ISAR robust imaging method based on sparse Bayesian learning network

Abstract

The invention discloses an ISAR (inverse synthetic aperture radar) robust imaging method based on a sparse Bayesian learning network, which mainly solves the problems of poor imaging performance under the condition of low signal-to-noise ratio and lack of robustness for echo imaging with different signal-to-noise ratios and defect rates in the prior art. According to the implementation scheme, the method comprises the following steps: firstly, establishing an ISAR sparse observation model under an echo defect condition, and constructing a training set and a test set according to the observation model; constructing a probability model according to the observation model, expanding a 2D-IFGaPL algorithm into a deep network according to the probability model, and embedding a CNN into the deep network to form a main network; constructing a super network to dynamically generate model parameters corresponding to echoes with different defect rates, and connecting the model parameters with the main network to form a sparse Bayesian learning network; and training the sparse Bayesian learning network by using the training set, and inputting the test set into the trained network to obtain a final ISAR high-resolution imaging result. The method improves the imaging precision and robustness under the condition of low signal-to-noise ratio, and can be used for ship-borne and airborne ISAR (Inverse Synthetic Aperture Radar) systems.

Description

Technical Field

[0001] The invention belongs to the field of radar technology, and in particular relates to an ISAR robust imaging method, which can be used for shipborne and airborne ISAR systems. Background Art

[0002] Inverse synthetic aperture radar (ISAR) is widely used in the fields of aerial target monitoring and space situational awareness. It has the advantages of all-day, all-weather, 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 range-Doppler RD algorithm can be used to obtain high-resolution focused images of stable targets. However, in actual situations, the signal-to-noise ratio of the observed echo of long-range and weakly scattering targets is low, and changes with the relative distance between the target and the radar during the observation period; interference suppression in the confrontation environment and the switching of the phased array radar working mode lead to echo azimuth defects, and the defect rate changes with the radar resource scheduling. These problems will cause the performance of traditional imaging methods to drop sharply or even fail.

[0003] The sparse characteristics of ISAR images can be used to transform ISAR imaging into a sparse signal reconstruction problem, and the sparse signal reconstruction theory is used to solve it, including numerical optimization methods and sparse Bayesian learning methods. Among them, it is difficult for numerical optimization methods to determine the optimal regularization parameters and the imaging performance is significantly reduced under low signal-to-noise ratio conditions. The sparse Bayesian learning method uses the prior information of the target and the environment to construct a statistical model, which can achieve high-resolution focused imaging in complex environments such as low signal-to-noise ratio and echo defects. However, this type of method often requires a large number of cyclic iteration steps, and the imaging performance is sensitive to hyperparameters, and the hyperparameter tuning process is often very complicated, resulting in a long algorithm time and low efficiency. The existing ISAR imaging method based on deep unfolding technology unfolds the iterative algorithm into a deep network and sets the hyperparameters that need to be adjusted as learnable parameters, thereby avoiding the manual parameter adjustment steps. However, due to the small number of network parameters and limited model expression ability of this type of method, it can only be trained under fixed signal-to-noise ratio and defect rate conditions. When the echo signal-to-noise ratio and defect rate change, the network often needs to be retrained, which lacks robustness.

[0004] The patent document with application publication number CN 117192548A discloses a method called "Sparse ISAR High-resolution Imaging Method Based on Deep Unfolding Network", which first unfolds the 2D-ISTA algorithm into an imaging network of gradient descent layer and proximal mapping layer, then embeds the controllable proximal mapping module into the proximal mapping layer to construct a controllable proximal mapping layer, and finally cascades multiple gradient descent layers and controllable proximal mapping layers to obtain an imaging network. Although this method can achieve robust imaging within a certain range of signal-to-noise ratio and defect rate, it is a numerical optimization method and therefore cannot utilize prior information of the target and environment, resulting in poor imaging performance of the algorithm under low signal-to-noise ratio conditions.

[0005] The patent document with application number and publication number CN 117706553A discloses an ISAR imaging method based on sparse Bayesian deep unfolding network, which first unfolds the sparse Bayesian learning iterative algorithm into a deep network, and sets the adjustable parameters of the iterative algorithm as network learnable parameters, and then automatically updates the network parameters through end-to-end training. Although this method can obtain better imaging results under low signal-to-noise ratio conditions, it lacks robustness to different echo signal-to-noise ratios and defect rates, and needs to train the network separately under different signal-to-noise ratios and defect rates, resulting in the algorithm requiring a large storage space and a long training time, resulting in high cost and low imaging efficiency. Summary of the invention

[0006] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art and propose an ISAR robust imaging method based on a sparse Bayesian learning network to reduce the time consumption of training the network under different signal-to-noise ratios and defect rates, compress the storage space, and improve the imaging robustness.

[0007] The technical idea of ​​the present invention is: by expanding the sparse Bayesian iterative algorithm into a finite-layer deep network with a number of layers far less than the number of iterations required for iterative convergence, the hyperparameters shared by each layer in the iterative algorithm and requiring fine adjustment are set to independent learnable parameters of each layer, so as to reduce the time consumption of training the network and compress the storage space at the same time; by introducing CNN in the image accuracy posterior estimation module of the expanded network, the features of the intermediate images in the reconstruction process are learned, and by combining the expanded network with the hypernetwork, the optimal parameters corresponding to echoes with different defect rates are generated to improve the robustness of imaging.

[0008] According to 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, the ISAR sparse observation model under echo defect conditions is established:

[0010] Y=AXB+N1

[0011] in, represents the echo matrix, represents the unknown ISAR image, N represents the distance dimension of the echo matrix, M represents the azimuth dimension of the echo matrix, P represents the distance dimension of the ISAR image, and Q represents the azimuth dimension of the ISAR image;

[0012] (2) Construct training set and test set:

[0013] 2a) generating multiple groups of point simulation label images whose positions and amplitudes of scattering points obey different distributions;

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

[0015] 2c) The echo data of the Yak-42 aircraft is used as the test set;

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

[0017]

[0018] Among them, CN(Y nm |A n· XB ·m ,α -1 ) indicates that the mean is A n· XB ·m , a complex Gaussian distribution with noise precision α, and α obeys the prior distribution p(α), X obeys the conditional distribution p(X|Λ), Y nm Represents the element of the nth distance dimension and the mth azimuth dimension in the echo matrix, A n· Indicates the nth distance dimension in the distance dictionary, B ·m represents the mth orientation dimension in the orientation dictionary, Λ is the image prior variance matrix;

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

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

[0021] 4b) constructing a convolutional neural network (CNN) containing multiple convolutional modules and embedding it into a deep network to obtain a main network;

[0022] 4c) constructing a super network, connecting the super network with the main network to obtain a sparse Bayesian learning network, and selecting its loss function;

[0023] (5) Inputting the training set into the sparse Bayesian learning network, training it by back propagation method and gradient descent method of the loss function, and obtaining a 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 by the present invention makes full use of the prior information and statistical characteristics of the target and the environment, and improves the imaging accuracy under low signal-to-noise ratio conditions.

[0027] Second, the present invention introduces a convolutional neural network (CNN) in the image accuracy posterior expectation estimation module in the expanded network to achieve robustness to the signal-to-noise ratio, and designs a hypernetwork to adaptively generate optimal hyperparameters corresponding to echoes with different defect rates to achieve robustness to the defect rate. It only requires one training to achieve robust imaging of echoes with different signal-to-noise ratios and defect rates, thereby improving imaging efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 Implementation flow chart of the present invention;

[0029] Figure 2 The network structure of the sparse Bayesian learning network constructed in the present invention;

[0030] Figure 3 The figure is a comparison diagram of the ISAR imaging effects of the present invention and the prior art under the conditions of fixed defect rate and different signal-to-noise ratios.

[0031] Figure 4 The figure is a comparison diagram of the ISAR imaging effects of the present invention and the prior art under the conditions of fixed signal-to-noise ratio and different defect rates. DETAILED DESCRIPTION

[0032] The technical scheme and effects of the present invention are further described in detail below in conjunction with the accompanying drawings and embodiments.

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

[0034] Part 1: Building the Model

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

[0036] 1.1) Let the inverse synthetic aperture radar ISAR transmit a linear frequency modulation LFM signal. After demultiplexing the linear frequency modulation, the echo of the dth scattering point in the range frequency-slow time domain can be expressed as:

[0037]

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

[0039] 1.2) According to the characteristic that the stable moving target has a small rotation angle in a short imaging accumulation time, the instantaneous slant distance ΔR d (t m ) is approximately expressed as:

[0040] ΔR d (t m )=x d ωt m +y d <2>

[0041] where x d and d denote the horizontal and vertical coordinates of the dth scattering point, respectively, and ω is the rotation angular frequency of the turntable model;

[0042] 1.3) <2> Type <1> In the formula, we get:

[0043]

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

[0045]

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

[0047]

[0048] Where n∈[1,N], 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) Yes <5> The Fourier transform in the range and azimuth directions is performed using the Fourier transform to obtain the echo s in the range frequency-slow time domain after the Fourier transform. d '(m,n):

[0050]

[0051] where i d(p,q) is the element of the pth range unit and the qth azimuth unit in the ISAR image. p∈[1,P],q∈[1,Q] represent the range and azimuth unit numbers respectively. The size of the ISAR image is P×Q, where P is the dimension of the ISAR image in the range direction, Q is the dimension of the ISAR image in the azimuth direction, and c 1n is the nth element in the distance defect vector c1, c 2m is the mth element in the azimuth defect vector c2;

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

[0053]

[0054] in,

[0055] 1.8) Let the expression of the complex field element in the qth row and the mth column of the complex field orientation dictionary B be:

[0056]

[0057] in,

[0058] 1.9) <7> Mode, <8> Type <6> In the formula, <6> The observation model of ISAR image is obtained by converting the formula into matrix form:

[0059] Y=AXB+N1.

[0060] In this embodiment, the size of the ISAR image is set to 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) Assume that the noise accuracy α follows the prior distribution p(α):

[0063] p(α)=Gam(α|g,h),

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

[0065] 2.2) Assume that the ISAR image X obeys the conditional distribution p(X|Λ):

[0066]

[0067] Where L(X pq |Λ pq ) indicates X pqFollows Laplace distribution, X pq Represents the element of the pth distance dimension and the qth azimuth dimension of the ISAR image, P represents the distance dimension of the ISAR image, Q represents the azimuth dimension of the ISAR image, Λ pq Represents the element of the pth distance dimension and the qth orientation dimension of the image prior variance matrix, and its prior distribution p(Λ pq ) is expressed as: p(Λ pq )=Gam(Λ pq |1 / PQ,d), 1 / PQ is the inverse of the product of the distance dimension and the direction dimension of the ISAR image, and d is the observed Λ pq The hyperparameters of the prior distribution of ;

[0068] 2.3) A probability model is established based on the prior distribution p(α) obeyed by the noise accuracy α and the conditional distribution p(X|Λ) obeyed by the ISAR image X:

[0069]

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

[0071] Step 3: Construct training and test sets.

[0072] 3.1) Generate multiple sets of point simulation label images whose positions and amplitudes of scattering points obey different distributions;

[0073] 3.2) The point simulation label image is brought into the observation model Y=AXB+N1 to obtain a point simulation echo matrix with different degrees of defects and random signal-to-noise ratio noise added, and the simulation echo matrix is ​​combined with the point simulation label image to form a training set;

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

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

[0076] Part II: 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 iterative algorithm 2D-IFGaPL.

[0079] 4.1) Scaling the lower bound function of the expected maximum EM algorithm to obtain the iterative algorithm 2D-IFGaPL;

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

[0081] 4.2.1) According to the iterative algorithm 2D-IFGaPL, the updated expression of the ISAR image posterior expectation in the k1th iteration is obtained: for:

[0082]

[0083] in is the posterior expectation of noise accuracy in the k1-1th iteration, is the matrix representation of the auxiliary variables in the k1-1th iteration, is the image accuracy posterior expectation matrix of the k1-1th iteration, is the posterior expectation of the ISAR image in the k1-1th iteration, L1 is the Lipschitz parameter in the k1th iteration, A is the distance dictionary, B is the azimuth dictionary, and A H It means taking the conjugate transpose of matrix A, B H It means taking the conjugate transpose of matrix B, Y is the echo matrix, I is the unit matrix, Represents the element-by-element division symbol;

[0084] 4.2.2) Update expression based on the posterior expectation of ISAR image Get the update expression of the matrix representation of the auxiliary variables in the k1th iteration for:

[0085]

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

[0087]

[0088] in express The square of the norm, is the posterior expectation of the ISAR image in the k1th iteration, N represents the distance dimension of the echo matrix, M represents the azimuth dimension of the echo matrix, 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 ISAR image Get the image accuracy posterior expectation matrix of the k1th iteration The p-th row and q-th column element 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, is the element of the pth distance dimension and the qth azimuth dimension of the posterior expectation of the k1th iteration ISAR image, d1 is the observed The hyperparameters of the prior distribution of ;

[0092] 4.3) Construct a deep network based on the updated expressions of multiple variables at the k1th iteration:

[0093] 4.3.1) Based on the updated expression of the ISAR image posterior expectation in the k1th iteration Obtain an image posterior expectation estimation module of the k-th layer sub-network of the deep network, which is used to calculate the image posterior expectation of the k-th layer sub-network;

[0094] 4.3.2) According to the matrix representation of the auxiliary variables in the k1th iteration The update expression of obtains the auxiliary variable estimation module of the k-th layer sub-network of the deep network, which is used to calculate the matrix representation of the auxiliary variables of the k-th layer sub-network;

[0095] 4.3.3) According to the posterior expectation of noise accuracy at the k1th iteration The update expression of 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) According to the image accuracy posterior expectation matrix of the k1th iteration The update expression of derives 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) The image posterior expectation estimation module of the k-th 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 k-th layer sub-network, and then the sub-networks of each layer are cascaded to obtain a K-layer deep network;

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

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

[0100] 5.1) constructing a second convolution module a1 consisting of a cascade of a standard convolution layer with 16 input channels, 16 output channels, a convolution kernel size of 3×3, and a rectified linear unit (ReLU) activation layer;

[0101] 5.2) constructing a second convolution module a2 consisting of a cascade of a standard convolution layer with 16 input channels, 16 output channels, a convolution kernel size of 3×3, and a rectified linear unit (ReLU) activation layer;

[0102] 5.3) constructing a third convolution module a3 consisting of a cascade of a standard convolution layer with 16 input channels, 16 output channels, a convolution kernel size of 3×3, and a rectified linear unit (ReLU) activation layer;

[0103] 5.4) constructing a third convolution module a4 consisting of a cascade of a standard convolution layer with 16 input channels, 16 output channels, a convolution kernel size of 3×3, and a rectified linear unit (ReLU) activation layer;

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

[0105] 5.6) Cascade the five convolutional modules a1, a2, a3, a4, and a5 to form the first convolutional neural network f θ , whose output matrix The p-th row and q-th column element for:

[0106]

[0107] Where X pq is the pth row and qth column element of the image posterior expectation, and d1 is the observation The hyperparameters of the prior distribution of pq | indicates X pq Take the absolute value, θ is the parameter of the first convolutional neural network.

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

[0109] Step 6: Build 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, where the convolution kernel size of each convolutional layer is 3×3, the number of channels is 32, the size of the pooling kernel of each pooling layer is 2×2, the step size is 2, and 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 to the fully connected network to form a super network The output of a set of Lipschitz parameters L and a set of hyperparameters d of the main network are:

[0113]

[0114] in is the RD image corresponding to the defective echo, mask represents the defect pattern, and MR represents the echo defect rate;

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

[0116] 6.5) Select an existing loss function as the loss function of the sparse Bayesian learning network. The existing loss functions include the sum of squares of the Frobenius norm of the inter-image error, the mean square error method, and the root mean square error method. This embodiment selects but is not limited to the sum of squares of the Frobenius norm of the inter-image error as the loss function of the sparse Bayesian learning network, which is expressed as follows:

[0117]

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

[0119] Part 3: Training the network and obtaining the final imaging results

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

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

[0122] 7.2) Let the network parameter of the sparse Bayesian learning network be θ0, which is 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, θ is the parameter of the first convolutional neural network in the sparse Bayesian learning network, Parameters of the hypernetwork in sparse Bayesian learning networks;

[0125] 7.3) Let lr be the learning rate, and use the back-propagation method and gradient descent method to calculate the gradient of the loss function L0 with respect to any parameter in the sparse Bayesian learning network. According to the gradient of the solution Update the network parameters of the sparse Bayesian learning network to obtain the network parameters θ1 of the current training phase:

[0126]

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

[0128] 7.5) Repeat 7.1) to 7.4) until Converge and obtain a trained sparse Bayesian learning network.

[0129] In this embodiment, the data in L are initialized to 0.5, the data in d are initialized to 5, and the parameters Random initialization is used, the batch size is set to 8 during training, and the learning rate lr is 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 results are obtained through network forward propagation.

[0132] The effect of the present invention can be further illustrated by the following simulation experiment:

[0133] 1. Simulation experiment conditions:

[0134] The software platform of the simulation experiment is: Windows 10 operating system and Pytorch 1.8.0, and the hardware configuration is: Intel Xeon Silver 4114CPU and NVIDIA GeForce RTX 3090GPU.

[0135] The training set of the simulation experiment consists of eight groups of label images and their corresponding echo matrices. The position distribution of the scattering points of the first four groups of label images all obeys uniform distribution, the amplitude distribution of the scattering points of the first group of label images obeys Gaussian distribution, the amplitude distribution of the scattering points of the second group of label images obeys chi-square distribution, the amplitude distribution of the scattering points of the third group of label images obeys gamma distribution, and the amplitude distribution of the scattering points of the fourth group of label images obeys exponential distribution. The position distribution of the scattering points of the last four groups of label images all obeys Gaussian distribution, the amplitude distribution of the scattering points of the fifth group of label images obeys Gaussian distribution, the amplitude distribution of the scattering points of the sixth group of label images obeys chi-square distribution, the amplitude distribution of the scattering points of the seventh group of label images obeys gamma distribution, and the amplitude distribution of the scattering points of the eighth group of label images obeys exponential distribution. The number of label images in the training set is 800.

[0136] 2. Simulation content and result analysis:

[0137] Simulation 1: Under the above simulation conditions, the echo defect rate is fixed, and the Yak-42 aircraft echo data is imaged using the present invention and the existing "ISAR imaging method based on sparse Bayesian deep expansion 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 the prior art on the measured Yak-42 aircraft echo data when the echo defect rate is 50% and the echo signal-to-noise ratio is 0dB.

[0139] Figure 3 (b) is the imaging result obtained by the prior art on the measured Yak-42 aircraft echo data when the echo defect rate is 50% and the echo signal-to-noise ratio is 5dB.

[0140] Figure 3(c) is the imaging result obtained by the present invention from the measured Yak-42 aircraft echo data when the echo defect rate is 50% and the echo signal-to-noise ratio is 0 dB.

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

[0142] Depend on Figure 3 It can be seen that when the defect rate is fixed and the signal-to-noise ratio is different, the image obtained by using the prior art is sparser, while the imaging results of the present invention under different signal-to-noise ratio conditions have more scattering points and a more complete target structure.

[0143] The two imaging evaluation indicators, structural similarity SSIM and peak signal-to-noise ratio PSNR, are calculated for the above imaging results respectively. The results are shown in Table 1.

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

[0145]

[0146] It can be seen from the evaluation indicators in Table 1 that compared with the prior art, when the echo defect rate is constant, the imaging results of the present invention under two signal-to-noise ratio conditions have a greater structural similarity and a greater peak signal-to-noise ratio, indicating that the imaging quality of the present invention is better when the signal-to-noise ratio changes with a constant echo defect rate.

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

[0148] Figure 4 (a) is the imaging result obtained by the prior art on the measured Yak-42 aircraft echo data when the echo defect rate is 30% and the echo signal-to-noise ratio is 0dB.

[0149] Figure 4 (b) is the imaging result obtained by the prior art on the measured Yak-42 aircraft echo data when the echo defect rate is 50% and the echo signal-to-noise ratio is 0 dB.

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

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

[0152] Depend on Figure 4 It can be seen that when the signal-to-noise ratio is fixed and the defect rate changes, the imaging results obtained by the prior art at two defect rates have different degrees of missing scattering points, while the imaging results obtained by the present invention have a complete structure and a clear outline.

[0153] The two imaging evaluation indicators, structural similarity SSIM and peak signal-to-noise ratio PSNR, are calculated for the above imaging results respectively. The results are shown in Table 2.

[0154] Table 2 List of evaluation indicators for echo imaging results with different defect rates

[0155]

[0156] It can be seen from the evaluation indicators in Table 2 that compared with the prior art, when the signal-to-noise ratio is constant, the imaging results of the present invention under two defect rate conditions have greater structural similarity and a greater peak signal-to-noise ratio, indicating that the imaging quality of the present invention is better when the defect rate changes at a constant signal-to-noise ratio.

[0157] In summary, the imaging results and evaluation indicators of ISAR echoes under the conditions of fixed defect rate and different signal-to-noise ratios and fixed signal-to-noise ratio and different defect rates of the present invention are better than those of the existing schemes, which verifies that when the inverse synthetic aperture radar works under the conditions of echo azimuth sparse aperture and low signal-to-noise ratio, the present invention can improve the imaging quality and imaging efficiency, and at the same time has the advantages of realizing automatic parameter adjustment through network training and avoiding manual parameter tuning.

[0158] The above description is only a specific example of the present invention and does not constitute any limitation to the present invention. It is obvious that for professionals in this field, after understanding the content and principles of the present invention, it is possible to make various modifications and changes in form and details without departing from the principles and structures 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 the present invention are only for a clear description of the implementation scheme of the present invention to facilitate understanding, and the sequence of the step numbers is not limited.

Claims

1. A robust ISAR imaging method based on sparse Bayesian learning network, characterized in that: The steps include: (1) Based on the distance dictionary A, the azimuth dictionary B, and the noise matrix N1, the ISAR sparse observation model under echo defect conditions is established: Y=AXB+N1 in, represents the echo matrix, represents the unknown ISAR image, N represents the distance dimension of the echo matrix, M represents the azimuth dimension of the echo matrix, P represents the distance dimension of the ISAR image, and Q represents the azimuth dimension of the ISAR image; (2) Construct training set and test set: 2a) generating multiple groups of point simulation label images whose positions and amplitudes of scattering points obey different distributions; 2b) Bringing the point simulation label image into the observation model to obtain the point simulation echo matrix Y1, and combining the simulation echo matrix with the point simulation label image to form a training set; 2c) The echo data of the Yak-42 aircraft is used as the test set; (3) Establish a probability model based on the ISAR sparse observation model: Among them, CN(Y nm |A n· XB ·m ,α -1 ) indicates that the mean is A n· XB ·m , a complex Gaussian distribution with noise precision α, and α obeys the prior distribution p(α), X obeys the conditional distribution p(X|Λ), Y nm Represents the element of the nth distance dimension and the mth azimuth dimension in the echo matrix, A n· Indicates the nth distance dimension in the distance dictionary, B ·m represents the mth orientation dimension in the orientation dictionary, Λ is the image prior variance matrix; (4) Constructing a sparse Bayesian learning network: 4a) Constructing a deep network based on the probability model and iterative algorithm 2D-IFGaPL; 4b) constructing a convolutional neural network (CNN) containing multiple convolutional modules and embedding it into a deep network to obtain a main network; 4c) constructing a super network, connecting the super network with the main network to obtain a sparse Bayesian learning network, and selecting its loss function; (5) Inputting the training set into the sparse Bayesian learning network, training it by back propagation method and gradient descent method of the loss function, and obtaining a 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) establishes an ISAR sparse observation model under echo defect conditions based on the distance dictionary A, the azimuth dictionary B, and the noise matrix N1, which is implemented as follows: 1a) Let the inverse synthetic aperture radar ISAR transmit a linear frequency modulation LFM signal, then the echo of the dth scattering point in the range frequency-slow time domain after demultiplexing the linear frequency modulation can be expressed as: Where d∈[1,D] represents the target scattering point number, σ d is the back reflection coefficient of the scattering point d, c is the speed of light, B is the bandwidth, fc is the carrier frequency, fr is the distance frequency, tm is the slow time, ΔR d (t m ) represents the instantaneous slant distance from the dth scattering point to the reference point, n1(t m ) represents additive noise, j is an imaginary unit, represents the unit rectangle function; 1b) According to the characteristic that the stable moving target has a small rotation angle in a short imaging accumulation time, the instantaneous slant distance ΔR d (t m ) is approximately expressed as: ΔR d (t m )=x d ωt m +y d <2> where x d and d denote the horizontal and vertical coordinates of the dth scattering point, respectively, and ω is the rotation angular frequency of the turntable model; 1c) <2> Type <1> In the formula, we get: 1d) Ignore step <3> The distance unit movement term in the formula gives the simplified echo formula s in the distance frequency-slow time domain. d '(f r ,t m ): 1e) f r =nΔf and t m =mT Substitute <4> The discretized echo in the range frequency-slow time domain can be expressed as: Where n∈[1,N], 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; 1f) Yes <5> The Fourier transform in the range and azimuth directions is performed using the Fourier transform to obtain the echo s in the range frequency-slow time domain after the Fourier transform. d '(m,n): where i d (p,q) is the element of the pth range unit and the qth azimuth unit in the ISAR image. p∈[1,P],q∈[1,Q] represent the range and azimuth unit numbers respectively. The size of the ISAR image is P×Q, where P is the dimension of the ISAR image in the range direction, Q is the dimension of the ISAR image in the azimuth direction, and c 1n is the nth element in the distance defect vector c1, c 2m is the mth element in the azimuth defect vector c2; 1g) Let the expression of the complex field element in the nth row and pth column of the complex field distance dictionary A be: in, 1h) Let the expression of the complex field element in the qth row and the mth column of the complex field orientation dictionary B be: in, 1i) <7> Mode, <8> Type <6> In the formula, <6> The observation model of ISAR image is obtained by converting the formula into matrix form: Y=AXB+N1.

3. The method according to claim 1, characterized in that In step 2a), multiple groups of point simulation label images are generated, each of which has a different distribution of the position and amplitude of the scattering points, and the implementation is as follows 2a1) Generate the first four groups of scattering points through simulation, the position distribution of each group of scattering points obeys uniform distribution, and the amplitude distribution of the first group of scattering points obeys Gaussian distribution, the amplitude distribution of the second group of scattering points obeys chi-square distribution, the amplitude distribution of the third group of scattering points obeys gamma distribution, and the amplitude distribution of the fourth group of scattering points obeys exponential distribution. Each group of scattering points has a total of u×v, u scattering points constitute a point simulation label image, v point simulation label images constitute a group of simulation label images, v≥100,u≥300; 2a2) The last four groups of scattering points are generated by simulation. The position distribution of each group of scattering points obeys Gaussian distribution, and the amplitude distribution of the fifth group of scattering points obeys Gaussian distribution, the amplitude distribution of the sixth group of scattering points obeys chi-square distribution, the amplitude distribution of the seventh group of scattering points obeys gamma distribution, and the amplitude distribution of the eighth group of scattering points obeys exponential distribution. Each group of scattering points has a total of u×v, u scattering points constitute a point simulation label image, v point simulation label images constitute a group of simulation label images, v≥100,u≥300.

4. The method according to claim 1, characterized in that: The point simulation echo matrix Y1 obtained in step 2b) is expressed as follows: Y1=AXB+N1 in, Represents the point simulation echo matrix, Represents a distance dictionary, Indicates the direction dictionary, represents the noise matrix, represents the point simulation label image, N represents the distance dimension of the point simulation echo matrix, M represents the azimuth dimension of the point simulation echo matrix, P represents the distance dimension of the point simulation label image, and Q represents the azimuth dimension of the point simulation label image.

5. The method according to claim 1, characterized in that In step (3), a probability model is established based on the ISAR sparse observation model, which is implemented as follows: 3a) Assume that the noise accuracy α follows the prior distribution p(α): p(α)=Gam(α|g,h), Where Gam(α|g,h) indicates that the noise accuracy α follows the Gamma distribution, and g and h represent different hyperparameters of the prior distribution of the observed noise accuracy α; 3b) Assume that the ISAR image X obeys the conditional distribution p(X|Λ): Where L(Xpq|Λpq) represents X pq Follows Laplace distribution, X pq Represents the element of the pth distance dimension and the qth azimuth dimension of the ISAR image, P represents the distance dimension of the ISAR image, Q represents the azimuth dimension of the ISAR image, Λ pq Represents the element of the pth distance dimension and the qth orientation dimension of the image prior variance matrix, and its prior distribution p(Λ pq ) is expressed as: p(Λ pq )=Gam(Λ pq |1 / PQ,d1), 1 / PQ is the reciprocal of the product of the distance dimension and the direction dimension of the ISAR image, and d1 is the observed Λ pq The hyperparameters of the prior distribution of . 3c) A probability model is established based on the prior distribution p(α) obeyed by the noise accuracy α and the conditional distribution p(X|Λ) obeyed by the ISAR image X:

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, which is implemented as follows: 4a1) Scaling the lower bound function of the expected maximum EM algorithm to obtain the iterative algorithm 2D-IFGaPL; 4a2) obtaining the update expressions of the k1th iteration of multiple variables in the iterative algorithm 2D-IFGaPL according to the probability model; 4a3) According to the posterior expectation of the ISAR image in the k1th iteration The update expression of constructs the image posterior expectation estimation module of the k-th layer subnetwork of the deep network; 4a4) According to the matrix representation of the auxiliary variables in the k1th iteration The update expression of constructs the auxiliary variable estimation module of the k-th layer sub-network of the deep network; 4a5) According to the posterior expectation of noise accuracy at the k1th iteration The update expression of constructs the noise accuracy posterior expectation estimation module of the k-th layer sub-network of the deep network; 4a6) According to the image accuracy posterior expectation matrix of the k1th iteration The update expression of constructs the image accuracy posterior expectation estimation module of the k-th layer sub-network of the deep network; 4a7) The image posterior expectation estimation module of the k-th 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 k-th layer sub-network, and then the sub-networks of each layer are 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) constructing a first convolution module a1 consisting of a cascade of a standard convolution layer with 16 input channels, 16 output channels, a convolution kernel size of 3×3, and a rectified linear unit (ReLU) activation layer; 4b2) constructing a second convolution module a2 consisting of a cascade of a standard convolution layer with 16 input channels, 16 output channels, a convolution kernel size of 3×3, and a rectified linear unit (ReLU) activation layer; 4b3) constructing a third convolution module a3 consisting of a cascade of a standard convolution layer with 16 input channels, 16 output channels, a convolution kernel size of 3×3, and a rectified linear unit (ReLU) activation layer; 4b4) constructing a fourth convolution module a4 consisting of a cascade of a standard convolution layer with 16 input channels, 16 output channels, a convolution kernel size of 3×3, and a rectified linear unit (ReLU) activation layer; 4b5) constructing a fifth convolution module a5 consisting of a standard convolution layer with 16 input channels, 16 output channels, and a convolution kernel size of 3×3; 4b6) Cascade the five convolution modules a1, a2, a3, a4, and a5 to form the first convolutional neural network f θ , whose output matrix The p-th row and q-th column element for: Where X pq is the pth row and qth column element of the image posterior expectation, and d1 is the observation The hyperparameters of the prior distribution of pq | indicates X pq Take the absolute value.

8. The method according to claim 1, characterized in that In step 4c), a super network is constructed, and the implementation steps include the following: 4c1) Construct a second convolutional neural network CNN consisting of five convolutional layers, three pooling layers and one fully connected layer, where the convolution kernel size of each convolutional layer is 3×3, the number of channels is 32, the size of the pooling kernel of each pooling layer is 2×2, the step size is 2, and 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; 4c2) construct a fully connected network consisting of a fully connected layer; 4c3) Connect the second convolutional neural network CNN to the fully connected network to form a super network The output of a set of Lipschitz parameters L and a set of hyperparameters d of the main network are: in It is the RD image corresponding to the defective echo, mask represents the defect pattern, and MR represents the echo defect 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, which is expressed as follows: in represents the imaging result corresponding to the i-th sample, represents the label image of the i-th sample, N t represents the total number of training samples, express The sum of the 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 by back propagation and gradient descent of the loss function, as follows: 5a) Each time, a batch of data of a certain size is selected from the training set and input into the sparse Bayesian learning network to calculate the loss function L0 in each batch; 5b) Apply back propagation and gradient descent to calculate the gradient of the loss function L0 with respect to any parameter in the sparse Bayesian learning network According to the gradient of the solution Update the network parameters of the sparse Bayesian learning network to obtain the network parameters θ1 of the current training phase: Where θ0 is the network parameter of the sparse Bayesian learning network, and lr is the learning rate; 5c) After all the data in the training set are selected, the loss functions obtained from all batches are summed and averaged to obtain the loss function after one training of the network. 5d) Repeat 5a) to 5c) until Converge and obtain a trained sparse Bayesian learning network.

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