[0093] 4.3.1) Update the expression based on the posterior expectation of the ISAR image in the k1th iteration. The image posterior expectation estimation module of the k-th layer subnetwork of the deep network is obtained and used to calculate the image posterior expectation of the k-th layer subnetwork.

[0094] 4.3.2) Based on the matrix representation of the auxiliary variables in the k1th iteration The update expression yields the auxiliary variable estimation module for the k-th layer subnetwork of the deep network, which is used to compute the matrix representation of the auxiliary variables of the k-th layer subnetwork.

[0095] 4.3.3) Based on the posterior expectation of noise accuracy in the k1th iteration The update expression is used to obtain the noise accuracy posterior expectation estimation module of the k-th layer sub-network of the deep network, which is used to calculate the noise accuracy posterior expectation in the k-th layer sub-network.

[0096] 4.3.4) Based on the posterior expectation matrix of image accuracy in the k1th iteration The update expression is used to obtain the image accuracy posterior expectation estimation module of the k-th layer sub-network of the deep network, which is used to calculate the image accuracy posterior expectation matrix in the k-th layer sub-network.

[0097] 4.3.5) Connect the image posterior expectation estimation module of the k-th sub-network to the auxiliary variable estimation module, the noise accuracy posterior expectation estimation module, and the image accuracy posterior expectation estimation module to form the k-th sub-network. Then cascade the sub-networks to obtain a K-layer deep network.

[0098] In this embodiment, the different hyperparameters g and h of the prior distribution of observation noise accuracy α in each layer of the deep network are all set to, but are not limited to, 10. -4 .

[0099] Step 5: Construct a convolutional neural network (CNN) containing multiple convolutional modules, and embed it into a deep network to obtain the main network.

[0100] 5.1) Construct a second convolutional module a1 consisting of a standard convolutional layer with 16 input channels, 16 output channels, and a kernel size of 3×3, and a cascaded ReLU activation layer;

[0101] 5.2) Construct a second convolutional module a2 consisting of a standard convolutional layer with 16 input channels, 16 output channels, and a kernel size of 3×3, and a cascaded ReLU activation layer;

[0102] 5.3) Construct a third convolutional module a3 consisting of a standard convolutional layer with 16 input channels, 16 output channels, and a kernel size of 3×3, and a cascaded ReLU activation layer;

[0103] 5.4) Construct a third convolutional module a4 consisting of a standard convolutional layer with 16 input channels, 16 output channels, and a kernel size of 3×3, and a ReLU activation layer cascaded together;

[0104] 5.5) Construct a fifth convolutional module a5 consisting of a standard convolutional layer with 16 input channels, 16 output channels, and a kernel size of 3×3;

[0105] 5.6) Concatenate the five convolutional modules a1, a2, a3, a4, and a5 to form the first convolutional neural network f. θ Its output matrix element in row p and column q for:

[0106]

[0107] Where X pq Let d1 be the element in the p-th row and q-th column of the image posterior expectation, and d1 be the observation. The hyperparameters of the prior distribution, X pq | indicates that X pq Take the absolute value, where θ is the parameter of the first convolutional neural network.

[0108] 5.7) Embed the first convolutional neural network into the deep network, replacing the original image accuracy posterior expectation estimation module in the deep network, to obtain the main network.

[0109] Step 6: Construct a sparse Bayesian learning network and select its loss function.

[0110] 6.1) Construct a second convolutional neural network (CNN) consisting of five convolutional layers, three pooling layers, and one fully connected layer. Each convolutional layer has a kernel size of 3×3 and 32 channels. Each pooling layer has a kernel size of 2×2 and a stride of 2. The connection relationship is: first convolutional layer → second convolutional layer → first pooling layer → third convolutional layer → fourth convolutional layer → second pooling layer → fifth convolutional layer → third pooling layer → fully connected layer.

[0111] 6.2) Construct a fully connected network consisting of a fully connected layer, which is used to map 32 1×1 feature maps into a 2K vector, where K is the number of layers in the main network;

[0112] 6.3) Connect the second convolutional neural network (CNN) with a fully connected network to form a supernetwork. Its output consists of a set of Lipschitz parameters L and a set of hyperparameters d from the main network:

[0113]

[0114] in This is the RD image corresponding to the missing echo, where mask represents the missing mode and MR represents the echo missing rate.

[0115] 6.4) Connect the supernetwork to the main network to obtain a sparse Bayesian learning network;

[0116] 6.5) Select an existing loss function as the loss function for the sparse Bayesian learning network. Existing loss functions include the sum of squares of the Frobenius norm of the inter-image errors, the mean square error method, and the root mean square error method. In this embodiment, the sum of squares of the Frobenius norm of the inter-image errors is selected as the loss function for the sparse Bayesian learning network, which is expressed as follows:

[0117]

[0118] in This represents the imaging result corresponding to the i-th sample. N represents the label image of the i-th sample. t This represents the total number of training samples. express The sum of squares of the Frobenius norm.

[0119] Part Three: Training the Network and Obtaining the Final Imaging Results

[0120] Step 7: Train the sparse Bayesian learning network.

[0121] 7.1) Each time, select data of batch size from the training set and input it into the sparse Bayesian learning network to calculate the loss function L0 in each batch;

[0122] 7.2) Let the network parameters of the sparse Bayesian learning network be θ0, which can be expressed as:

[0123]

[0124] Where L is a set of Lipschitz parameters of the sparse Bayesian learning network, d is a set of hyperparameters of the sparse Bayesian learning network, and θ is the parameter of the first convolutional neural network in the sparse Bayesian learning network. Parameters of the supernetwork in a sparse Bayesian learning network;

[0125] 7.3) Let lr be the learning rate, and use backpropagation and gradient descent to calculate the gradient of the loss function L0 with respect to any parameter in the sparse Bayesian learning network. Based on the gradient obtained from the solution Update the network parameters of the sparse Bayesian learning network to obtain the network parameters θ1 for the current training phase:

[0126]

[0127] 7.4) After all the data in the training set has been selected, the loss functions obtained from all batches are summed and averaged to obtain the loss function after one round of network training.

[0128] 7.5) Repeat steps 7.1) to 7.4) above until... Convergence yields a well-trained sparse Bayesian learning network.

[0129] In this embodiment, all data in L are initialized to 0.5, and all data in d are initialized to 5. The parameters... Random initialization is used, and the batch size is set to 8 during training, with the learning rate (lr) set to 0.0001.

[0130] Step 8: Obtain the final high-resolution ISAR imaging results.

[0131] The test set is input into the trained sparse Bayesian learning network, and the final high-resolution ISAR imaging result is obtained through forward propagation of the network.

[0132] The effects of this invention can be further illustrated by the following simulation experiments:

[0133] I. Simulation Experiment Conditions:

[0134] The simulation experiment used a Windows 10 operating system and PyTorch 1.8.0 as the software platform, and an Intel Xeon Silver 4114 CPU and an NVIDIA GeForce RTX 3090 GPU as the hardware configuration.

[0135] The training set for the simulation experiment consists of eight sets of labeled images and their corresponding echo matrices. The position distribution of the scattering points in the first four sets of labeled images follows a uniform distribution. The amplitude distribution of the scattering points in the first set of labeled images follows a Gaussian distribution, the amplitude distribution of the scattering points in the second set of labeled images follows a chi-square distribution, the amplitude distribution of the scattering points in the third set of labeled images follows a gamma distribution, and the amplitude distribution of the scattering points in the fourth set of labeled images follows an exponential distribution. The position distribution of the scattering points in the last four sets of labeled images follows a Gaussian distribution, the amplitude distribution of the scattering points in the fifth set of labeled images follows a Gaussian distribution, the amplitude distribution of the scattering points in the sixth set of labeled images follows a chi-square distribution, the amplitude distribution of the scattering points in the seventh set of labeled images follows a gamma distribution, and the amplitude distribution of the scattering points in the eighth set of labeled images follows an exponential distribution. The training set contains 800 labeled images.

[0136] II. Simulation Content and Result Analysis:

[0137] Simulation 1: Under the above simulation conditions, with a fixed echo loss rate, the echo data of the Yak-42 aircraft were imaged using the present invention and the existing "ISAR imaging method based on sparse Bayesian deep unfolded network" at different signal-to-noise ratios. The results are as follows: Figure 3 ,in:

[0138] Figure 3 (a) is the imaging result obtained by existing technology on the measured echo data of Yak-42 aircraft under the conditions of 50% echo loss rate and 0dB echo signal-to-noise ratio.

[0139] Figure 3 (b) is the imaging result obtained by existing technology on the measured echo data of Yak-42 aircraft under the conditions of 50% echo loss rate and 5dB echo signal-to-noise ratio.

[0140] Figure 3(c) is the imaging result obtained by the present invention on the measured echo data of the Yak-42 aircraft under the condition that the echo loss rate is 50% and the echo signal-to-noise ratio is 0dB.

[0141] Figure 3 (d) is the imaging result obtained by the present invention on the measured echo data of the Yak-42 aircraft under the conditions of 50% echo loss rate and 5dB echo signal-to-noise ratio.

[0142] Depend on Figure 3 It can be seen that, with a fixed defect rate, the images obtained using existing technologies are sparser under different signal-to-noise ratios, while the imaging results of the present invention under different signal-to-noise ratios show more scattering points and a more complete target structure.

[0143] The structural similarity score (SSIM) and peak signal-to-noise ratio (PSNR) were calculated for the above imaging results, and the results are shown in Table 1.

[0144] Table 1. Overview of evaluation indicators for echo imaging results with different signal-to-noise ratios

[0145]

[0146] As can be seen from the evaluation indicators in Table 1, when the echo defect rate is constant, the imaging results of the present invention have greater structural similarity and higher peak signal-to-noise ratio under the two signal-to-noise ratio conditions. This indicates that the present invention has better imaging quality when the echo defect rate is constant and the signal-to-noise ratio varies.

[0147] Simulation 2: Under the above simulation conditions, with a fixed signal-to-noise ratio, the echo data of the Yak-42 aircraft were imaged using the present invention and the existing "ISAR imaging method based on sparse Bayesian depth unfolded network" at different echo loss rates. The results are as follows: Figure 4 ,in:

[0148] Figure 4 (a) is the imaging result obtained by existing technology on the measured echo data of Yak-42 aircraft under the conditions of 30% echo loss rate and 0dB echo signal-to-noise ratio.

[0149] Figure 4 (b) is the imaging result obtained by existing technology on the measured echo data of Yak-42 aircraft under the conditions of 50% echo loss rate and 0dB echo signal-to-noise ratio.

[0150] Figure 4 (c) is the imaging result obtained by the present invention on the measured echo data of Yak-42 aircraft under the conditions of 30% echo loss rate and 0dB echo signal-to-noise ratio.

[0151] Figure 4(d) is the imaging result obtained by the present invention on the measured echo data of the Yak-42 aircraft under the conditions of 50% echo loss rate and 0dB echo signal-to-noise ratio.

[0152] Depend on Figure 4 It can be seen that, with a fixed signal-to-noise ratio and varying defect rate, the imaging results obtained using existing technologies at both defect rates exhibit varying degrees of missing scattering points, while the imaging results obtained using this invention have complete structures and clear outlines.

[0153] The structural similarity score (SSIM) and peak signal-to-noise ratio (PSNR) were calculated for the above imaging results, and the results are shown in Table 2.

[0154] Table 2. Overview of Evaluation Indicators for Echo Imaging Results with Different Defect Rates

[0155]

[0156] As can be seen from the evaluation indicators in Table 2, the present invention has a greater structural similarity and a higher peak signal-to-noise ratio than the prior art when the signal-to-noise ratio is constant, resulting in better imaging quality under different defect rates.

[0157] In summary, the imaging results and evaluation indicators of ISAR echoes under conditions of fixed defect rate and different signal-to-noise ratios are superior to existing schemes. This verifies that when inverse synthetic aperture radar operates under conditions of sparse aperture in echo azimuth and low signal-to-noise ratio, the present invention can improve imaging quality and imaging efficiency. It also has the advantages of achieving automated parameter tuning through network training, avoiding manual parameter tuning.

[0158] The above description is merely a specific example of the present invention and does not constitute any limitation on the present invention. Obviously, those skilled in the art, after understanding the content and principles of the present invention, may make various modifications and changes in form and details without departing from the principles and structure of the present invention. However, these modifications and changes based on the ideas of the present invention are still within the scope of protection of the claims of the present invention.

[0159] It should be noted that the step numbers in the specification and claims of this invention are only for the purpose of clearly describing the embodiments of this invention and facilitating understanding, and their order is not limited.

Claims

1. A robust ISAR imaging method based on a sparse Bayesian learning network, characterized in that, Includes the following steps: (1) According to the distance dictionary directional dictionary noise matrix Establish an ISAR sparse observation model under echo loss conditions: ； in, Represents the echo matrix. , , , This represents an unknown ISAR image, where N represents the range dimension of the echo matrix, M represents the azimuth dimension of the echo matrix, P represents the range dimension of the ISAR image, and Q represents the azimuth dimension of the ISAR image. (2) Construct the training and test sets: 2a) Generate multiple sets of simulated label images where the positions and amplitudes of the scattering points follow different distributions; 2b) Substitute the point simulation label image into the observation model to obtain the point simulation echo matrix. The simulated echo matrix and the point simulated label image are combined to form a training set; 2c) Use the echo data from the Yak-42 aircraft as the test set; (3) Establish a probabilistic model based on the ISAR sparse observation model: ； in The mean is Noise accuracy is The complex Gaussian distribution, and Follows prior distribution , Follows conditional distribution , This represents the element in the nth distance dimension and the mth orientation dimension of the echo matrix. This represents the nth distance dimension in the distance dictionary. This represents the m-th orientation dimension in the orientation dictionary. The prior variance matrix of the image; (4) Constructing a sparse Bayesian learning network: 4a) Construct a deep network based on the probabilistic model and the iterative algorithm 2D-IFGaPL; 4b) Construct a convolutional neural network (CNN) containing multiple convolutional modules and embed it into a deep network to obtain the main network; 4c) Construct a supernetwork, connect the supernetwork to the main network to obtain a sparse Bayesian learning network, and select its loss function; (5) Input the training set into the sparse Bayesian learning network and train it by backpropagation and gradient descent of the loss function to obtain the trained sparse Bayesian learning network. (6) Input the test set into the trained sparse Bayesian learning network to obtain the final high-resolution ISAR imaging results.

2. The method according to claim 1, characterized in that, Step (1) Based on the distance dictionary directional dictionary noise matrix A sparse ISAR observation model under echo loss conditions is established, as follows: 1a) If the inverse synthetic aperture radar (ISAR) transmits a linear frequency modulated (LFM) signal, then the LFM signal after decoding is... The echo of a scattering point in the range-frequency-slow-time domain can be represented as: <1>； in Indicates the target scattering point number. For scattering points The back reflection coefficient, At the speed of light, For bandwidth, For carrier frequency, For distance frequency, For slow time, Indicates the first The instantaneous slant distance from each scattering point to the reference point. This represents additive noise, where j is the imaginary unit. Represents a unit rectangle function; 1b) Based on the characteristic that a stable moving target has a small turning angle during a short imaging accumulation time, the instantaneous slant range is... Approximately expressed as: <2>； in and They represent the first The x and y coordinates of each scattering point ω is the rotational angular frequency of the turntable model; 1c) will <2> Substitution <1> From the formula, we get: <3>； 1d) Ignore steps <3> The distance element movement term in the formula yields the simplified distance frequency-slow time domain echo equation. : <4>； 1e) will and Substitution <4> The discretized distance-frequency-slow-time domain echo can be expressed as follows: <5>； in , These represent the distance and azimuth unit numbers, respectively. Indicates the distance-frequency interval. Indicates the pulse repetition interval; 1f) To <5> Perform Fourier transforms on the range and azimuth directions to obtain the range-frequency-slow-time domain echoes after Fourier transform. : <6>； in The first in the ISAR image The distance unit is the Elements of each orientation unit, These represent the distance and azimuth unit numbers, respectively. Range-directed defect vector The first in One element, Azimuth defect vector The first in One element; 1g) Let the complex field distance dictionary The Line number The expression for the complex field element of the column is: <7>； in, , 1h) Let the complex field orientation dictionary The Line number The expression for the complex field element of the column is: <8> ； in, ; 1i) will <7> Mode, <8> Substitution <6> In the formula, <6> The equation is transformed into matrix form to obtain the observation model of ISAR images: 。 3. The method according to claim 1, characterized in that, Step 2a) generates multiple sets of simulated label images where the positions and amplitudes of the scattering points follow different distributions, as follows: 2a1) Four sets of scattering points were generated through simulation. The position distribution of each set of scattering points follows a uniform distribution. The amplitude distribution of the first set of scattering points follows a Gaussian distribution, the second set follows a chi-square distribution, the third set follows a gamma distribution, and the fourth set follows an exponential distribution. Each set of scattering points has a total of indivual, Each scattering point constitutes a dot-matrix label image. The simulated label images at various points constitute a set of simulated label images. ; 2a2) Four sets of scattering points were generated through simulation. The position distribution of each set of scattering points follows a Gaussian distribution. The amplitude distribution of the fifth set of scattering points follows a Gaussian distribution, the sixth set follows a chi-square distribution, the seventh set follows a gamma distribution, and the eighth set follows an exponential distribution. Each set of scattering points has a total of indivual, Each scattering point constitutes a dot-matrix label image. The simulated label images at various points constitute a set of simulated label images. .

4. The method according to claim 1, characterized in that, The point simulation echo matrix is ​​obtained in step 2b). , means as follows: ； in, Represents the simulated echo matrix at the point. Represents a dotted simulated label image; This represents the distance dimension of the simulated echo matrix at a point. This represents the azimuth dimension of the point simulation echo matrix. This represents the distance dimension of the simulated label image. This represents the orientation dimension of the simulated label image.

5. The method according to claim 1, characterized in that, In step (3), a probabilistic model is established based on the ISAR sparse observation model, as follows: 3a) Assume noise accuracy To conform to the prior distribution : ， in Indicates noise accuracy Following a Gamma distribution, g and h represent the accuracy of the observation noise. Different hyperparameters of the prior distribution; 3b) Assuming ISAR image Follows conditional distribution : ； in express Follows a Laplace distribution. Represents the first ISAR image distance Vydi Elements in each directional dimension Represents the distance dimension of the ISAR image. Indicates the orientation dimension of the ISAR image. The first element of the prior variance matrix of the image is... distance Vydi The prior distribution of elements in each orientation dimension. Represented as: , It is the reciprocal of the product of the range dimension and the orientation dimension of the ISAR image. For observation The hyperparameters of the prior distribution; 3c) Based on noise accuracy To obey the prior distribution With ISAR images Obeying the conditional distribution Establish a probability model: 。 6. The method according to claim 1, characterized in that, In step 4a), a deep network is constructed based on the probability model and the iterative algorithm 2D-IFGaPL, as follows: 4a1) Scaling the lower bound function of the Expected Maximum EM algorithm yields the iterative algorithm 2D-IFGaPL; 4a2) Based on the probability model, the multiple variables in the iterative algorithm 2D-IFGaPL are obtained. The update expression for the next iteration; 4a3) According to the first Posterior expectation of ISAR images in the next iteration The update expression is used to construct the image posterior expectation estimation module of the k-th layer subnetwork of the deep network; 4a4) According to the first Matrix representation of auxiliary variables in the next iteration The update expression is used to construct the auxiliary variable estimation module of the k-th layer subnetwork of the deep network; 4a5) According to the Posterior expectation of noise accuracy in the next iteration The update expression is used to construct the noise accuracy posterior expectation estimation module of the k-th layer subnetwork of the deep network; 4a6) According to the The posterior expectation matrix of image accuracy in the next iteration The update expression is used to construct the image accuracy posterior expectation estimation module of the k-th layer subnetwork of the deep network; 4a7) will the first The image posterior expectation estimation module of the layer sub-network is connected to the auxiliary variable estimation module, the noise accuracy posterior expectation estimation module, and the image accuracy posterior expectation estimation module to form the third... Layered sub-networks are then cascaded to obtain a K-layer deep network.

7. The method according to claim 1, characterized in that, Step 4b) Construct a convolutional neural network (CNN) containing multiple convolutional modules, as follows: 4b1) Construct the first convolutional module consisting of a standard convolutional layer with 16 input channels, 16 output channels, and a kernel size of 3×3, and a cascaded ReLU activation layer. ; 4b2) Construct a second convolutional module consisting of a standard convolutional layer with 16 input channels, 16 output channels, and a 3×3 kernel size, and a cascaded ReLU activation layer. ; 4b3) Construct a third convolutional module consisting of a standard convolutional layer with 16 input channels, 16 output channels, and a 3×3 kernel size, and a cascaded ReLU activation layer. ; 4b4) Construct a fourth convolutional module consisting of a standard convolutional layer with 16 input channels, 16 output channels, and a 3×3 kernel size, and a cascaded ReLU activation layer. ; 4b5) Construct a fifth convolutional module consisting of standard convolutional layers with 16 input channels, 16 output channels, and a kernel size of 3×3. ; 4b6) 5 convolutional modules , , , , Cascaded to form the first convolutional neural network Its output matrix element in row p and column q for: ； in Let p be the p-th row and q-th column element of the image posterior expectation. For observation The hyperparameters of the prior distribution, Indicates to Take the absolute value.

8. The method according to claim 1, characterized in that, Step 4c) involves constructing a supernetwork, which includes the following steps: 4c1) Construct a second convolutional neural network (CNN) consisting of five convolutional layers, three pooling layers, and one fully connected layer, where the kernel size of each convolutional layer is [size missing]. The number of channels is 32, and the size of the pooling kernel in each pooling layer is [value missing]. With a stride of 2, the connection relationship is: the first convolutional layer Second convolutional layer First pooling layer Third convolutional layer Fourth convolutional layer Second pooling layer Fifth convolutional layer Third pooling layer Fully connected layer; 4c2) Construct a fully connected network consisting of a fully connected layer; 4c3) Connect the second convolutional neural network (CNN) with a fully connected network to form a supernetwork. Its output is a set of Lipschitz parameters With a set of hyperparameters of the main network for: ； in This is the RD image corresponding to the missing echo. Indicates the defect pattern. This indicates the echo loss rate.

9. The method according to claim 1, characterized in that, In step 4c), the loss function is selected for the sparse Bayesian learning network, as shown below: ； in Indicates the first Imaging results corresponding to each sample Indicates the first Label images of each sample, This represents the total number of training samples. express The sum of squares of the Frobenius norm.

10. The method according to claim 1, characterized in that, In step (5), the training set is input into the sparse Bayesian learning network, and it is trained using backpropagation and gradient descent methods on the loss function, as follows: 5a) Each time, select data of batch size from the training set and input it into the sparse Bayesian learning network to calculate the loss function for each batch. ; 5b) Calculate the loss function using backpropagation and gradient descent. Gradients of arbitrary parameters in sparse Bayesian learning networks According to the gradient of the solution Update the network parameters of the sparse Bayesian learning network to obtain the network parameters for the current training phase. : ； in To learn the network parameters of a sparse Bayesian learning network, The learning rate; 5c) After all the data in the training set has been selected, the loss functions obtained from all batches are summed and averaged to obtain the loss function after one round of network training. ; 5d) Repeat steps 5a) through 5c) until... Convergence yields a well-trained sparse Bayesian learning network.

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