A radar high-resolution imaging method based on fast shrinkage iterative threshold network

Abstract

The application discloses a radar high-resolution imaging method based on a fast shrinkage iterative threshold network, which is applied to the field of radar detection and imaging. The low-pass characteristic of a radar antenna pattern makes the deconvolution problem a pathological problem, the frequency band width of which is limited, and direct inverse filtering can cause high-frequency noise amplification and cannot obtain stable inversion results. The application combines the interpretability of an iterative algorithm and the advantages of deep learning, expands a fast iterative shrinkage threshold algorithm into a deep network, and can be used to solve the problems of low azimuth resolution of an existing scanning radar and difficulty in manually selecting parameters, so as to realize super-resolution imaging of the scanning radar. The application has the characteristics that two-dimensional radar data is divided into one-dimensional azimuth vectors, one-dimensional convolution is used to fully learn the characteristics of the azimuth data, the optimal parameters in the fast shrinkage threshold algorithm are obtained, and the azimuth resolution of the radar image is effectively improved.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of radar detection and imaging, and particularly relates to a kind of azimuth high-resolution imaging technology suitable for airborne scanning radar. BACKGROUND

[0002] Airborne scanning radar imaging is of great significance in many key applications, and has a wide range of applications in scene monitoring, autonomous landing, terrain mapping and other fields. However, its azimuth resolution is limited by the size of the antenna. Radar super-resolution imaging technology mainly refers to the improvement of signal processing methods to achieve angular resolution capability beyond the diffraction limit of the real aperture beam width of the radar.

[0003] Since the azimuth echo signal of scanning radar can be established as a convolution form of the real beam antenna pattern function and the scene target scattering distribution after motion compensation technology such as range walk correction, the target scattering coefficient can be estimated and the target information can be reconstructed by deconvolution technology. But due to the low-pass characteristic of the radar antenna pattern, the deconvolution problem is a pathological problem, and the frequency band width is limited, so direct inverse filtering will lead to amplification of high-frequency noise and cannot obtain stable inversion results. Therefore, many scholars have studied various methods to alleviate the pathological state of convolution inversion to obtain the solution of the problem, including multi-channel deconvolution, iterative deconvolution, etc. The literature“M. Niu, W. Li, Z. Liu, Y. Zhang and J. Yang, An Accelerated Iterative Shrinkage-Thresholding Algorithm for Real-Beam Scanning Radar Super-Resolution,”2019 IEEE Radar Conference (RadarConf), Boston, MA, USA, 2019.” uses the iterative shrinkage-thresholding algorithm (ISTA) to realize the super-resolution imaging of scanning radar, but this method has the problem of difficulty in manual selection of model parameters. The deep unfolding network realizes the end-to-end learning of the iterative process by converting the iterative optimization process into the structure of the neural network, and inherits the interpretability of the iterative algorithm, while avoiding the need for manual parameter tuning. The literature“Jinxi Xiang, Yonggui Dong, and Yunjie Yang,“Fista-net: Learning a fast iterative shrinkage thresholding network for inverse problems in imaging,”IEEE Transactions on Medical Imaging, vol. 40, no. 5, pp. 1329-1339, 2021.” maps the iterative steps of the fast iterative shrinkage-thresholding algorithm (FISTA) into a deep network, called FISTA-Net, and is used for medical imaging tasks. The experimental results show superior performance under different noise levels. Although the effectiveness of deep learning has been proven in many research fields, it has not been fully utilized in the field of scanning radar. SUMMARY

[0004] To solve the above technical problems, the present application provides a radar high-resolution imaging method based on a fast shrinkage iterative threshold network, introduces a deep unfolding network based on a fast iterative shrinkage threshold algorithm (FISTA-Net) into the field of scanning radar imaging, and improves it to adapt to the azimuth super-resolution task.

[0005] The technical scheme adopted by the present application is: a radar high-resolution imaging method based on a fast shrinkage iterative threshold network, comprising:

[0006] S1, establishing a radar echo model;

[0007] S2, based on the original radar data, combining the radar echo model established in step S1, generating echo data; taking the generated echo data as a training set;

[0008] S3, establishing a scanning radar super-resolution target optimization function;

[0009]

[0010] Wherein, The estimated value of the target scattering cross section is represented by H, x represents the target scattering coefficient vector, b represents the received azimuth echo vector, λ is the regularization parameter, ||·||2 is the L2 norm, and ||·||1 is the L1 norm;

[0011] S4, constructing a FISTA-Net network model for solving the target optimization function established in step S3; the FISTA-Net network model comprises: an acceleration module, a gradient descent module and a proximal mapping module; the acceleration module uses the linear combination of the output results of the previous two iterations as the input to obtain an auxiliary variable; the gradient descent module minimizes The proximal mapping module maps the output of the gradient descent module to the sparse domain and applies a soft threshold function to obtain a solution in the sparse domain, and performs inverse transformation on the solution in the sparse domain to obtain a solution in the original data domain;

[0012] S5, training the FISTA-Net network model constructed in step S4 based on the training set of step S2;

[0013] S6, scanning radar imaging based on the trained FISTA-Net network model.

[0014] The beneficial effects of the present application: the present application proposes a scanning radar super-resolution method based on fast iterative shrinkage threshold network, compared with the traditional method, the present application has obvious advantages in solving the problems of low azimuth resolution of scanning radar image, difficulty in manual selection of parameters and the like. The traditional method usually has the problem of insufficient azimuth resolution, which leads to unclear imaging results. By dividing the two-dimensional radar data into one-dimensional azimuth angle vectors, the characteristics of the azimuth angle data are fully learned through one-dimensional convolution, and the scattering coefficient is recovered from the radar echo by combining the fast iterative shrinkage threshold algorithm, which solves the problems of low azimuth resolution of scanning radar image, difficulty in manual selection of parameters and the like, and effectively improves the azimuth resolution of scanning radar imaging. BRIEF DESCRIPTION OF DRAWINGS

[0015] Figure 1 The scheme flowchart provided for the embodiments of the present application is provided.

[0016] Figure 2 The network structure diagram of FISTA-Net at the kth iteration provided for the embodiments of the present application is provided.

[0017] Figure 3 The structure diagram of the sparse transform network in the proximal mapping module provided for the embodiments of the present application is provided.

[0018] Figure 4 A radar imaging original scene graph in the network test stage provided for the embodiments of the present application is provided.

[0019] Figure 5 The imaging result graph generated by the original scene provided for the embodiments of the present application is provided.

[0020] Figure 6 The imaging result graph processed by FISTA-Net provided for the embodiments of the present application is provided. DETAILED DESCRIPTION

[0021] In order to facilitate those skilled in the art to understand the technical content of the present application, the content of the present application will be further explained below in combination with the drawings. The implementation flowchart of the present application is shown in Figure 1 The operation steps of the method for implementing the present application will be given below.

[0022] Step one, establish a scanning radar echo model

[0023] The airborne radar scanning mode obtains the real beam image of the observation area through continuous scanning of the antenna. It is assumed that the radar antenna transmits a linear frequency modulation signal with a certain frequency as follows:

[0024]

[0025] Where, τ represents the fast time, T rrepresents the pulse width of the linear frequency modulation signal, f0represents the signal carrier frequency, and K r represents the frequency modulation slope of the linear frequency modulation signal, represents a rectangular pulse, which can be expressed as

[0026] The radar scans the target scene at a certain angular velocity, and the received echo can be expressed as:

[0027]

[0028] where R(t) is the distance between the target and the radar, x represents the scattering coefficient of the point target, h(t) represents the antenna direction function, c is the speed of light, and Ω is the target area.

[0029] After the received signal is processed by matching filtering, pulse compression, and range migration correction, etc., the received echo can be simplified as:

[0030]

[0031] where sinc(·) represents the range pulse compression response function, B represents the bandwidth of the linear frequency modulation signal, and B=K r T r .

[0032] Step two, generating simulated echo data

[0033] In this embodiment, the parameters shown in Table 1 are used to configure the parameters of the scanning radar, and the simulated echo data is generated from the original radar data based on the echo model obtained in step one. Specifically, in this example, 1130 synthetic aperture radar images in the SSDD data set are used as the original scene to generate simulated echoes, of which 1100 are used for training and 30 are used for testing. In order to more fully understand the characteristics of the radar data, each input data is converted into a 1x257 one-dimensional vector.

[0034] Table 1 Radar parameters

[0035] Parameter Value Carrier frequency 9.3 GHz Signal bandwidth 20 MHz Pulse width 2 MHz Antenna scanning speed 72° / s Antenna beam width 5.1° Scanning range -45°～45° Distance range 4000 m ~ 5000 m

[0036] Step three, establishing a scanning radar super-resolution target optimization function

[0037] After the azimuth echo of the airborne real-aperture scanning radar is compensated by the motion compensation technology such as range migration correction, the azimuth echo in the same range bin can be approximated as the convolution result of the antenna pattern and the target scattering coefficient, and its matrix vector form can be expressed as:

[0038] b=Hx+n

[0039] where b∈C M×1represents the received azimuth echo vector, C represents a complex number set, M represents the number of sampling points of the echo vector in the azimuth direction, x∈C K×1 represents the target scattering coefficient vector, K represents the number of sampling points of the target region scattering coefficient vector, n∈C M×1 represents an additive noise vector, H∈C M×K represents a convolution matrix of the antenna pattern, L is the number of sampling points of the antenna pattern vector, and M, K, L satisfy the relationship K = M - L + 1.

[0040] Therefore, the scattering coefficient of the target can be recovered from the observed echo by convolution inversion, and the azimuth direction super-resolution is obtained. However, since the azimuth direction super-resolution of the real beam scanning radar is an inverse problem, it is ill-posed. In order to suppress the amplification of noise in the deconvolution, the least squares regularization method can be used for solving, and a sparse term is usually introduced to control the sparsity of the solution, and the solving formula is:

[0041]

[0042] wherein, represents the estimated value of the target scattering coefficient, ||·||2 is the L2 norm, ||·||1 is the L1 norm, λ is a regularization parameter, which is generally determined by experience, and the purpose is to balance the relationship between the observed data (radar echo data) and the prior information (antenna pattern function), and Ψ is a sparse transformation operator, and the L1 norm is used to enhance the sparsity.

[0043] Step four, constructing the FISTA-Net network model

[0044] According to the optimization objective function determined in step three, the fast iterative threshold shrinkage algorithm (FISTA) can be used for solving. However, the traditional FISTA has problems such as long iteration step number and difficult parameter predefinition. Therefore, by combining deep learning technology, the fast threshold iterative shrinkage algorithm is unfolded into a network, i.e. FISTA-Net, which uses the powerful feature extraction and representation ability of convolutional neural network to extract more information, so as to reduce the number of iterations, improve the algorithm efficiency and realize the adaptive selection of iteration parameters. As shown in the following formula: Figure 1 As shown in the formula, FISTA-Net maps each iteration step of the traditional FISTA algorithm into a network, which includes three modules: an acceleration module, a gradient descent module and a proximal mapping module.

[0045] The acceleration module uses the linear combination of the output results of the previous two iterations as the input to obtain the auxiliary variable y (k+1) , which can effectively accelerate the convergence of the model, and the acceleration step size ρ (k+1) is a learnable parameter, and the specific calculation formula of y (k+1) is as follows:

[0046] y (k+1) = x (k) + p (k+1) (x (k) - x (k-1) )

[0047] The goal of the gradient descent module is to minimize (k+1) based on the output y of the previous module. Since the iterative point approaches the optimal solution as the number of iterations increases, the iterative step length will theoretically gradually decrease, therefore, the gradient descent step length μ(k) is set as a parameter dynamically learned in each iteration, as follows:

[0048]

[0049] where denotes the derivative operation.

[0050] The proximal mapping module can obtain the solution in the sparse domain by mapping the input data to the sparse domain and applying the soft threshold function, and then obtain the solution in the original data domain by inverse transformation, whose expression is as follows:

[0051]

[0052] where denotes the soft threshold function, whose expression can be expanded as:

[0053]

[0054] and the threshold value θ (k) is set as a learnable parameter. denotes a learnable sparse transformation function, which can map data to a suitable sparse domain. In fact, this sparse transformation is a simple convolutional neural network, whose network structure is shown in Figure 3 . This module consists of four convolutional layers (Conv) and three rectified linear units (ReLU). The role of the convolutional layer is to extract features from the input data through convolution operation. In order to make the network model adapt to the super-resolution of the azimuth direction of the scanning radar, the two-dimensional radar data is converted into a one-dimensional azimuth vector and input into the network for training, and a one-dimensional convolution kernel (size 7x1) is used to effectively learn the azimuth vector features of the radar data. And through ReLU, the nonlinear characteristics are introduced to improve the expression ability of the model, solve the gradient vanishing problem, and promote the convergence speed and accuracy of the model. denotes the inverse transformation of , which is constrained by , the network structure of is the identity operator, and the network structure of is the same as that of

[0055] The loss function is a metric for evaluating the performance of a network during training. In this invention, the loss function is composed of mean squared error loss and symmetry loss from sparse transform inversion. The mean squared error loss calculates the square of the difference between the predicted and true values ​​of the scattering coefficients and takes the average. By minimizing the mean squared error loss, the model strives to make the predicted values ​​closer to the true values ​​during training. Its specific expression is as follows:

[0056]

[0057] Where N is the total number of iterations, in this example N = 9, x (N) This is the final predicted output of the network, where x is the corresponding true value. To ensure the invertibility of the sparse transformation in the near-end mapping module, a symmetry loss for sparse transformation inversion is defined to constrain the sparse transformation, and its expression is as follows:

[0058]

[0059] The final overall loss function of the network is:

[0060]

[0061] Where α and β represent the weight coefficients of the corresponding loss function, and in this example, α = 1 and β = 0.01 are taken.

[0062] Step 5: Train the FISTA-Net network

[0063] The FISTA-Net constructed in step four is trained as follows: The simulated azimuth echoes from the training set generated in step two are input into the network for forward propagation. The loss function value is calculated, and the network parameters are updated using the backpropagation algorithm. This process is iterated until the loss function converges, and finally, the trained network model is saved. This example is implemented based on the PyTorch framework, using the Adam optimizer, on an NVIDIA GeForce RTX 2060 GPU, with a learning rate set to 0.0001.

[0064] Step 6: Test the trained FISTA-Net model.

[0065] During the testing phase, an original scenario is selected from the test set as follows: Figure 4 The simulated echo data shown is as follows: Figure 5 As shown, its azimuth resolution is low, making it unable to clearly distinguish small targets adjacent to each other within the same range cell. The output after processing by the trained FISTA-Net is as follows... Figure 6 As shown, it restored the clear outline and sharpness of the target.

[0066] In order to objectively evaluate the imaging quality of the FISTA-Net, the present embodiment uses FISTA for a comparative experiment, and respectively calculates a structural similarity index measure (SSIM) and a peak signal-to-noise ratio (PSNR), and the results are shown in Table 2. The two indicators of the FISTA-Net are higher than those of the FISTA.

[0067] Table 2 Comparison table of imaging quality of the present application and the existing FISTA method

[0068] Method SSIM PSNR FISTA 0.68 23.85 FISTA-Net 0.87 26.93

[0069] Those skilled in the art will realize that the embodiments described herein are for the purpose of illustration and should not be construed as limiting the scope of the present application. The present application can be modified and varied in various ways, and any modification, equivalent replacement, improvement, etc. within the spirit and principle of the present application should be included in the scope of the claims of the present application.

Claims

1. A radar high-resolution imaging method based on fast shrinkage iterative threshold network, characterized in that, Comprise: S1, establish a radar echo model; S2, based on the original radar data, combined with the radar echo model established in step S1, generate echo data; The generated echo data is used as a training set; S3, establish a scanning radar super-resolution target optimization function; ； wherein an estimate of the target scatterer cross section, denotes a convolution matrix, denotes a target scatterer coefficient vector, denotes a received azimuthal echo vector, is a regularization parameter, is an L2 norm, is an LI norm; S4, a FISTA-Net network model is constructed for solving the objective optimization function established in step S3; the FISTA-Net network model comprises an acceleration module, a gradient descent module and a proximal mapping module; the acceleration module uses a linear combination of the output results of the previous two iterations as input to obtain an auxiliary variable; the gradient descent module minimizes the objective optimization function based on the auxiliary variable ; the proximal mapping module maps the output of the gradient descent module to a sparse domain and then applies a soft threshold function to obtain a solution in the sparse domain, and performs inverse transformation on the solution in the sparse domain to obtain a solution in the original data domain; The output of the acceleration module is represented as: ； wherein, is an auxiliary variable, the first output result of the second iteration, the first output result of the second iteration, is an acceleration step, is a learnable parameter; The output of the gradient descent module is represented as: ； wherein, denotes a derivation operation, is an output of the gradient descent module, is a gradient descent step size; The expression of the solution in the original data domain in step S4 is: ； wherein, is an output of the proximal mapping module, denotes a soft threshold function, is a threshold, denotes a learnable sparse transform function, denotes an inverse transform of is implemented by a convolutional neural network, the convolutional neural network comprises four convolutional layers and three rectified linear units, an input of the first convolutional layer is an input of the convolutional neural network, an output of the first convolutional layer is an input of the first rectified linear unit, an output of the first rectified linear unit is an input of the second convolutional layer, an output of the second convolutional layer is an input of the second rectified linear unit, an output of the second rectified linear unit is an input of the third convolutional layer, an output of the third convolutional layer is an input of the third rectified linear unit, an output of the third rectified linear unit is an input of the fourth convolutional layer, and an output of the fourth convolutional layer is an output of the convolutional neural network; the four convolutional layers adopt one-dimensional convolutional kernels; S5, based on the training set of step S2, train the FISTA-Net network model constructed in step S4; S6, based on the trained FISTA-Net network model, scanning radar imaging is carried out.

2. The radar high-resolution imaging method based on fast shrinkage iterative threshold network according to claim 1, characterized in that, The radar echo model in step S1 is represented as: ； wherein, is the distance between the target and the radar, denotes the scattering coefficient of the point target, denotes the antenna directivity function, c is the speed of light, denotes the signal carrier frequency, denotes the range pulse compression response function, denotes the bandwidth of the linear frequency modulated signal.

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