Network construction method for maneuvering target sparse ISAR imaging based on unfolding technology

Abstract

The application discloses a network construction method for sparse ISAR imaging of a maneuvering target based on an unfolding technology, which is composed of a nonlinear phase compensation module based on Sinc interpolation and an ISAR image reconstruction module based on an alternating direction multiplier method (ADMM) in cascade, wherein the nonlinear phase compensation module realizes motion parameter estimation by minimizing image entropy, and then completes interpolation compensation of the nonlinear phase; the image reconstruction module is expanded in a hierarchical mode based on the ADMM algorithm, the connection of iterative variables between layers is strengthened, and fast and robust sparse reconstruction performance is realized; the network is trained by joint optimization, and network parameters are jointly optimized. The application makes up for the defect that the existing ISAR imaging method under the SA condition generally needs target uniform motion, and realizes high-quality imaging of a maneuvering target.

Description

Technical Field

[0001] This invention relates to the field of radar data processing technology, and in particular to a method for constructing a sparse ISAR imaging network for moving targets based on Unfolding technology. Background Technology

[0002] Inverse Synthetic Aperture Radar (ISAR) imaging technology is widely used for high-resolution imaging of non-cooperative targets in all-weather, all-time environments, playing a crucial role, especially in remote sensing and target recognition. In ISAR imaging, the range-Doppler (RD) algorithm is one of the fundamental methods for acquiring target images. However, in modern multi-functional radar systems, multiple tasks, such as target detection, tracking, and imaging, are typically performed simultaneously, often leading to resource constraints on the radar system. Furthermore, noise can cause some echoes to have excessively low signal-to-noise ratios, failing to effectively reflect target characteristics. These issues can be summarized as the sparse aperture (SA) problem of the echo, i.e., non-uniform sampling in the azimuth direction of the radar echo. This non-uniform sampling significantly impacts image quality, resulting in severe grating lobes in images based on traditional Fourier transforms.

[0003] To suppress image lobes caused by sparse apertures, researchers have introduced compressed sensing technology into ISAR imaging, proposing various high-quality image reconstruction methods based on sparse reconstruction. These methods can generally be categorized into three types: greedy pursuit methods, Lp-norm-based regularization methods, and sparse Bayesian learning (SBL) methods. Greedy pursuit methods, such as matching pursuit (MP) and orthogonal matching pursuit (OMP), have proven effective in many SA-ISAR applications. Lp-norm methods, especially L1-norm methods, can reduce computational complexity without significantly degrading image quality and are widely used in practice. Sparse Bayesian learning methods operate within a statistical framework, reconstructing images by establishing sparse prior probability models. While they have achieved some research results, their heavy computational burden limits their use in real-time applications.

[0004] Existing SA-ISAR imaging methods often rely on the assumption of relatively stable target motion during the imaging time. However, in reality, observed targets typically exhibit complex motion states, and their echoes contain high-order phase terms, leading to defocusing in images obtained using these methods and affecting image quality. Motion compensation for moving targets is a major challenge in ISAR imaging research, primarily involving translational compensation and non-uniform rotational compensation. Translational compensation often employs a two-step method: range alignment and initial phase correction. However, under SA conditions, due to the disruption of inter-pulse phase continuity, the performance of traditional initial phase correction methods such as phase gradient autofocus (PGA) typically degrades significantly, or even becomes unusable. Non-uniform rotational compensation methods face issues such as missing random data and Doppler frequency jumps. Traditional methods often suffer significant signal-to-noise ratio losses or high computational complexity when dealing with these problems.

[0005] Therefore, achieving high-quality ISAR imaging under SA conditions, especially robust real-time imaging of complex moving targets, remains a pressing technical challenge. Designing efficient target motion compensation methods, robust image sparse reconstruction methods, and reducing computational burden are the core challenges in the current SA-ISAR imaging field. Summary of the Invention

[0006] The purpose of this invention is to provide a method for constructing a sparse ISAR imaging network for a moving target based on Unfolding technology. This method overcomes the constraint that existing ISAR imaging methods under SA conditions usually require the target to be fixed in motion, and can effectively eliminate phase errors caused by non-uniform rotation.

[0007] The technical solution to achieve the purpose of this invention is: a method for constructing a sparse ISAR imaging network for maneuvering targets based on Unfolding technology, comprising the following steps:

[0008] Step 1: Acquire radar echo data, preprocess and model the radar echo data; the preprocessing of radar echo data involves translational compensation of radar echo data, which includes: using the cumulative cross-correlation method to perform range alignment of the echo and using the eigenvector-based method to perform initial phase correction of the echo.

[0009] Step 2: Based on the echo signal model established in Step 1, a model-driven deep learning imaging algorithm and an objective optimization function are established using the Unfolding framework; the deep learning imaging algorithm includes a nonlinear phase compensation algorithm and a sparse reconstruction algorithm based on compressed sensing.

[0010] Step 3: Based on the imaging algorithm established in Step 2, construct an algorithm-expanded neural network model. The algorithm-expanded neural network model consists of a nonlinear phase compensation module, a reconstruction layer, a denoising layer, and a Lagrange multiplier update layer of the fast-ADMM algorithm. The nonlinear phase compensation module is used to compensate for the nonlinear phase term caused by the non-uniform rotation of the target to the echo. The reconstruction layer, denoising layer, and Lagrange multiplier update layer of the fast-ADMM algorithm expand the fast-ADMM iterative process into a cascaded structure of each layer of the neural network, which is used to quickly reconstruct the preprocessed undersampled echo signal into an ISAR image.

[0011] Step 4: Generate a dataset for the ISAR echo data; the training set label in the dataset is the RD imaging result of the ISAR echo data under full aperture conditions after translational and non-uniform rotation compensation; the training set input is the sparse echo obtained by random sparse sampling after the ISAR echo data is translated and compensated.

[0012] Step 5: Determine the loss function based on the objective optimization function in Step 2 and the dataset in Step 4;

[0013] Step 6: Train the network model constructed in Step 3 based on the dataset from Step 4 and the loss function from Step 5;

[0014] Step 7: Image the processed echo based on the network model trained in Step 6.

[0015] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the above-described method for constructing a sparse ISAR imaging network for maneuvering targets based on Unfolding technology.

[0016] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described method for constructing a sparse ISAR imaging network for maneuvering targets based on Unfolding technology.

[0017] A computer program product includes a computer program that, when executed by a processor, implements the above-described method for constructing a sparse ISAR imaging network for maneuvering targets based on Unfolding technology.

[0018] Compared with existing technologies, the significant features of this invention are as follows: 1) This invention proposes an effective SA-ISAR imaging network for maneuvering targets, which suppresses the influence of sparse aperture (SA) and can effectively compensate for the high-order phase caused by non-uniform target rotation; 2) Compared with traditional algorithm-based network expansion, this invention achieves full complex domain computation and makes full use of the amplitude and phase information of ISAR echoes; 3) This invention designs a hierarchical expansion network based on the ADMM algorithm, sets the Lagrange penalty parameter and regularization coefficient in the algorithm as learnable parameters and fixes them through training, which is more robust than traditional algorithms; 4) The network structure proposed in this invention is simple, highly scalable and has low computational burden. Attached Figure Description

[0019] Figure 1 This is a flowchart of the method for constructing a sparse ISAR imaging network for maneuvering targets based on Unfolding technology, as described in this invention.

[0020] Figure 2 This is the network structure diagram of the algorithm proposed in this invention.

[0021] Figure 3 The image is a tagged RD image generated from the full-aperture ISAR echo in Example 1 after translational compensation and non-uniform rotation compensation.

[0022] Figure 4 This is the RD diagram generated after translational compensation of sparse aperture ISAR echoes in Example 1.

[0023] Figure 5 This is a reconstruction image of sparse aperture ISAR echoes processed using the traditional ADMM algorithm in Example 1.

[0024] Figure 6 Example 1 shows the reconstructed image of sparse aperture ISAR echoes processed by the algorithm proposed in this invention through a network expansion. Detailed Implementation

[0025] Existing inverse synthetic aperture radar (ISAR) imaging methods under sparse aperture (SA) conditions typically assume that the target is in stationary motion during the observation time, limiting their performance in practical applications. This invention proposes an efficient and robust SA-ISAR imaging framework for maneuvering targets, which can effectively compensate for the higher-order phase of the echo caused by non-uniform target rotation. This framework decomposes the multi-factor coupled imaging problem into easily solvable cascaded subproblems, and designs a complex domain neural network based on unfolding to achieve robust solutions to each subproblem. The proposed framework fully utilizes the complex information of the ISAR echo, and has the advantages of simple and robust structure, strong scalability, and low computational burden.

[0026] Combination Figure 1A method for constructing a sparse ISAR imaging network for maneuvering targets based on Unfolding technology is proposed. This network can achieve high-quality ISAR image reconstruction from sparse echo data of maneuvering targets, suppressing defocus caused by maneuvering and the raster lobe effect caused by non-uniform sampling in the azimuth direction. The method specifically includes the following steps:

[0027] Step 1: Acquire radar echo data and preprocess and model the echo data. The preprocessing of the radar echo data involves translational compensation, which includes range alignment and initial phase correction. Traditional range alignment methods still work well under SA conditions. This invention uses the cumulative cross-correlation method for range alignment of the echo. Regarding initial phase correction, eigenvector-based methods have been proven to be applicable to SA echoes. This invention uses an eigenvector-based method for initial phase correction of the echo.

[0028] After translational compensation, the target observation model can be represented by a turntable model. For a maneuvering target, its rotation angle θ(t) during the observation time varies nonlinearly and can be modeled using Taylor series expansion.

[0029]

[0030] Where ω1 is the coefficient of the first term in the Taylor series expansion of non-uniform rotation, and ω2 is the coefficient of the second term. For ease of expression, assume the target is rotating with constant acceleration, then θ(t) can be approximated as...

[0031]

[0032] Let b = ω2 / ω1 be the moment of inertia.

[0033] Assuming the target is equivalent to I scattering bodies, the echo signal model after translational compensation can be expressed as:

[0034]

[0035] Where h(m,n) is the discretized echo model, σ i Let P be the amplitude of the i-th scattering, m represent discrete slow time units, n represent discrete distance units, and P is the amplitude of the i-th scattering. r It is the radar's pulse repetition frequency (PRF), f s For fast sampling rates, f c B is the carrier frequency, B is the bandwidth, c is the propagation speed of the radar signal, and x is the speed of the radar signal. i ,y i These are the coordinates from the i-th scattering point to the center of rotation.

[0036] Step 2: Based on the echo signal model established in Step 1, an algorithm-driven deep learning imaging algorithm and an objective optimization function are established using the Unfolding framework. The imaging algorithm includes a nonlinear phase compensation algorithm and a sparse reconstruction algorithm based on compressed sensing.

[0037] Non-uniform rotation of the target introduces a non-linear phase term into the echo. Interpolation and resampling can be used to convert this non-linear phase into a linear phase. Sinc interpolation can be used to compensate for the higher-order phase caused by target maneuvering.

[0038]

[0039] Where y 2n For the nth range cell after interpolation, y 1n The nth range cell before interpolation, T is the pulse repetition time interval (PRI), m res The calculation method is as follows

[0040]

[0041] Where M represents the number of pulses in the fully sampled radar echo, b is the ratio of the coefficients of the quadratic term to the coefficients of the linear term in the non-uniform rotating Taylor series expansion, and is set as the rotation parameter. When b = 0, the model degenerates into a uniform rotating model.

[0042] The aforementioned compensation for the nonlinear phase term can be further expressed in matrix form as follows:

[0043] Y2=S1EY1

[0044] Where Y2 is an M×N compensated matrix, Y1 is an M×N pulse sparse matrix, E is an M×M interpolation matrix, and S1 is an update of the undersampled matrix determined by the pulse energy after interpolation of EY1.

[0045] The problem of SA-ISAR imaging after nonlinear phase compensation can be described as follows:

[0046] Y2 = S1FX + N

[0047] Where F is an M×M Fourier matrix, X is the target ISAR image matrix, and N is noise.

[0048] Establish the target sparse aperture ISAR imaging optimization function as follows:

[0049]

[0050] stz=x

[0051] Where y is the echo matrix, x is the reconstructed ISAR matrix, S1 is the undersampling matrix, λ is the regularization coefficient, ||·||2 is the L2 norm, and ||·||1 is the L1 norm;

[0052] The sparse reconstruction algorithm is solved using fast-ADMM:

[0053]

[0054] A (k+1) =A (k) +ρ(X (k+1) -Z (k+1) )

[0055] Where k represents the k-th iteration, . / denotes element-wise division, Z is an auxiliary variable; A and ρ represent the Lagrange multiplier and penalty parameter, respectively; λ represents the regularization coefficient that determines the sparsity of the reconstructed ISAR image; Mask is the sampling matrix of SA data, where the element value is 1 or 0 to indicate whether an element is sampled, 1 M×N It is a matrix of all ones, and S(·) is a soft thresholding function used for real-valued threshold t and complex data x:

[0056]

[0057] The final reconstructed image entropy is

[0058]

[0059] Here, `sum` represents the sum of all elements in the matrix. The reconstructed image entropy is related to the moment of inertia `b`. Since the entropy of the focused image is minimized, the entropy reaches its global minimum when the estimated `b` equals the true value. Therefore, the parameter estimation of the moment of inertia can be approximated as an optimization problem based on minimizing image entropy:

[0060]

[0061] Step 3: Based on the imaging algorithm established in Step 2, construct the algorithm unfolding neural network model.

[0062] Traditional fast-ADMM suffers from long iteration steps and difficulties in parameter predefinition. Therefore, by combining deep learning techniques, the fast alternating direction multiplier method is expanded into a network. More information is extracted from the data through layer cascading and pre-defined learnable parameters, reducing the number of iterations, improving algorithm efficiency, and enabling adaptive selection of iteration parameters. In the minimum image entropy optimization problem, since the entropy reaches its global minimum when non-uniform rotation compensation is most effective, the non-uniform rotation compensation algorithm is expanded into a network for joint optimization of the reconstructed image.

[0063] The nonlinear phase compensation module in the network is obtained by expanding the Sinc interpolation function in step 2, using the moment of inertia b as a learnable parameter. After the interpolation module compensates for the input echo, the energy of each echo is passed through a complex domain softmax layer to obtain the updated undersampling matrix. The interpolation module serves as the first layer in each stage of the network.

[0064] The ISAR image reconstruction module in the network is obtained by expanding the fast-ADMM algorithm, which is divided into a reconstruction layer, a denoising layer, and a Lagrange multiplier update layer. The iterative process is as follows: Figure 2 The cascaded architecture is shown; let the number of iterations of the fast-ADMM algorithm be n, and the number of stages of the cascaded network also be n; each stage of the network contains two unknown parameters, namely λ and ρ; in order to obtain more degrees of freedom, this invention assumes that the model parameters λ and ρ are different in each stage, and ρ is different in each layer, and they are learned from the training dataset as learnable parameters.

[0065] Step 4: Generate a dataset based on the ISAR echo data. The training set label in the dataset consists of the RD imaging results of the ISAR echo data under full aperture conditions after translational and non-uniform rotation compensation. The input to the training set consists of sparse echoes obtained by random sparse sampling after translational compensation of the ISAR echo data.

[0066] Step 5: Based on the optimization function in Step 2 and the dataset in Step 4, determine the loss function. The loss function is a metric for evaluating the network's performance during training. In this invention, the mean squared error loss and the reconstructed image entropy are used to form the loss function. The mean squared error loss calculates the square of the difference between the output reconstructed image and the label image and takes the average. By minimizing the mean squared error loss, the model will make the reconstructed image closer to the label image during training. Its specific expression is as follows:

[0067]

[0068] in It is the image reconstructed from the i-th undersampled data. Let C be the corresponding labeled data image, and C be the logarithm of the reconstructed image and the corresponding labeled data image in this batch of datasets. This represents the Frobenius norm.

[0069] The target rotation parameters are estimated by jointly optimizing the image entropy to ensure compensation accuracy. The specific expression is as follows:

[0070]

[0071] Where sum represents the sum of all elements in the matrix, and ⌒ represents element-wise multiplication. Let be the image reconstructed from the i-th undersampled data, and C be the logarithm of the reconstructed image and the corresponding labeled data image in this batch of datasets.

[0072] The final overall loss function of the network is:

[0073]

[0074] Where α and β represent the weight coefficients of the corresponding loss function, respectively.

[0075] Step 6: Based on the dataset from Step 4, train the network model constructed in Step 3 using the loss function from Step 5. Input the sparse echoes from the dataset generated in Step 4 into the network for forward propagation, calculate the loss function value, update the network parameters using the backpropagation algorithm, iterate continuously until the loss function converges, and finally save the trained network model.

[0076] Step 7: Image the processed echoes based on the network model trained in Step 6. Use sparse ISAR echo data of the maneuvering target as network input to obtain the reconstructed image. Conduct comparative experiments using the traditional fast-ADMM algorithm with the same number of iterations as the network layers, and calculate image entropy (ENTROPY) and peak signal-to-noise ratio (PSNR) respectively.

[0077] Example

[0078] Combination Figure 1 A method for constructing a sparse ISAR imaging network for maneuvering targets based on Unfolding technology includes the following steps:

[0079] Step 1: Acquire radar echo data and preprocess and model the echo data. The preprocessing of the radar echo data involves translational compensation, which includes range alignment and initial phase correction. Traditional range alignment methods still work well under SA conditions. This invention uses the cumulative cross-correlation method for range alignment of the echo. Regarding initial phase correction, eigenvector-based methods have been proven to be applicable to SA echoes. This invention uses an eigenvector-based method for initial phase correction of the echo.

[0080] After translational compensation, the target observation model can be represented by a turntable model. For a maneuvering target, its rotation angle θ(t) during the observation time varies nonlinearly and can be modeled using Taylor series expansion.

[0081]

[0082] For ease of description, assume the target is rotating with constant acceleration, then θ(t) can be approximated as:

[0083]

[0084] Let b = ω2 / ω1 be the moment of inertia.

[0085] Assuming the target is equivalent to I scattering bodies, the echo signal model after translational compensation can be expressed as:

[0086]

[0087] Where h(m,n) is the discretized echo model, σ i Let P be the amplitude of the i-th scattering, m represent discrete slow time units, n represent discrete distance units, and P is the amplitude of the i-th scattering. r It is the radar's pulse repetition frequency (PRF), f s For fast sampling rates, f c B is the carrier frequency, B is the bandwidth, c is the propagation speed of the radar signal, and x is the speed of the radar signal. i ,y i These are the coordinates from the i-th scattering point to the center of rotation.

[0088] Step 2: Based on the echo model established in Step 1, an algorithm-driven deep learning imaging algorithm is built using the Unfolding framework. The imaging algorithm includes a nonlinear phase compensation algorithm and a sparse reconstruction algorithm based on compressed sensing.

[0089] Non-uniform rotation of the target introduces a non-linear phase term into the echo. Interpolation and resampling can be used to convert this non-linear phase into a linear phase. Sinc interpolation can be used to compensate for the higher-order phase caused by target maneuvering.

[0090]

[0091] Where y 2n For the nth range cell after interpolation, y 1n The nth range cell before interpolation, T is the pulse repetition time interval (PRI), m res The calculation method is as follows

[0092]

[0093] Where M represents the number of pulses in the fully sampled radar echo, and when b = 0, the model degenerates into a uniform rotation model;

[0094] The aforementioned compensation for the nonlinear phase term can be further expressed in matrix form as follows:

[0095] Y2=S1EY1

[0096] Where Y2 is an M×N compensated matrix, Y1 is an M×N pulse sparse matrix, E is an M×M interpolation matrix, and S1 is an update of the undersampled matrix determined by the pulse energy after interpolation of EY1.

[0097] The problem of SA-ISAR imaging after nonlinear phase compensation can be described as follows:

[0098] Y2 = S1FX + N

[0099] Where F is an M×M Fourier matrix and N is noise.

[0100] Establish the target sparse aperture ISAR imaging optimization function as follows:

[0101]

[0102] stz=x

[0103] Where y is the echo matrix, x is the reconstructed ISAR matrix, S1 is the undersampling matrix, λ is the regularization coefficient, ||·||2 is the L2 norm, and ||·||1 is the L1 norm;

[0104] The sparse reconstruction algorithm is solved using fast-ADMM:

[0105]

[0106] A (k+1) =A (k) +ρ(X (k+1) -Z (k+1) )

[0107] Where k represents the k-th iteration, . / denotes element-wise division, Z is an auxiliary variable; A and ρ represent the Lagrange multiplier and penalty parameter, respectively; λ represents the regularization coefficient that determines the sparsity of the reconstructed ISAR image; Mask is the sampling matrix of SA data, where the element value is 1 or 0 to indicate whether an element is sampled, 1 M×N It is a matrix of all ones, and S(·) is a soft thresholding function used for real-valued threshold t and complex data x:

[0108]

[0109] The final reconstructed image entropy is

[0110]

[0111] Here, `sum` represents the sum of all elements in the matrix. The reconstructed image entropy is related to the moment of inertia `b`. Since the entropy of the focused image is minimized, the entropy reaches its global minimum when the estimated `b` equals the true value. Therefore, the parameter estimation of the moment of inertia can be approximated as an optimization problem based on minimizing image entropy:

[0112]

[0113] Step 3: Based on the imaging algorithm established in Step 2, construct the algorithm unfolding neural network model.

[0114] Traditional fast-ADMM suffers from long iteration steps and difficulties in parameter predefinition. Therefore, by combining deep learning techniques, the fast alternating direction multiplier method is expanded into a network. More information is extracted from the data through layer cascading and pre-defined learnable parameters, reducing the number of iterations, improving algorithm efficiency, and enabling adaptive selection of iteration parameters. In the minimum image entropy optimization problem, since the entropy reaches its global minimum when non-uniform rotation compensation is most effective, the non-uniform rotation compensation algorithm is expanded into a network for joint optimization of the reconstructed image.

[0115] The nonlinear phase compensation module in the network is obtained by expanding the Sinc interpolation function in step 2, using the moment of inertia b as a learnable parameter. After the interpolation module compensates for the input echo, the energy of each echo is passed through a complex domain softmax layer to obtain the updated undersampling matrix. The interpolation module serves as the first layer in each stage of the network.

[0116] The ISAR image reconstruction module in the network is derived from the fast-ADMM algorithm, which is expanded into a reconstruction layer, a denoising layer, and a Lagrange multiplier update layer. The fast-ADMM algorithm iterates n times, and the number of stages in the cascaded network is also set to n. Each stage of the network contains two unknown parameters, λ and ρ. To obtain more degrees of freedom, this invention assumes that the model parameters λ and ρ are different in each stage, and that ρ is different in each layer. These parameters are learned as learnable parameters from the training dataset. The initial values ​​of all learnable parameters are set to 1.0.

[0117] Step 4: Generate a dataset for the ISAR echo data. In this embodiment, an aircraft model consisting of 250 scattering points is used as the observation target. The maneuvering target rotates around its center of gravity at an angular velocity of 0.2 rad / s and has random additional angular acceleration. The simulated radar operates in the X-band, transmitting a linear frequency modulated signal. The bandwidth is 1 GHz, and the PRF is 300 Hz. In addition, Gaussian noise is added to set the signal-to-noise ratio of the compressed echo to 10 dB. First, we extract 200 radar echo matrices. Each echo matrix has 256 pulses in the azimuth direction and 256 samples in the range direction. The raw data matrix is ​​preprocessed using a motion compensation procedure including range alignment and initial phase correction. Then, the data matrix is ​​converted into RD imaging results as label data using FFT. The corresponding training set input is a sparse echo matrix obtained by random sparse sampling of the corresponding echo data. 150 are randomly selected as the training set, and 50 are selected as the test set.

[0118] Step 5: Based on the optimization function in Step 2 and the dataset in Step 4, determine the loss function. The loss function is a metric for evaluating the network's performance during training. In this invention, the mean squared error loss and the reconstructed image entropy are used to form the loss function. The mean squared error loss calculates the square of the difference between the output reconstructed image and the label image and takes the average. By minimizing the mean squared error loss, the model will make the reconstructed image closer to the label image during training. Its specific expression is as follows:

[0119]

[0120] in It is the image reconstructed from the i-th undersampled data. Let C be the corresponding labeled data image, and C be the logarithm of the reconstructed image and the corresponding labeled data image in this batch of datasets. This represents the Frobenius norm.

[0121] The target rotation parameters are estimated by jointly optimizing the image entropy to ensure compensation accuracy. The specific expression is as follows:

[0122]

[0123] Where sum represents the sum of all elements in the matrix. Let be the image reconstructed from the i-th undersampled data, and C be the logarithm of the reconstructed image and the corresponding labeled data image in this batch of datasets.

[0124] The final overall loss function of the network is:

[0125]

[0126] Where α and β represent the weight coefficients of the corresponding loss function. In this example, α = 1 and β = 0.01.

[0127] Step 6: Based on the dataset from Step 4, train the network model constructed in Step 4 using the loss function from Step 5. Input the sparse echoes from the dataset generated in Step 5 into the network for forward propagation, calculate the loss function value, update the network parameters using the backpropagation algorithm, iterate until the loss function converges, and finally save the trained network model. This example is specifically implemented based on the PyTorch framework, using the Adam optimizer, an Intel(R) Core(TM) i7-8750H CPU, and 16GB of memory. The learning rate is set to 0.0001.

[0128] Step 7: Image the processed echoes based on the network model trained in Step 6. Sparse ISAR echo data is used as network input to obtain the reconstructed image, as shown below. Figure 6 As shown. The tag RD image generated from the corresponding full-aperture ISAR echo is as follows. Figure 4 As shown, the RD image generated from the sparse ISAR echo is as follows: Figure 3 As shown in the figure, a comparative experiment was conducted using the traditional fast-ADMM algorithm with 9 iterations to obtain the reconstructed image, as shown in the figure. Figure 5 As shown.

[0129] As can be seen from the figure, the traditional RD algorithm suffers from severe main lobe broadening and side lobe rise due to the random missing pulses. The traditional fast-ADMM algorithm can suppress the side effects caused by SA (Simultaneous Aperture Separation). However, due to its assumption of uniform target rotation, it can only obtain defocused images for non-uniformly rotating targets. Our proposed imaging framework is not only unaffected by SA, but can also achieve focused ISAR images of moving targets.

[0130] To obtain a rigorous evaluation of the above method, we calculated the image entropy (ENTROPY) and peak signal-to-noise ratio (PSNR) of the reconstructed image, respectively. The results are shown in Table 1. Our method outperforms the traditional fast-ADMM algorithm in both metrics.

[0131] Table 1 Comparison of imaging quality between the present invention and the traditional fast-ADMM algorithm

[0132] fast-ADMM 7.5046 22.29dB Unfolding-Net 6.8617 31.38dB

[0133] The specific embodiments of the present invention have been described in detail above. It should be noted that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various modifications or variations within the scope of the claims, which do not affect the essence of the present invention.

Claims

1. A method for constructing a sparse ISAR imaging network for maneuvering targets based on Unfolding technology, characterized in that, Includes the following steps: Step 1: Acquire radar echo data, and preprocess and model the radar echo data; The preprocessing of radar echo data involves translational compensation of the radar echo data. The translational compensation includes: using the cumulative cross-correlation method to perform range alignment of the echo and using the eigenvector-based method to perform initial phase correction of the echo. Step 2: Based on the echo signal model established in Step 1, a model-driven deep learning imaging algorithm and an objective optimization function are established using the Unfolding framework; the deep learning imaging algorithm includes a nonlinear phase compensation algorithm and a sparse reconstruction algorithm based on compressed sensing. Step 3: Based on the imaging algorithm established in Step 2, construct an algorithm-expanded neural network model. The algorithm-expanded neural network model consists of a nonlinear phase compensation module, a reconstruction layer, a denoising layer, and a Lagrange multiplier update layer of the fast-ADMM algorithm. The nonlinear phase compensation module is used to compensate for the nonlinear phase term caused by the non-uniform rotation of the target to the echo. The reconstruction layer, denoising layer, and Lagrange multiplier update layer of the fast-ADMM algorithm expand the fast-ADMM iterative process into a cascaded structure of each layer of the neural network, which is used to quickly reconstruct the preprocessed undersampled echo signal into an ISAR image. By combining deep learning technology, the fast alternating direction multiplier method is expanded into a network, and more information is extracted from the data through the cascading of layers and preset learnable parameters; the non-uniform rotation compensation algorithm is expanded into part of the network to jointly optimize the reconstructed image; The nonlinear phase compensation module in the network is obtained by expanding the Sinc interpolation function in step 2, and the moment of inertia is... As a learnable parameter, the interpolation module compensates for the input echoes, and the energy of each echo is passed through a complex domain softmax layer to obtain an updated undersampling matrix; the interpolation module serves as the first layer in each stage of the network; The ISAR image reconstruction module in the network is obtained by expanding the fast-ADMM algorithm, which is divided into a reconstruction layer, a denoising layer, and a Lagrange multiplier update layer. Let the number of iterations of the fast-ADMM algorithm be... The number of stages in the cascaded network is also set to Each stage of the network contains two unknown parameters, namely... and Assuming model parameters , It is different at each stage, and They are different in each layer, and are learned from the training dataset as learnable parameters; Step 4: Generate a dataset for the ISAR echo data; the training set label in the dataset is the RD imaging result of the ISAR echo data under full aperture conditions after translational and non-uniform rotation compensation; the training set input is the sparse echo obtained by random sparse sampling after the ISAR echo data is translated and compensated. Step 5: Determine the loss function based on the objective optimization function in Step 2 and the dataset in Step 4; Step 6: Train the network model constructed in Step 3 based on the dataset from Step 4 and the loss function from Step 5; Step 7: Image the processed echo based on the network model trained in Step 6.

2. The method for constructing a sparse ISAR imaging network for maneuvering targets based on Unfolding technology according to claim 1, characterized in that, In step 1, it is assumed that the objective is equivalent to The echo signal model of a scattering body after translational compensation is expressed as follows: ； in For the discretized echo model, For the first The amplitude of the secondary scattering, Represents a pulse unit. Represents the range unit, It is the radar pulse repetition frequency. For fast sampling rate, For carrier frequency, For bandwidth, For the propagation speed of radar signals, It is the first The coordinates of each scattering point to the center of rotation; These are the coefficients of the first-order terms in the non-uniformly rotated Taylor series expansion. The coefficient of the quadratic term.

3. The method for constructing a sparse ISAR imaging network for maneuvering targets based on Unfolding technology according to claim 1, characterized in that, In step 2, the nonlinear phase compensation algorithm uses Sinc interpolation to compensate for the higher-order phase caused by target maneuvering. The interpolation formula is as follows: ； in For the interpolated first A range unit, The first before interpolation A range unit, The pulse repetition time interval. The calculation method is as follows ； ； in This represents the number of pulses in a fully sampled radar echo. Let the ratio of the coefficients of the quadratic term to the coefficients of the linear term in the non-uniformly rotated Taylor series expansion be defined as the rotation parameter. At that time, the model degenerates into a uniform rotation model; The problem of SA-ISAR imaging after nonlinear phase compensation is described as ； in It is The Fourier matrix, For the target ISAR image matrix, For noise, yes The compensated matrix, The update of the undersampling matrix is ​​determined by the interpolated pulse energy.

4. The method for constructing a sparse ISAR imaging network for maneuvering targets based on Unfolding technology according to claim 3, characterized in that, In step 3, the target sparse aperture ISAR imaging optimization function is: ； in It is the echo matrix. It is to reconstruct the ISAR matrix. It is an undersampling matrix. It is the regularization coefficient. for Norm, for Norm; The sparse reconstruction algorithm is solved using fast-ADMM: ； ； ； in Indicates the first iteration This represents element-wise division. As an auxiliary variable; and Let these represent the Lagrange multipliers and the penalty parameter, respectively. This represents the regularization coefficient that determines the sparsity of the reconstructed ISAR image; This is the sampling matrix for SA data, where an element value of 1 or 0 indicates whether the element was sampled or not. It is a matrix of all 1s. It is a soft thresholding function used for real-valued thresholding. and complex data : ； The final reconstructed image entropy is: ； Reconstructing image entropy and moment of inertia Relatedly, since the entropy of the focused image is minimized, when the estimated... When the value equals the true value, the entropy reaches its global minimum. Therefore, the parameter estimation of the moment of inertia can be approximated as an optimization problem based on minimizing image entropy: 。 5. The method for constructing a sparse ISAR imaging network for maneuvering targets based on Unfolding technology according to claim 1, characterized in that, In step 5, based on the optimization function from step 2 and the dataset from step 4, the loss function is determined, and the joint optimization loss function is set as follows: ； in From the first An image reconstructed from undersampled data. For the corresponding label data image, This represents the number of reconstructed images and corresponding labeled images in this batch of datasets. Denotes the Frobenius norm. This represents the sum of all elements in the matrix. This represents element-wise multiplication. , These represent the weight coefficients of the corresponding loss functions.

6. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method as described in any one of claims 1-5.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the method as described in any one of claims 1-5.

8. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method described in any one of claims 1-5.

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