Scanning radar super-resolution imaging method based on data-driven adaptive parameter learning

Abstract

The invention discloses a scanning radar super-resolution imaging method based on data-driven adaptive parameter learning, which is applied to the technical field of radar imaging and aims to overcome the defects that a traditional super-resolution method is high in parameter sensitivity and an existing network expansion method has a redundant structure and poor adaptability. The method comprises the following steps: firstly, converting a non-differentiable L1 regularization problem into a differentiable L2 problem based on a maximum-minimum principle; secondly, expanding an iteration process into a multi-stage cascade neural network, and performing adaptive learning on regularization parameters in a data driving mode; and finally, layered parameter optimization and super-resolution reconstruction are realized through an end-to-end network architecture. By adopting the method of the invention, the super-resolution imaging performance of the radar is effectively improved.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of radar imaging, and particularly relates to a scanning radar angle super-resolution imaging technology. BACKGROUND

[0002] A real-aperture radar can obtain omnidirectional target detection information through beam scanning, but the angular resolution thereof is limited by the antenna size and is usually low.

[0003] To improve the angular resolution of real aperture radar, the paper "Yulin Huang, Yuebo Zha, Yue Wang, and Jianyu Yang, "Forward looking radar imaging by truncated singular value decomposition and its application for adverse weather aircraft landing," Sensors, vol. 15, no. 6, pp. 14397-14414, 2015" proposes a radar super-resolution imaging method based on truncated singular value decomposition, which can achieve angular super-resolution under low signal-to-noise ratio conditions, but its resolution capability is limited in scenes containing close-range targets. Subsequently, the paper "Yongchao Zhang, Yin Zhang, Wenchao Li, Yulin Huang, and Jianyu Yang, "Super-resolution surface mapping for scanning radar: inverse filtering based on the fast iterative adaptive approach," IEEE transactions on geoscience and remote sensing, vol. 56, no. 1, pp. 127-144, 2017" applies the fast iterative adaptive method to scanning radar super-resolution, which improves the imaging resolution through spectral estimation, but this method requires multiple inverse operations on high-dimensional matrices, and its real-time performance is not good. Further, the paper "Juezhu Lai, Ding Yuan, Jifang Pei, Deqing Mao, Yin Zhang, Xingyu Tuo, and Yulin Huang, "Scanning radar scene reconstruction with deep unfolded ista neural network," in 2023IEEE Radar Conference (RadarConf23). IEEE, 2023, pp. 1-6" proposes ISTA-Net for complex scene super-resolution imaging, which shows good reconstruction performance on simulated data, but its adaptability to scenes is still insufficient. SUMMARY

[0004] In view of the defects of high parameter sensitivity of traditional super-resolution methods, redundant structure and adaptability of existing unfolding network methods, the application provides a scanning radar super-resolution imaging method based on data-driven adaptive parameter learning.

[0005] The technical scheme adopted by the application is as follows: a scanning radar super-resolution imaging method based on data-driven adaptive parameter learning, comprising:

[0006] S1, pulse compression and range migration correction are performed on the two-dimensional echo signals obtained by the radar to obtain real beam echo s;

[0007] S2, based on the real beam echo s obtained in step S1, a regularization method is introduced to obtain an expression for estimating the target scattering coefficient;

[0008] S3, the target scattering coefficient is approximately solved by constructing an upper bound function, so as to obtain a target scattering reconstruction expression and a diagonal update expression;

[0009] S4, in combination with a hierarchical adaptive MM learning architecture, a target scattering reconstruction module and a diagonal update module are set for each layer iteration, and the update process in each layer is as follows: the diagonal update module is updated based on the regularization parameter of the current iteration, and the output of the diagonal update module is used as the input of the target scattering reconstruction module; the interlayer update process is as follows: the output result of the target scattering reconstruction module of the previous layer is used as the input of the diagonal update module of the next layer.

[0010] The reconstruction error between the output of the target scattering reconstruction module of the last layer and the target real scattering coefficient is used as a loss function, and the parameters in the diagonal update module are updated by backward propagation based on the loss function, so as to perform a new iteration calculation process until the maximum iteration number is reached, and then the output of the target scattering reconstruction module of the last layer is used as the final target scattering reconstruction result.

[0011] The application has the following beneficial effects: the method firstly converts the non-differentiable L1 regularization problem into a differentiable L2 sub-problem based on the MM principle; then the MM iteration process is unfolded into a multi-level cascading neural network, each layer corresponds to one MM iteration, and the regularization parameter of each layer is adaptively learned in a data-driven manner; finally, through hierarchical parameter design, the traditional single fixed parameter is expanded to KxN learnable parameters, improving the flexibility and adaptive ability of the network. Compared with the traditional super-resolution method, the method effectively combines the interpretability of the MM framework and the data-driven advantage of deep learning, and realizes better super-resolution reconstruction performance through end-to-end learning. BRIEF DESCRIPTION OF DRAWINGS

[0012] Figure 1 The working principle and echo acquisition process of the forward-looking scanning radar;

[0013] Figure 2 Network structure diagram of the present application;

[0014] Figure 3 Data set example;

[0015] Wherein, (a) is a real scene, (b) is a real beam echo;

[0016] Figure 4 Processing results of different super-resolution methods;

[0017] Wherein, (a) is a real scene, (b) is a real beam echo, (c) is the processing result of Tikhonov L2 algorithm, (d) is the processing result of L1-SplitBregman method, (e) is the processing result of L1-MM method, and (f) is the processing result of the method of the present application;

[0018] Figure 5 Profile results of different super-resolution methods;

[0019] Wherein, (a) is a simulation scene, (b) is a real beam echo, (c) is the processing result of Tikhonov L2 method, (d) is the processing result of L1-SplitBregman method, (e) is the processing result of L1-MM method, and (f) is the processing result of the method of the present application. DETAILED DESCRIPTION

[0020] In order to facilitate those skilled in the art to understand the technical content of the present application, the content of the present application is further explained below in combination with the drawings.

[0021] The present application is mainly verified by simulation experiment method, and all steps and conclusions are verified correct on Pycharm2024. The method of the present application is further described below in combination with the drawings and specific embodiments.

[0022] The specific implementation steps are as follows:

[0023] Step one: azimuth echo convolution model establishment

[0024] The working principle of scanning radar is as shown in Figure 1 The radar system observes the scene by beam scanning to obtain two-dimensional echo signals. The received echo is modulated by linear frequency modulation waveform and antenna pattern, producing the following echo model:

[0025]

[0026] Wherein, s p represents the two-dimensional target echo of the target at the target point p, τ is the distance dimension fast time, x P is the scattering coefficient of the target P, and θ is the azimuth angleP is the azimuth angle corresponding to the target P, K r is the frequency modulation, τ P is the two-way echo delay, T r is the pulse duration, f0is the carrier frequency.

[0027] After pulse compression and range migration correction, the real beam echo s can be obtained as shown in Fig. Figure 3 (b), which is expressed as the convolution of the antenna pattern and the target scattering coefficient:

[0028] s = Hx + n (2)

[0029] wherein, is the echo matrix, denotes the signal preprocessed in the range direction, is the target scattering coefficient matrix, denotes the target scattering coefficient located at the azimuth angle θ1, and similarly, denotes the target scattering coefficient located at the azimuth angle θ2, denotes the target scattering coefficient located at the azimuth angle θ N ; is the noise matrix. H is the antenna measurement matrix composed of the circular convolution of the antenna pattern H(θ), and N is the number of azimuth sampling points.

[0030] Step two: maximization-minimization approximation

[0031] Due to the ill-posedness of the antenna measurement matrix, the target cannot be directly inverted from the noise-contaminated echo. To alleviate the ill-conditioning, a regularization method is introduced:

[0032]

[0033] wherein, is the estimated target scattering coefficient, argmin x denotes the value of the variable x that makes the objective function minimum, and λ is the regularization coefficient; denotes the square of the L2 norm, ||f(x)| p is the generalized regularization term, and p denotes the generalized norm. Let f(x) = x and p = 1, and the commonly used coefficient regularization method

[0034]

[0035] Due to the nondifferentiability of ||x||1, the maximization-minimization (MM) principle is adopted to solve it approximately by constructing its upper bound function, which needs to satisfy G(x|x k) = ||x||1. A direct approach is to use a quadratic function as an upper bound, which is

[0036]

[0037] where G(x|x k ) represents the upper bound function of L1 norm ||x||1 based on the current iteration value x k ; x k represents the target scattering coefficient of the kth iteration, the superscript T represents the transpose of the matrix / vector, and k = diag(1 / |x k |), diag represents a diagonal matrix, and by the above method, the sparse regularization problem can be approximated as:

[0038]

[0039] The above solving strategy contains two variables, i.e., x and k , which can be decomposed into the following sub-problems:

[0040]

[0041] The derivatives of the above two sub-problems are obtained by derivation, and the derivatives are set to 0, i.e., the following equations are obtained:

[0042]

[0043] In the inversion process, the diagonal loading of k is loaded into the matrix to correct the ill-conditioned property, thereby enhancing the stability of the inversion. The traditional sparse MM method has significant limitations. The regularization parameter lambda is fixed under the constraint of the iteration layer and the interlayer parameter, which restricts the performance of the algorithm. Specifically, the traditional method shares the same regularization strength lambda among different azimuth elements in a single iteration; meanwhile, the fixed parameter (k) = lambda (0) is used between different iteration layers, which cannot dynamically adjust the regularization weight according to the iteration process, leading to the difficulty in balancing the fidelity and sparsity requirements in the reconstruction process.

[0044] Step three: MM expansion network design

[0045] To solve the above problems, the present application proposes a hierarchical adaptive MM learning architecture: first, the regularization parameter set of each iteration layer is independently designed, i.e., the kth layer parameter is to realize the differentiation of the intra-layer parameters; in addition, the inter-layer dynamic parameter (k) is designed to update the intra-layer and inter-layer parameters in a data-driven manner, wherein i represents the ith azimuth element, and N represents the number of azimuth sampling points. The iteration process can be updated as follows:

[0046] 1) Scattering reconstruction module:

[0047] x k+1 =(H T H+Λ k ) -1 H T s (9)

[0048] x (0) For the initial coarse imaging results, x (0) =(H T H+I) -1 H T The initial value s serves as the starting point for the first iteration, providing a preliminary estimate of the target scattering coefficient.

[0049] 2) Diagonal update module:

[0050] Λ k =λ (k) diag(1 / |x k |) (10)

[0051] Λ0 is updated by the diagonal update module based on the initial value x (0) and the first layer's regularization parameter set λ (0) Calculations show that all parameters in this invention are initialized to 1, and the formula is Λ0 = λ. (0) diag(1 / |x 0 |).

[0052] Network architecture such as Figure 2 As shown, the number of unfolded layers K is set to 10. The sparse reconstruction of the target scattering coefficients is achieved by using the unfolded MM algorithm and iterating alternately between the two modules. The initialization module can be considered as coarse imaging, designed to accelerate network convergence, i.e., x (0 )=(H T H+I) -1 H T s, where I represents the identity matrix, and the coarse imaging result is as follows: Figure 2 The image obtained after initialization is shown.

[0053] In practical applications, the values ​​of the regularization parameter set for each layer are learned from the training data through a data-driven approach.

[0054] Step 4: Establishing the loss function

[0055] In radar super-resolution imaging tasks, the primary objective of this invention is to recover the target scattering coefficients from observation echoes affected by noise. The loss function can be defined as the sum of the network reconstruction results and... Figure 3 The reconstruction error between the true scattering coefficients x of the target shown in (a) is expressed as follows:

[0056]

[0057] where K represents the maximum number of iterations, x K represents the iteration result of the Kth time.

[0058] Then the obtained loss is calculated by the chain rule to calculate the gradient of the loss function to the diagonal element of the Kth layer Finally, the parameters are updated by the stochastic gradient descent method, as shown in the following formula:

[0059]

[0060] where η is the learning rate, which is set to 1e-5.

[0061] In order to verify the effectiveness of the method, the simulation parameters shown in Table 1 are set, and the simulation results are shown in Figure 4 The scanning area is set to -10°-10°, wherein the original target scene is shown in Figure 4 (a), the target interval gradually increases from the center to both sides, and all target intervals are less than the main lobe width.

[0062] Table 1 Simulation system parameters

[0063] Parameter Value Carrier frequency 9.6 GHz Bandwidth 45 MHz Antenna scanning speed 60° / s Main lobe beam width 5° Pulse repetition frequency 1000 Hz Scanning range -10°～10°

[0064] The real beam echo is shown in Figure 4 (b), it can be seen that the real beam echo has low resolution and aliasing phenomenon, which leads to the inability to distinguish targets. After the target reconstruction algorithm, as shown in Figure 4 (c), the Tikhonov L2 algorithm improves the resolution to a certain extent, but cannot effectively distinguish the near-range target and the reconstructed target width is quite wide. And Figure 4 (d) and Figure 4 (e) respectively show the processing results of L1-SplitBregman and L1-MM methods, which have good resolution for distant targets and relatively narrow target reconstruction width, but are insufficient to distinguish near-range targets. Finally, Figure 4 (f) shows the results of the method, which effectively distinguishes the near-range target, and the reconstructed target width is significantly smaller than other methods, although the amplitude information of the minimum interval target in the middle is lost, but the overall resolution is improved obviously.

[0065] In order to more intuitively compare the resolution ability of different methods for dense targets, we select the distance profile with the smallest target interval in Figure 4 , and the results are shown in Figure 5 ​The simulation results are shown in FIG. 6, where the black dashed line represents the real target position. It can be seen that the conventional method cannot distinguish the dense targets. In contrast, the method of the present application significantly improves the resolution, and achieves distinguishable separation of the adjacent targets, although there is a certain loss of amplitude information. For the simulation results shown in FIG. 7, Table 2 gives the corresponding quantitative indicators. It can be seen that the method of the present application achieves good results in both indicators, proving the superiority of the method. Figure 4 The simulation results are shown in FIG. 6, where the black dashed line represents the real target position. It can be seen that the conventional method cannot distinguish the dense targets. In contrast, the method of the present application significantly improves the resolution, and achieves distinguishable separation of the adjacent targets, although there is a certain loss of amplitude information. For the simulation results shown in FIG. 7, Table 2 gives the corresponding quantitative indicators. It can be seen that the method of the present application achieves good results in both indicators, proving the superiority of the method.

[0066] Table 2 Performance comparison of the method of the present application and the existing method in terms of PSNR and SSIM

[0067] Method PSNR (dB) SSIM Tikhonov L2 method 22.0409 0.2448 [L1 -Split Bregman method] 30.4601 0.9004 [L1-MM method] 27.2071 0.7865 Method of the present invention 33.4289 0.9475

[0068] Those skilled in the art will realize that the embodiments described herein are for the purpose of helping to understand the principles of the present application and should be understood as not limiting the scope of protection of the present application to such specific statements and embodiments. The present application can have various modifications and changes for those skilled in the art. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present application shall be included in the scope of protection of the claims of the present application.

Claims

1. A scanning radar super-resolution imaging method based on data-driven adaptive parameter learning, characterized in that, include: S1. Perform pulse compression and range migration correction on the two-dimensional echo signal acquired by the radar to obtain the real beam echo s; S2. Based on the real beam echo s obtained in step S1, a regularization method is introduced to obtain an expression for estimating the target scattering coefficient; S3. The target scattering coefficient is approximated by constructing an upper bound function, thereby obtaining the target scattering reconstruction expression and the diagonal update expression; S4. Combining the hierarchical adaptive MM learning architecture, each layer iteration sets up a target scattering reconstruction module and a diagonal update module. The target scattering reconstruction module is constructed based on the target scattering reconstruction expression, and the diagonal update module is constructed based on the diagonal update expression. Each layer iteration independently designs a set of regularization parameters. The update process within each layer is as follows: the diagonal update module updates based on the regularization parameters corresponding to the current iteration, and the output of the diagonal update module is used as the input of the target scattering reconstruction module. The update process between layers is as follows: the output of the target scattering reconstruction module of the previous layer is used as the input of the diagonal update module of the next layer. The reconstruction error between the output of the last layer target scattering reconstruction module and the true scattering coefficient of the target is used as the loss function. The regularization parameters of each layer in the next iteration are updated by backpropagation based on the loss function, and a new iterative calculation process is carried out until the maximum number of iterations is reached. Then the output of the last layer target scattering reconstruction module is used as the final target scattering reconstruction result.

2. The scanning radar super-resolution imaging method based on data-driven adaptive parameter learning according to claim 1, characterized in that, The real beam echo s is represented as the convolution of the antenna pattern and the target scattering coefficient: s=Hx+n Where H represents the antenna measurement matrix, x represents the target scattering coefficient matrix, and n represents the noise matrix.

3. The scanning radar super-resolution imaging method based on data-driven adaptive parameter learning according to claim 2, characterized in that, The expression for estimating the target scattering coefficient in step S2 is: in, For the estimated target scattering coefficient, argmin x λ represents the value of variable x that minimizes the objective function, and λ is the regularization coefficient. Let ||·||1 represent the square of the L2 norm, and ||·||1 represent the L1 norm.

4. The scanning radar super-resolution imaging method based on data-driven adaptive parameter learning according to claim 3, characterized in that, The implementation process of step S3 is as follows: Due to the non-differentiability of ||x||1, we can approximate the solution by constructing an upper bound function using the maximization-minimization principle. This upper bound function must satisfy G(x|x) k G(x|x)>=||x||1, G(x|x) k The expression is: Where, x k Λ represents the target scattering coefficient in the k-th iteration. k =diag(1 / |x k |), diag represents a diagonal matrix; Will Transform into: The decomposition yields the following subproblems: Taking the derivatives with respect to x and Λ respectively, and setting the derivatives to 0, we get:

5. The scanning radar super-resolution imaging method based on data-driven adaptive parameter learning according to claim 4, characterized in that, The set of regularization parameters designed independently for each iteration in step S4 is represented as follows: Where, λ (k) This represents the set of regularization parameters for the k-th layer. represents the regularization parameter of the i-th azimuth unit in the k-th layer, and N represents the number of azimuth sampling points.

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