ISAR Imaging Method Based on Sparse Bayesian Deep Unfolding Network

Abstract

This invention discloses an ISAR imaging method based on a sparse Bayesian deep unfolding network. The steps are as follows: The sparse Bayesian learning iterative imaging algorithm is unfolded into a finite-layer sparse Bayesian deep unfolding network using algorithmic unfolding techniques; the hyperparameters of the prior distribution of target ISAR image accuracy and the Lipschitz constant in the sparse Bayesian iterative algorithm are set as independent learnable parameters for each layer of the network; the hyperparameters of the prior distribution of observation noise accuracy are set as shared learnable parameters for each layer of the network; the unfolded network is trained end-to-end, and the network parameters are automatically updated using an optimization algorithm. The sparse Bayesian deep unfolding network proposed in this invention has higher representation flexibility and can obtain ISAR imaging results with higher accuracy and better focusing. This unfolded network can automatically optimize parameters, achieving a higher degree of automation in ISAR focusing imaging.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, and more specifically relates to an inverse synthetic aperture radar (ISAR) imaging method based on a sparse Bayesian depth unfolding network within the field of radar signal processing technology. This invention enables two-dimensional high-resolution ISAR imaging even when the ISAR echo signal-to-noise ratio of non-cooperative targets in space and air is low, and when azimuth sparse apertures exist. Background Technology

[0002] Due to its advantages such as all-weather, all-day operation, long range, and high-resolution imaging, Inverse Synthetic Aperture Radar (ISAR) plays a crucial role in space and air target surveillance. In practical applications, ISAR typically faces complex observation environments such as low echo signal-to-noise ratio (SNR) and echo loss, where the performance of classical imaging methods deteriorates sharply or even fails. Because the distribution of target scattering points in ISAR images is sparse, the ISAR imaging problem under complex observation environments can be transformed into a sparse signal reconstruction problem. Sparse signal reconstruction methods are mainly divided into numerical optimization methods and sparse Bayesian learning methods. Although existing numerical optimization methods have advantages such as fast computation speed and the ability to obtain a globally optimal solution, their imaging performance deteriorates significantly under low SNR conditions, and they require manual setting of regularization coefficients to obtain a focused image. Sparse Bayesian learning methods fully utilize prior information about the target and environment to construct statistical probability models, enabling ISAR focused imaging in complex environments such as low signal-to-noise ratio and echo defects. However, the related algorithms still involve a large number of iterative steps and high computational complexity. Furthermore, the imaging performance of the algorithms is significantly affected by the hyperparameters of the prior distribution, requiring manual adjustment of the hyperparameters in the prior distribution of the probability model based on the target echo characteristics. This heavily relies on experience and expert knowledge, making it difficult to achieve automated real-time imaging.

[0003] Xi'an University of Electronic Science and Technology disclosed a fast two-dimensional ISAR imaging method based on sparse Bayesian learning in its invention patent application, "A Fast Two-Dimensional ISAR Imaging Method Based on Sparse Bayesian Learning" (Patent Application No.: 2021104313293, Publication No.: CN 113126095 A). The implementation steps of this method are as follows: sparse observation modeling of the echo signal; establishing a probability model based on the statistical characteristics of the target ISAR image and environmental noise; deriving the inverse-free solution steps for the posterior distribution parameters of the target ISAR image using the sparse Bayesian learning method; iteratively solving these steps to obtain the ISAR imaging result. This method has two shortcomings: firstly, the large number of iterative steps leads to a long imaging time; secondly, the method requires manual adjustment of hyperparameters according to different observation environments and target echo characteristics to obtain optimal imaging performance, resulting in low automation. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of the prior art by proposing an ISAR imaging method based on a sparse Bayesian depth unfolding network. This method solves the problems of long imaging time due to numerous iterative cycles and low automation due to manual parameter tuning under different observation environments and target echo conditions.

[0005] The approach to achieving the objective of this invention is as follows: A sparse ISAR observation model is established for radar echoes; the prior distributions of the target ISAR image and observation noise are defined; a two-dimensional iterative update formula for the approximate posterior distribution parameters of each variable in the sparse observation model is obtained using an iterative imaging algorithm based on sparse Bayesian learning; the sparse Bayesian learning iterative imaging algorithm is expanded into a finite-layer sparse Bayesian depth expansion network using algorithm expansion techniques; and the fixed prior distribution hyperparameters of the target ISAR image accuracy in the sparse Bayesian learning iterative imaging algorithm are then integrated with the network. The constants are set as independent learnable parameters for each layer of the network, while the prior distribution hyperparameter of the observation noise accuracy is set as a shared learnable parameter for each layer of the network. This contrasts with the sparse Bayesian learning iterative imaging algorithm, where each iteration uses a fixed prior distribution hyperparameter of the target ISAR image accuracy. The proposed sparse Bayesian deep unfolded network uses different image precision prior distribution hyperparameters and constants at different layers. Because it uses constants, the corresponding probability model is more flexible and has stronger representational capabilities. It can achieve higher accuracy and better focusing with far fewer network layers than existing technologies, reducing imaging time and improving imaging efficiency. Furthermore, this invention trains the unfolded network end-to-end and automatically updates network parameters using an optimization algorithm through gradient backpropagation, effectively improving the automation level of the algorithm and overcoming the problem of manual parameter tuning that heavily relies on experience and expert knowledge in existing technologies.

[0006] The specific steps of this invention are as follows:

[0007] Step 1: Construct a training set consisting of at least 200 data pairs;

[0008] Step 2: Establish a one-dimensional sparse observation model of ISAR for radar echoes of targets with small turning angles, define the radar echo observation noise and the prior distribution of the target ISAR image, and based on the one-dimensional sparse observation model of ISAR and the prior distribution of each variable in the model, use the sparse Bayesian learning iterative imaging algorithm to derive the two-dimensional iterative update formula of the approximate posterior distribution parameters of each variable in the model.

[0009] Step 3: Using algorithm expansion techniques, the iterative imaging algorithm's... The two-dimensional iterative update formula in the nth iteration maps to the nth iteration in the sparse Bayesian deep unfolded network. The four-variable approximate posterior distribution parameter update module in the layered subnetwork and The corresponding values ​​are equal. =1,2,…,K, where K represents the total number of layers in the sparse Bayesian deep unfolded network; the prior distribution hyperparameters in each subnetwork are... , , , and The constant is set as a learnable parameter of the network;

[0010] Step 4: Input the training set into the sparse Bayesian deep unfolded network, define the loss function, and implement an end-to-end method.

[0011] The network is trained by backpropagation of gradients and the network parameters are automatically updated using an optimization algorithm. When the loss function of the network converges, a well-trained sparse Bayesian deep unfolded network is obtained.

[0012] Step 5: Input the measured ISAR echo matrix with sparse aperture and noise into the trained sparse Bayesian depth unfolding network, and output the corresponding imaging result through the forward propagation of the network.

[0013] Compared with the prior art, the present invention has the following advantages:

[0014] First, this invention uses algorithmic unfolding techniques to unfold the sparse Bayesian learning iterative imaging algorithm into a finite-layer sparse Bayesian algorithm.

[0015] The Yess Deep Unfolding Network overcomes the shortcomings of existing technologies that require multiple iterations to estimate distribution parameters, resulting in long processing times. This invention achieves more efficient ISAR imaging processing with a network layer count that is much smaller than that required by existing technologies.

[0016] Second, this invention incorporates the hyperparameters of the prior distribution of target ISAR image accuracy in the sparse Bayesian iterative algorithm and The constants are set as independent learnable parameters for each layer of the network, and the hyperparameters of the prior distribution of observation noise accuracy are set as learnable parameters shared by each layer of the network. This overcomes the limitations of existing technologies that share the prior distribution hyperparameters of target ISAR image accuracy and the prior distribution hyperparameters of observation noise accuracy in each iteration step. The limitation of model representation ability caused by constants makes the sparse Bayesian depth unfolding network proposed in this invention more flexible in representation, and can obtain ISAR imaging results with higher accuracy and better focus.

[0017] Third, this invention trains the unfolded network in an end-to-end manner and uses optimization algorithms to automatically update the network parameters, overcoming the shortcomings of existing technologies that rely heavily on experience and expert knowledge for manual parameter tuning. This enables the invention to automatically tune parameters and achieve ISAR focusing imaging with a higher degree of automation. Attached Figure Description

[0018] Figure 1 This is a flowchart of the present invention;

[0019] Figure 2 A schematic diagram of the sparse Bayesian deep unfolded network constructed in this invention;

[0020] Figure 3 This is a simulation diagram of the present invention. Detailed Implementation

[0021] The present invention will now be further described with reference to the accompanying drawings and embodiments.

[0022] Reference Figure 1 The specific implementation steps of the embodiments of the present invention will be further described below.

[0023] Step 1: Construct a training set consisting of at least 200 data pairs.

[0024] Each data pair contains a random point simulated ISAR image label matrix and a sparse aperture noisy random point simulated ISAR echo matrix. Each data pair is generated by the following steps:

[0025] Step 1.1: Generate a random point simulation ISAR image label matrix from the data pair, generating a... A matrix of all zeros, randomly selected Each coordinate is assigned a value based on a two-dimensional coordinate system. The values ​​of each coordinate follow a complex Gaussian distribution and satisfy the following conditions: This yields a random point simulated ISAR image label matrix.

[0026] Step 1.2: Generate a random point simulation ISAR image label matrix from the data pairs. Corresponding sparse aperture noisy random point simulation ISAR echo matrix ,Will Substitute the following ISAR two-dimensional sparse observation model under sparse aperture conditions:

[0027]

[0028] in, This represents the noisy ISAR echo matrix under sparse aperture conditions. , Represents the ISAR image label matrix. , , These represent the distance dictionary matrix and the azimuth dictionary matrix under sparse aperture observation conditions, respectively. , , , Represents the noise matrix. , and These represent the number of sampling points for the echo of a pulse signal and the total number of transmitted pulses, respectively. and These represent the length and width of the ISAR image, respectively; in embodiments of the present invention, but not limited to, , , This indicates that the echo loss rate is [missing information]. .

[0029] Step 2: Establish a one-dimensional sparse observation model of ISAR for radar echoes of targets with small turning angles, define the radar echo observation noise and the prior distribution of the target ISAR image, and based on the one-dimensional sparse observation model of ISAR and the prior distribution of each variable in the model, use the sparse Bayesian learning iterative imaging algorithm to obtain the two-dimensional iterative update formula of the approximate posterior distribution parameters of each variable in the model.

[0030] Step 2.1: The target echo received by the radar at a small turning angle, after demodulation and frequency modulation processing, is represented in the range-frequency-slow time domain as follows:

[0031]

[0032] in, This represents the radar echo of a small-angle target after demodulation and frequency modulation processing. Indicates the first target The reflection coefficient of each scattering center , These represent the echo center frequency and the speed of light, respectively. Indicates distance frequency, Indicates the bandwidth of the transmitted signal. , Indicates the first The position coordinates of each scattering center in the reference coordinate system , These represent the target rotation angular frequency and the slow time, respectively. The echo... Discretizing and representing it in matrix form yields the ISAR two-dimensional sparse observation model:

[0033]

[0034] in, This represents noisy ISAR echoes under sparse aperture conditions. , Represents a two-dimensional target ISAR image. , , These represent the distance dictionary and the orientation dictionary under sparse aperture observation conditions, respectively. , , , and These represent the number of sampling points for the echo of a pulse signal and the total number of transmitted pulses, respectively. and These represent the length and width of the two-dimensional target ISAR image, respectively. Represents the observation noise matrix. Since sparse signal reconstruction algorithms are applicable to one-dimensional signal models, the properties of the Kronecker product are used to transform the ISAR two-dimensional sparse observation model into an ISAR one-dimensional sparse observation model:

[0035]

[0036] in, This represents the noisy observation echo of a one-dimensional sparse aperture. , Represents a one-dimensional target ISAR image. , This represents one-dimensional observation noise. , A dictionary representing sparse observations. , This indicates that the operation stacks the matrices column-wise into a vector. This indicates the transpose operation. This represents the Kronecker product operation.

[0037] Step 2.2: In order to fully utilize the prior information of the ISAR image to achieve a smaller image entropy in the imaging result, and to reduce radar echo observation noise... and target ISAR images The prior distribution of follows a complex Gaussian distribution, and its probability density function is as follows:

[0038]

[0039] in, This represents the prior probability density function. Indicates a complex Gaussian distribution. Indicates the accuracy of observation noise. This indicates the inverse operation. Represents the identity matrix. The precision matrix representing the target ISAR image is a column vector whose diagonal elements are... The diagonal matrix is ​​used to further strengthen the sparsity constraint on the imaging results and improve the accuracy of observation noise. The first diagonal of the target ISAR image accuracy matrix item The prior distribution follows a Gamma distribution, with the following probability density function:

[0040]

[0041] in, Represents the Gamma distribution. , Indicates the accuracy of observation noise The prior distribution hyperparameters, , The first line represents the diagonal of the target ISAR image precision matrix. item The prior distribution hyperparameters. All four hyperparameters need to be manually tuned based on experience and expert knowledge.

[0042] Step 2.3, combining the ISAR one-dimensional sparse observation model and the prior distribution of each model variable, the specific steps for solving the above model using the sparse Bayesian learning iterative imaging algorithm—two-dimensional fast mean-field sparse Bayesian learning (2D-FMFSBL) algorithm—are as follows:

[0043] Based on the "mean field" assumption, the approximate total a posteriori distribution of all variables in the model is used. break down:

[0044]

[0045] in, This represents the approximate posterior probability density function.

[0046] Let the target ISAR image Approximate posterior probability density function It can be in the following form:

[0047]

[0048] in, express Expectations express The variance is the column vector corresponding to the diagonal elements. The diagonal matrix is ​​obtained using the VI algorithm to obtain the first... Variables The formula for calculating the approximate posterior distribution is as follows:

[0049]

[0050] in, express The approximate posterior distribution hyperparameter, This represents a constant that is independent of all model variables. Denotes the joint likelihood probability density function. Indicates to about Integration operations, .

[0051] Substituting the prior distributions of each variable in the model into the approximate posterior distribution calculation formula, we obtain the observation noise accuracy. The column vector corresponding to the diagonal elements of the target ISAR image precision matrix Approximate posterior probability density function , as follows:

[0052]

[0053] in, , Represents the approximate posterior distribution The distribution parameters, Indicates the length of the radar echo vector. This indicates the conjugate transpose operation. This represents the operation of extracting diagonal elements to form a column vector. This indicates a multiplication operation. Indicates the length of the target ISAR image vector. , Represents the approximate posterior distribution The distribution parameters, and They represent the approximate posterior distributions, respectively. Expectations and The variance of the diagonal elements corresponds to the column vector. The item, This indicates the conjugate operation;

[0054] use Norms in the complex field Lemma-scaling variational lower bound yields relaxed lower bound The specific formula is as follows:

[0055] ;

[0056] in, Represents auxiliary variables. Expressing the request Norm squaring operation express constant, This represents the operation of calculating the expectation of a variable. This indicates the operation of taking the real part. This represents the summation operation. Representation and Variables Irrelevant constant terms. Expected accuracy of observation noise. and ISAR image accuracy expectation matrix Substitute the lower bound of relaxation ,make , Get the first In the next iteration and Update formula:

[0057]

[0058] in, and They represent the first The second iteration and the first Variables at the next iteration Let represent the expected operation, let , This represents the first element of the column vector formed by taking the diagonal elements. item;

[0059] Using the properties of the Kronecker product, the one-dimensional iterative update formula for each variable in the model is transformed into the following two-dimensional iterative update formula:

[0060]

[0061] in, , , In order to represent , and In matrix form, , This indicates the operation of finding the largest eigenvalue. and Let and represent the conjugate transposes of the distance dictionary matrix and the distance dictionary matrix, respectively. and Let represent the conjugate transposes of the orientation dictionary matrix and the orientation dictionary matrix, respectively. This indicates a division operation on the corresponding element. This indicates that all elements are 1. A 3D matrix This indicates the operation of calculating the Hadamard product. This represents the operation of squaring the F-norm. This represents the summation operation on all elements of the matrix;

[0062] When the relative error between two adjacent target ISAR images satisfies At that time, the final imaging result is obtained. , For the set error threshold, This indicates the operation of calculating the F-norm.

[0063] Step 3: Using algorithm expansion techniques, the iterative imaging algorithm's... The two-dimensional iterative update formula in the nth iteration maps to the nth iteration in the sparse Bayesian deep unfolded network. The four-variable approximate posterior distribution parameter update module in the layered subnetwork and The corresponding values ​​are equal. =1,2,…,K, where K represents the total number of layers in the sparse Bayesian deep unfolded network; the prior distribution hyperparameters in each subnetwork are... , , , and The constants are set as learnable parameters. The structure of the sparse Bayesian deep unfolded network constructed in the embodiments of the present invention is as follows: Figure 2 As shown.

[0064] Step 3.1, the first The two-dimensional iterative update formula in the nth iteration maps to the nth iteration in the sparse Bayesian deep unfolded network. The four-variable approximate posterior distribution parameter update module in the layered subnetwork and The corresponding values ​​are equal. =1,2,…,K, where K represents the total number of layers in the sparse Bayesian deep unfolded network. In embodiments of the present invention, the number of layers in the sparse Bayesian deep unfolded network is set to, but is not limited to, 12. The four-variable approximate posterior distribution parameter update module in the layered subnetwork includes:

[0065] The target ISAR image approximate posterior expectation update module performs the following operations:

[0066]

[0067] in, and They represent the first Sub-networks and the first Variables in a layered subnetwork Indicates the first In layered networks constant;

[0068] The target ISAR image approximate posterior variance update module performs the following operations:

[0069]

[0070] The target ISAR image accuracy approximate posterior expectation update module performs the following operations:

[0071]

[0072] in, and Indicates the first Observation noise accuracy in layered networks The prior distribution hyperparameters;

[0073] The observation noise accuracy approximate posterior expectation update module performs the following operations:

[0074]

[0075] in, and Indicates the first The first diagonal of the target ISAR image accuracy matrix in the layered sub-network item The prior distribution hyperparameters.

[0076] The first The outputs of the four modules in the layered network , , and The first The sub-networks, following this pattern, cyclically pass through the layers, eventually reaching the output layer.

[0077] Step 3.2: Extract the prior distribution hyperparameters from all layers of the sparse Bayesian depthwise unfolded network. , Set the learnable parameters shared by all layers, and expand the sparse Bayesian deep unfolded network to the level of... Prior distribution hyperparameters of layered subnetworks , and constant Set as learnable parameters independent for each layer. =1,2,…,K.

[0078] Step 4: Input the training set into the sparse Bayesian deep unfolded network, define the loss function, and implement an end-to-end method.

[0079] The network is trained by backpropagation of gradients and the network parameters are automatically updated using an optimization algorithm. When the loss function of the network converges, a well-trained sparse Bayesian deep unfolded network is obtained.

[0080] Step 4.1, make the radar echo with noise in the two-dimensional sparse aperture. Two-dimensional target ISAR image as network input As network output.

[0081] The loss function is defined as follows:

[0082]

[0083] in, This means drawing a batch of data pairs from the training set. and These represent the outputs of the sparse Bayesian depth expansion network. The first two-dimensional target ISAR image and its corresponding second A two-dimensional target label image, This indicates a summation operation.

[0084] Step 4.2: Set the number of training algebras and initialize the learnable parameters. In this example, the number of training algebras is set to, but is not limited to, 150, and the initial values ​​for each learnable parameter are set to, but are not limited to, [missing information]. , , , .

[0085] Step 4.3: Through gradient backpropagation, the network parameters are automatically updated using an optimization algorithm. When the network's loss function converges, the trained sparse Bayesian deep unfolded network is obtained.

[0086] The Adam optimization algorithm is used to optimize the network's learnable parameter set. renew, Represents the set of learnable parameters of a network. The first in One parameter.

[0087] Adam optimization algorithm on parameters The specific update steps are as follows:

[0088] First step, calculate the... Learnable parameters in layered networks Partial first moment estimator and partial second moment estimator :

[0089]

[0090] in, and They represent the first Learnable parameters in layered networks The partial first-order moment estimator and the partial second-order moment estimator This represents the loss function with respect to learnable parameters. gradient, and This represents hyperparameters.

[0091] The second step is to calculate the first-moment estimator for bias correction. Second-order moment estimator with bias correction :

[0092]

[0093] The third step is to use the bias-corrected first-moment estimator. and second-order moment estimator For the first Learnable parameters in layered networks The update formula is as follows:

[0094]

[0095] in, , They represent the first Sub-networks and the first Learnable parameters in layered subnetworks The parameter value, Indicates the learning rate. This represents the error constant. In this example, it represents the learning rate. Suppose, but not limited to .

[0096] For observed echoes under observation conditions with a defined signal-to-noise ratio and loss rate, a sparse Bayesian deep expansion network suitable for echoes under the corresponding observation conditions is trained separately.

[0097] Step 5: Input the measured ISAR echo matrix with sparse aperture and noise into the trained sparse Bayesian depth unfolding network, and output the corresponding imaging result through the forward propagation of the network.

[0098] In an embodiment of the present invention, measured data of the Yak-42 aircraft is used as a test set. That is, the echo matrix of the Yak-42 aircraft obtained under various signal-to-noise ratios and loss rates is input into the unfolded network trained under the same observation conditions to obtain high-resolution images of the Yak-42 aircraft.

[0099] The numbering in the above steps is for the purpose of clearly illustrating the implementation of the present invention, and the order of the numbers is not limited.

[0100] The effects of the present invention will be further described through the following simulation experiments.

[0101] 1. Simulation experimental conditions:

[0102] The hardware platform for the simulation experiment of this invention is: Core i9-10920X CPU and NVIDIA GeForce RTX3090.

[0103] GPU.

[0104] The software platform for the simulation experiment of this invention is: Windows 10 operating system and PyTorch 1.8.0.

[0105] The training set of the simulation experiments in this invention consists of randomly distributed, Gaussian-distributed simulated ISAR images, containing 200 data pairs. Each data pair includes a random-point simulated ISAR image label and a corresponding sparse-aperture, noisy, random-point simulated ISAR echo, where the azimuth loss rate of the observed echo is 50%. The test set consists of ISAR images corresponding to measured data from the Yak-42 aircraft under full-aperture, high signal-to-noise ratio conditions, containing one data pair. Each data pair includes a measured ISAR image label and a sparse-aperture, noisy measured ISAR echo, where the azimuth loss rate of the observed echo is also 50%. The label images of both the training and test sets have a dimension of [missing information]. .

[0106] 2. Simulation content and result analysis:

[0107] The simulation experiment of this invention uses the present invention and a prior art to conduct imaging experiments on the echo data of the Yak-42 aircraft under observation conditions of ISAR echo signal-to-noise ratio of 0dB and 10dB, and azimuth loss rate of 50%. Specifically, the present invention uses a network trained on a training set with the same signal-to-noise ratio and loss rate as the Yak-42 aircraft's measured echo data for testing, while the prior art involves manually adjusting parameters for imaging.

[0108] The existing technologies used in simulation experiments refer to:

[0109] Xi'an University of Electronic Science and Technology proposed a fast two-dimensional ISAR imaging method based on sparse Bayesian learning in its patent application document "A fast two-dimensional ISAR imaging method based on sparse Bayesian learning" (application number: 2021104313293, application publication number: CN 113126095 A).

[0110] The results of the imaging experiments using the two methods are as follows Figure 3 As shown. Wherein:

[0111] Figure 3 (a) is the imaging result of the prior art under the conditions of 0dB echo signal-to-noise ratio and 50% defect rate;

[0112] Figure 3 (b) is the imaging result of the prior art under the conditions of an echo signal-to-noise ratio of 10dB and a defect rate of 50%;

[0113] Figure 3 (c) shows the imaging results of this invention under the conditions of 0dB echo signal-to-noise ratio and 50% defect rate.

[0114] Figure 3 (d) shows the imaging results of the present invention under the conditions of an echo signal-to-noise ratio of 10dB and a defect rate of 50%.

[0115] Figure 3 The horizontal axis of each image represents the orientation unit of the imaging result, and the vertical axis represents the distance unit of the imaging result.

[0116] Depend on Figure 3 As can be seen from (a) and (b), the imaging results obtained using existing techniques under both signal-to-noise ratio conditions are too sparse, resulting in the loss of some target structures in the imaging results. Figure 3 (c)(d) and Figure 3 As can be seen from the comparison of (a) and (b), in the imaging results obtained by the method proposed in this invention under the two signal-to-noise ratio conditions, the target scattering point has a higher relative brightness to the background, a more complete structure, and better image focusing.

[0117] For the above imaging results, three evaluation metrics were calculated: structural similarity, image entropy, and single-image imaging time.

[0118] The indicators and results are shown in Table 1.

[0119] Table 1. Overview of Evaluation Indicators for Echo Imaging Results of Measured Data under a 50% Azimuthal Defect.

[0120]

[0121] As can be seen from the evaluation indicators in Table 1, the imaging results of the present invention are more structurally similar to the tag images under the two signal-to-noise ratio conditions than the prior art, with lower image entropy and shorter single-image imaging time, indicating that the imaging quality of the present invention is better and the imaging speed is faster.

[0122] In summary, this invention outperforms existing schemes in imaging results and evaluation metrics for ISAR echoes under conditions of fixed defect rate and different signal-to-noise ratios. It verifies that when inverse synthetic aperture radar operates under conditions of sparse aperture in echo azimuth and low signal-to-noise ratio, this invention can improve imaging quality and imaging efficiency. It also has advantages such as achieving automated parameter tuning through network training, avoiding manual parameter optimization.

Claims

1. An ISAR imaging method based on a sparse Bayesian depth unfolded network, characterized in that, A two-dimensional iterative update formula for the approximate posterior distribution parameters of each variable in the ISAR sparse observation model is obtained using an iterative imaging algorithm based on sparse Bayesian learning. The sparse Bayesian learning iterative imaging algorithm is then expanded into a sparse Bayesian deep unfolding network using algorithm expansion techniques. The specific steps of this imaging method include the following: Step 1: Construct a training set consisting of at least 200 data pairs; each data pair contains a random point simulated ISAR image label matrix and a sparse aperture noisy random point simulated ISAR echo matrix. Step 2: Establish a one-dimensional sparse observation model of ISAR for radar echoes of targets with small turning angles, define the radar echo observation noise and the prior distribution of the target ISAR image, and based on the one-dimensional sparse observation model of ISAR and the prior distribution of each variable in the model, use the sparse Bayesian learning iterative imaging algorithm to derive the two-dimensional iterative update formula of the approximate posterior distribution parameters of each variable in the model. Step 3: Using algorithm expansion techniques, the iterative imaging algorithm's... The two-dimensional iterative update formula in the nth iteration maps to the nth iteration in the sparse Bayesian deep unfolded network. The four-variable approximate posterior distribution parameter update module in the layered subnetwork and The corresponding values ​​are equal. =1,2,…,K, where K represents the total number of layers in the sparse Bayesian deep unfolded network; the prior distribution hyperparameters in each subnetwork are... , , , and The constant is set as a learnable parameter of the network; Step 4: Input the training set into the sparse Bayesian deep unfolded network, define the loss function and train the unfolded network in an end-to-end manner. Through gradient backpropagation, the network parameters are automatically updated using the optimization algorithm. When the network's loss function converges, the trained sparse Bayesian deep unfolded network is obtained. Step 5: Input the measured ISAR echo matrix with sparse aperture and noise into the trained sparse Bayesian depth unfolding network, and output the corresponding imaging result through the forward propagation of the network.

2. The ISAR imaging method based on sparse Bayesian depth unfolded network according to claim 1, characterized in that, The data pair described in step 1 is generated by the following steps: The first step is to generate a simulated ISAR image label matrix for random points in the data pair, thus generating a... A matrix of all zeros, randomly selected Each coordinate is assigned a value based on a two-dimensional coordinate system. The values ​​of each coordinate follow a complex Gaussian distribution and satisfy the following conditions: This yields a random point simulated ISAR image label matrix; where, and These represent the length and width of the ISAR image, respectively. The second step is to generate a simulated ISAR image label matrix for random points in the data pairs. Corresponding sparse aperture noisy random point simulation ISAR echo matrix ,Will Substitute the following ISAR two-dimensional sparse observation model under sparse aperture conditions: ； in, This represents the noisy ISAR echo matrix under sparse aperture conditions. , and These represent the number of sampling points for the echo of a pulse signal and the total number of transmitted pulses, respectively. Represents the ISAR image label matrix. , , These represent the distance dictionary matrix and the azimuth dictionary matrix under sparse aperture observation conditions, respectively. , , , Represents the noise matrix. .

3. The ISAR imaging method based on sparse Bayesian depth unfolded network according to claim 2, characterized in that, The ISAR one-dimensional sparse observation model described in step 2 is as follows: ； in, This indicates radar echoes from targets at small angles. This represents the ISAR image of the target corresponding to the radar echo. This represents the observation noise in the radar echo. A dictionary representing sparse observations. , This indicates the transpose operation. This represents the Kronecker product operation.

4. The ISAR imaging method based on sparse Bayesian depth unfolded network according to claim 3, characterized in that, The specific steps for defining the radar echo observation noise and the prior distribution of the target ISAR image described in step 2 are as follows: Increase radar echo observation noise and target ISAR images The prior distributions of all of them follow a complex Gaussian distribution, and the probability density functions are as follows: ； in, This represents the prior probability density function. Indicates a complex Gaussian distribution. Indicates the accuracy of observation noise. This indicates the inverse operation. Represents the identity matrix. The precision matrix representing the target ISAR image is a column vector whose diagonal elements are... The diagonal matrix of the observation noise accuracy is improved. The first diagonal of the target ISAR image accuracy matrix item The prior distribution follows a Gamma distribution, with the following probability density function: ； in, Represents the Gamma distribution. , Indicates the accuracy of observation noise The prior distribution hyperparameters, , The first line represents the diagonal of the target ISAR image precision matrix. item The prior distribution hyperparameters.

5. The ISAR imaging method based on sparse Bayesian depth unfolded network according to claim 4, characterized in that, The specific steps of the sparse Bayesian learning iterative imaging algorithm described in step 2 are as follows: Based on the "mean field" assumption, the approximate total a posteriori distribution of all variables in the model is used. break down: ； in, This represents the approximate posterior probability density function. Let the target ISAR image Approximate posterior probability density function It can be in the following form: ； in, express Expectations express The variance matrix is ​​a column vector whose diagonal elements are... The diagonal matrix is ​​obtained using the VI algorithm to obtain the first... Variables The formula for calculating the approximate posterior distribution is as follows: ； in, express The approximate posterior distribution hyperparameter, This represents a constant that is independent of all model variables. Denotes the joint likelihood probability density function. Indicates to about The points operation, ; Substituting the prior distributions of each variable in the model into the approximate posterior distribution calculation formula, we obtain the observation noise accuracy. The column vector corresponding to the diagonal elements of the target ISAR image precision matrix Approximate posterior probability density function , as follows: ； in, , Represents the approximate posterior distribution The distribution parameters, , Let represent the length and width of the two-dimensional radar echo matrix, respectively. This represents the length of the corresponding one-dimensional radar echo vector. This indicates the conjugate transpose operation. This represents the operation of extracting diagonal elements to form a column vector. This indicates a multiplication operation. , Let represent the length and width of the two-dimensional target ISAR image matrix, respectively. This represents the length of the corresponding one-dimensional target ISAR image vector. , Represents the approximate posterior distribution The distribution parameters, and They represent the approximate posterior distributions, respectively. Expectations and The variance of the diagonal elements corresponds to the column vector. The item, This indicates the conjugate operation; Combination Lipschitz lemma in the norm complex field, expectation of observation noise accuracy and the expected accuracy matrix of the target ISAR image Obtain the lower bound of relaxation ,make , Get the first In the next iteration and Update formula: ； in, and They represent the first The second iteration and the first Variables at the next iteration This indicates the operation of finding the expected value. This represents the Lipschitz constant. As an auxiliary variable, , This represents the first element of the column vector formed by taking the diagonal elements. item; Using the properties of the Kronecker product, the one-dimensional iterative update formula for each variable in the model is transformed into the following two-dimensional iterative update formula: ； in, , , In order to represent , and In matrix form, , This indicates the operation of finding the largest eigenvalue. and Let and represent the conjugate transposes of the distance dictionary matrix and the distance dictionary matrix, respectively. and Let represent the conjugate transposes of the orientation dictionary matrix and the orientation dictionary matrix, respectively. This indicates a division operation on the corresponding element. This indicates that all elements are 1. A 3D matrix This indicates the operation of calculating the Hadamard product. This represents the operation of squaring the F-norm. This represents the summation operation on all elements of the matrix; When the relative error between two adjacent target ISAR images satisfies At that time, the final imaging result is obtained. , For the set error threshold, This indicates the operation of calculating the F-norm.

6. The ISAR imaging method based on sparse Bayesian depth unfolded network according to claim 5, characterized in that, The four-variable approximate posterior distribution parameter update module mentioned in step 3 includes: The target ISAR image approximate posterior expectation update module performs the following operations: ； in, and They represent the first Sub-networks and the first Variables in a layered subnetwork Indicates the first In layered networks constant; The target ISAR image approximate posterior variance update module performs the following operations: ； The target ISAR image accuracy approximate posterior expectation update module performs the following operations: ； in, and Indicates the first Observation noise accuracy in layered networks The prior distribution hyperparameters; The observation noise accuracy approximate posterior expectation update module performs the following operations: ； in, and Indicates the first The first diagonal of the target ISAR image accuracy matrix in the layered sub-network item The prior distribution hyperparameters; The first The outputs of the four modules in the layered network , , and The first The sub-networks, following this pattern, cyclically pass through the layers, eventually reaching the output layer.

7. The ISAR imaging method based on sparse Bayesian depth unfolded network according to claim 6, characterized in that, Step 3 describes the prior distribution hyperparameters in each sub-network layer. , , , and Setting constants as learnable parameters of the network refers to the prior distribution hyperparameters across all layers of the sparse Bayesian depthwise unfolded network. , Set the learnable parameters shared by all layers, and expand the sparse Bayesian deep unfolded network to the level of... Prior distribution hyperparameters of layered subnetworks , and constant Set as learnable parameters independent for each layer. =1,2,…,K.

8. The ISAR imaging method based on sparse Bayesian depth unfolded network according to claim 6, characterized in that, The loss function described in step 4 is as follows: ； in, This means drawing a batch of data pairs from the training set. and These represent the outputs of the sparse Bayesian depth expansion network. The first two-dimensional target ISAR image and its corresponding second A two-dimensional target label image, This indicates a summation operation.

9. The ISAR imaging method based on sparse Bayesian depth unfolded network according to claim 7, characterized in that, The optimization algorithm mentioned in step 4 refers to the Adam optimization algorithm used to optimize the network's learnable parameter set. renew, Represents the set of learnable parameters of a network. The first in One parameter: Calculate the first Learnable parameters in layered networks Partial first moment estimator and partial second moment estimator : ； in, and They represent the first Learnable parameters in layered networks The partial first-order moment estimator and the partial second-order moment estimator This represents the loss function with respect to learnable parameters. gradient, and Indicates hyperparameters; Calculate the first moment estimator with bias correction. Second-order moment estimator with bias correction : ； First-moment estimator after bias correction and second-order moment estimator For the first Learnable parameters in layered networks The update formula is as follows: ； in, , They represent the first Sub-networks and the first Learnable parameters in layered subnetworks The parameter value, Indicates the learning rate. This represents the error constant.

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