Sparse trajectory SAR imaging method based on untrained complex valued neural network

Abstract

The invention relates to a sparse trajectory SAR (Synthetic Aperture Radar) imaging method based on an untrained complex valued neural network. The method comprises the following steps: constructing a basic mathematical model and an optimization target of sparse SAR imaging; setting a sparse rate r, selecting sparse trajectory configuration, and determining a trajectory index of the synthetic aperture radar; a radar system is controlled, and an echo signal s is collected; filling a preset zero matrix with the obtained echo signal s, generating a sparse signal s', and generating a mask matrix M; reconstructing an optimization target of sparse SAR imaging under the sparse trajectory; building a complex valued neural network F theta based on U-Net; the optimization target is re-expressed as # imgabs0 # imgabs1 #, the network parameter theta is continuously adjusted by minimizing the target, and after the optimal parameter # imgabs2 # is obtained, the output # imgabs3 # of the network is the optimal SAR imaging result. The method is short in scanning time, small in data acquisition amount, high in matching degree between the sparse sampling mode and the physical trajectory, and high in imaging quality.

Description

Technical Field

[0001] The invention relates to the field of radar imaging technology, in particular to a sparse trajectory SAR imaging method based on an untrained complex-valued neural network. Background Art

[0002] Millimeter-wave synthetic aperture radar (SAR) is a radar technology with high-resolution imaging capabilities, which is widely used in security inspection, non-destructive testing, and medical diagnosis. It uses the high-frequency characteristics of millimeter waves to detect through clothing, walls, and non-metallic barriers. However, in order to achieve high-resolution imaging, the millimeter-wave SAR system needs to sample data along a predetermined dense trajectory to meet the requirements of the Nyquist sampling theorem. This sampling method usually takes a long scanning time, ranging from tens of minutes to several hours, resulting in low system operation efficiency. At the same time, the amount of data collected is huge, which poses a severe challenge to the efficiency of subsequent imaging algorithm processing.

[0003] In order to reduce scanning time and data size, sparse sampling technology has been introduced into millimeter wave SAR imaging systems. Sparse SAR imaging methods are based on the theory of compressed sensing (CS). By assuming the sparsity of collected data, high-quality images can be reconstructed when the sampling data is reduced, which significantly improves the processing and computational efficiency of SAR imaging algorithms. However, there are still many problems in the implementation of existing sparse sampling schemes: on the one hand, the theory of compressed sensing relies on random non-uniform sampling to meet the restricted isometry property (RIP), but the scanning trajectory in the SAR system is usually subject to physical constraints, making it difficult to achieve highly randomized sampling. On the other hand, if a non-random, highly regular sparse sampling pattern is adopted, the method based on compressed sensing may not meet the RIP criterion, resulting in a significant decrease in the image reconstruction effect. In addition, traditional SAR imaging algorithms (such as back-projection algorithms and range migration algorithms) are prone to artifacts, distortion, or even failure when the sampling trajectory or data volume is reduced, further limiting the practicality of sparse sampling strategies.

[0004] In the existing technology, although the compressed sensing method has shown certain advantages in reducing the data size, it has not effectively solved the contradiction between scanning trajectory optimization and actual physical configuration. Therefore, how to design an imaging method that can take into account the sparse sampling strategy and the actual constraints of the SAR scanning trajectory while ensuring the imaging quality has become a key challenge in the current millimeter wave SAR imaging technology. Summary of the invention

[0005] In view of the problems in the above-mentioned existing millimeter-wave synthetic aperture radar (SAR) imaging technology, such as long scanning time, large amount of data collection, and mismatch between sparse sampling mode and physical trajectory resulting in reduced imaging quality, the present invention provides a sparse trajectory SAR imaging method based on an untrained complex-valued neural network.

[0006] The technical solution adopted by the present invention to solve its technical problem is:

[0007] A sparse trajectory SAR imaging method based on an untrained complex-valued neural network comprises the following steps:

[0008] S1. Construct the basic mathematical model and optimization objectives of sparse SAR imaging;

[0009] S2, setting the sparse rate r and selecting the sparse trajectory configuration, and determining the trajectory index of the synthetic aperture radar;

[0010] S3, controlling the radar system according to the sparse trajectory configuration and trajectory index in step S2 to collect the echo signal s;

[0011] S4, filling the obtained echo signal s into a preset zero matrix to generate a sparse signal s′, and generating a mask matrix M based on the sampling position;

[0012] S5, reconstructing the optimization target of sparse SAR imaging under sparse trajectory according to the sparse signal s' and the mask matrix M;

[0013] S6. Build a complex-valued neural network F based on U-Net θ , θ is the parameter of the complex-valued neural network. The input of the network is a fixed value z, which is sampled from complex random variables that obey an independent uniform distribution U(0,1) and has the same size as the image.

[0014] S7. The optimization objective is restated as:

[0015] S8, by minimizing the above objectives, continuously adjust the network parameters θ, and when the optimal parameters are obtained After that, the network output This is the optimal SAR imaging result.

[0016] Furthermore, in step S7,

[0017] According to the frequency domain SAR imaging method, the observation approximation operator O(·) of the observation matrix Φ is obtained by azimuth-range decoupling; the mapping relationship between the reconstructed echo signal s, the observation matrix Φ and the scattering coefficient σ is approximately as follows: Introducing the structured sparse regularization term L SS

[0018]

[0019] in, represents the convolution operation, g is the Gaussian kernel function, the kernel size is set to 3×3, and Υ is an arbitrary small positive number used to avoid the denominator being zero; the final optimization goal is:

[0020]

[0021] Furthermore, in step S8, the learning rate of the network is set to 9e-4, AdamW is used as the optimizer, the iteration number is 1000 rounds, the loss function is minimized in an iterative manner, and the network parameter θ is updated during the optimization process. When the iteration is terminated, the network output This is the SAR imaging result.

[0022] Furthermore, in step S1, the imaging scene is represented by a discretized pixel grid, and the matrix form of the echo signal is used respectively. and the matrix form of the target scattering coefficient To describe the relationship between the radar echo signal and the reflectivity function; the observation matrix The relationship between radar echo and target scattering coefficient is established, and its mathematical model is expressed as:

[0023] s=Φσ+∈

[0024] Among them, ∈ is white Gaussian noise in complex form;

[0025] The approximate target scattering coefficient is estimated by optimizing the following objective

[0026]

[0027] Among them, the first is the fidelity term, ensuring the accuracy of data fitting; the second term |σ| 1 is a regularization term that encourages the sparsity of the solution; the parameter λ plays a trade-off between fitting the data and promoting sparsity.

[0028] Furthermore, in step S2, before starting the SAR device, the configuration of the sparse trajectory is selected as EVS configuration or RHS configuration according to the specific scenario; then, the sparse rate r is set according to the total number of vertical sampling points N V Calculate the number of sparse trajectories l = N that need to be collected V ×r, calculate l sparse trajectories in N according to the sparse trajectory configuration V The corresponding index I={i 1 ,i 2,…,i M}, if it is EVS configuration, the index is evenly distributed among l sampling points; if it is RHS configuration, you only need to determine the starting point of the index.

[0029] Furthermore, in step S4, the zero matrix is represents a fully sampled grid; according to index I, the value of the echo signal s is inserted into the zero matrix G to form a sparse signal s';

[0030] The mask matrix is ​​defined as:

[0031] The mask matrix M records the positions of the sampling indices.

[0032] Furthermore, in step S5, the optimization goal is:

[0033]

[0034] Where ⊙ represents the Hadamard product, and (s'-Φσ)⊙M ensures that only sampled points are used for error calculation.

[0035] The beneficial effects of the present invention are:

[0036] The present invention does not require the use of supervised data for pre-training, and directly performs unsupervised sparse imaging on single-shot acquisition data. By designing a sparse trajectory configuration, the scanning time and data acquisition are reduced by 75% while maintaining the key resolution while reducing the number of samples. An untrained complex-valued neural network (CV-UNet) is used to directly invert and reconstruct single-shot sampling data, and the observation approximation operator is integrated with the structured sparse regularization to achieve high-precision reconstruction of sparse echo signals, thereby greatly reducing the acquisition and computing costs and meeting the needs of fast, high-resolution imaging under resource-constrained conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 Two sparse trajectory design diagrams of the present invention;

[0038] Figure 2 The perceptual target map used in the experiment of the present invention;

[0039] Figure 3 An imaging diagram of the EVS sparse trajectory configuration of the present invention;

[0040] Figure 4 An imaging diagram of the RHS sparse trajectory configuration of the present invention; DETAILED DESCRIPTION

[0041] In order to better understand the present invention, the technical solutions in the embodiments of the present invention are clearly and completely described below. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0042] The sparse trajectory SAR imaging method based on an untrained complex-valued neural network of the present invention is introduced in the following two parts:

[0043] Part I: Determine sparse trajectory configuration and sparse data preprocessing:

[0044] The basic mathematical model and optimization objectives of sparse SAR imaging are modeled, the sparse rate r is set, the sparse trajectory configuration (extended vertical spacing sampling (EVS) or reduced vertical height sampling (RHS)) is selected, and the trajectory index of the synthetic aperture radar is determined. The radar system is controlled according to the designed sparse trajectory configuration and trajectory index to collect echo signals. The obtained echo signals are filled into the preset zero matrix to generate a sparse echo matrix, and a mask matrix is ​​generated based on the sampling position. According to the sparse echo matrix and the mask matrix, the optimization objectives of sparse SAR imaging under sparse trajectory are reconstructed.

[0045] The specific steps are as follows: In sparse SAR imaging, the imaging scene is represented by a discretized pixel grid. Assume that the number of sampling points of the radar sensor in the horizontal and vertical directions is N respectively. H and N V , the height and width of the target scattering coefficient area are N x and N y , respectively using the matrix form of the echo signal and the matrix form of the target scattering coefficient To describe the relationship between the radar echo signal and the reflectivity function. The observation matrix The relationship between radar echo and target scattering coefficient is established, and its mathematical description can be expressed as:

[0046] s=Φσ+∈

[0047] Where ∈ is white Gaussian noise in complex form, and the approximate target scattering coefficient can be estimated by the following optimization objective

[0048]

[0049] Among them, the first is the fidelity term, ensuring the accuracy of data fitting. The second term |σ| 1is a regularization term that encourages sparsity of the solution. The parameter λ plays a trade-off between fitting the data and promoting sparsity.

[0050] The present invention proposes two sparse trajectory configuration schemes to reduce the number of samples while ensuring accurate reconstruction of reflectivity. Figure 1 These configurations can simplify the control of the radar system and reduce the sampling complexity. The specific strategies are as follows:

[0051] Expanded Vertical Sampling (EVS): Reduce the total number of sampling points by increasing the vertical sampling interval. When the vertical resolution is lower than the azimuth resolution, the extended vertical sampling interval can significantly reduce the number of samples without affecting the azimuth resolution.

[0052] Reduced Height Sampling (RHS): Limits the vertical sampling range and excludes sampling points at the top of the grid. By reducing the vertical range, the number of sampling points is reduced while maintaining the azimuth distribution density. This method is suitable for scenes where targets are concentrated in a specific vertical area, such as when targets are distributed in a narrow height range.

[0053] First, before starting the SAR device, select the configuration of sparse trajectories according to the specific scenario.

[0054] Next, set the sparse rate r in the range [0.25, 1.0], based on the total number of vertical sampling points N. V Calculate the number of sparse trajectories l = N that need to be collected V ×r, calculate l sparse trajectories in N according to the sparse trajectory configuration V The corresponding index set I={i 1 ,i 2 ,…,i l}, if it is EVS configuration, the index is evenly distributed among l sampling points; if it is RHS configuration, it is only necessary to determine the starting point of the index. After determining the index, the SAR radar imaging system moves along a predefined sparse trajectory by programming the control driver in the PLC control chassis to achieve virtual synthetic aperture and continuous data acquisition, and the collected echo signal is recorded as s.

[0055] Then, the echo signal s is sparsely processed. Construct a zero matrix Represents a fully sampled grid. According to the index I, the value of the echo signal s is inserted into the zero matrix G to form a sparse signal s'. In addition, a mask matrix M is generated to record the position of the sampling index. The definition of the mask matrix is:

[0056]

[0057] Since the sparse trajectory leads to uneven distribution of sampled data, the missing values ​​in s′ need to be processed during the recovery process. Therefore, the optimization objective is reconstructed:

[0058]

[0059] Where ⊙ represents the Hadamard product, and (s'-Φσ)⊙M ensures that only sampled points are used for error calculation.

[0060] Part II: Untrained complex-valued neural network initialization, iterative optimization and image inversion:

[0061] An untrained neural network with a complex-valued U-Net (CV-UNet) structure is constructed; a random code vector z from a uniform distribution is used as the network input, without the need for pre-training with a large-scale data set; the network input result is transformed by the observation approximation operator to obtain the restored sparse echo signal, and the consistency loss between the restored sparse echo signal and the actual sparse echo data is calculated by the minimum mean square error. At the same time, the structured sparse loss of the restored sparse echo signal is calculated using structured sparse regularization, and the parameters of the network are jointly iteratively optimized by combining the two losses. After the network iterative optimization is completed, the optimized network output is used as the scattering coefficient distribution of the target scene, which is the result of sparse SAR imaging.

[0062] The specific steps are as follows: First, build a complex-valued neural network F based on U-Net θ , θ is the parameter of the complex-valued neural network. The network parameters do not need to be trained in advance using large-scale data sets. The input of the network is a fixed value z. The input data z is sampled from complex random variables that obey independent uniform distribution U(0,1) and has the same size as the image. According to the prior assumptions of the neural network, there is a parameter representation of the generated target image in the network structure, that is, the output F of the network θ (z) = σ is the result of SAR imaging, so the optimization objective can be restated as:

[0063]

[0064] By minimizing the above objectives, the network parameters θ are continuously adjusted, and the optimal parameters are obtained. After that, the network output That is the optimal SAR imaging result. However, the observation matrix Φ is usually very large, and direct storage and calculation are not feasible. To this end, the present invention obtains the observation approximation operator O(·) of the observation matrix Φ through azimuth-range decoupling based on the frequency domain SAR imaging method, and significantly reduces the calculation and storage costs by avoiding the direct use of the full observation matrix. Among them, the frequency domain SAR imaging method adopts the range migration algorithm RMA, and the RMA method can be simplified as the imaging operator I(·), and the specific formula is as follows:

[0065]

[0066] in, Represents the 2D inverse Fourier transform, FT 2D represents the 2D Fourier transform, ⊙ is the Hadamard product, and Ψ is the phase compensation factor. The mapping relationship between the echo signal s, the measurement matrix Φ, and the scattering coefficient σ can be approximated as It is not difficult to find that σ=I(s)=O -1 (σ), so the imaging operator I(·) and the observation approximation operator O(·) have an inverse relationship, so O(·) is the inverse operation of I(·), expressed as:

[0067]

[0068] in, is the conjugate of Ψ. Therefore, s=Φσ can be approximated as s=O(σ).

[0069] The mapping relationship between the reconstructed echo signal s, the measurement matrix Φ and the scattering coefficient σ can be approximated as Secondly, L1 regularization only considers the sparsity of radar images, but radar images usually have structured sparsity. We introduce the structured coefficient regularization term L SS

[0070]

[0071] in, represents the convolution operation, is a Gaussian kernel function, the kernel size is set to 3×3, and Υ is an arbitrary small positive number used to avoid the denominator being zero. The final optimization goal is the final loss function:

[0072]

[0073] The learning rate of the network is set to 9e-4, AdamW is used as the optimizer, the iteration number is 1000 rounds, the loss function is minimized in an iterative manner, and the network parameters θ are updated during the optimization process.

[0074] When the iteration ends, the network outputs This is the SAR imaging result.

[0075] The complex-valued U-Net network mentioned above consists of an encoder and a decoder. The input of the network is a fixed randomly encoded noise image z of size 512×512×1. The encoder consists of five complex-valued convolution blocks (Complex ConvBlock). Each block gradually reduces the spatial size from 512×512 to 16×16, and the number of channels increases in sequence [4, 8, 16, 32, 64]. Each block includes complex-valued convolution, complex-valued batch normalization and complex-valued LeakyReLU activation function, and finally downsamples through complex-valued maximum pooling. The decoder gradually restores the spatial resolution through complex-valued neighbor upsampling. The skip connections (Skip Connections) between the encoder and decoder fuse low-level details and high-level features through element-by-element addition to avoid increasing computational overhead. The final output is generated through a complex-valued convolution layer to restore a complex-valued SAR image of size 512×512×1.

[0076] The effect of the present invention is verified by experiments as follows:

[0077] In order to verify and compare the imaging capability of the present invention (hereinafter referred to as mmUSAR) under sparse trajectory configuration, experiments were conducted on publicly available measured data, and compared with the traditional imaging algorithm RMA, the compressed sensing-based method ISTA, ADMM, and the untrained neural network method CCN, ComDecoder. All experiments were performed on a workstation equipped with 32GB RAM, Intel Corei9-10900K CPU and NVIDIA GeForce RTX 4090GPU. In order to quantitatively evaluate the imaging quality, we used two indicators: image entropy (IE) and image contrast (IC). Image entropy (IE) is a measure of the amount of information contained in the image, and lower values ​​indicate better noise suppression. On the other hand, image contrast (IC) quantifies the sharpness of the image and its noise suppression, and higher values ​​indicate better reconstruction quality. Figure 2 is the perceived target map.

[0078] The results of EVS sparse trajectory configuration are as follows Figure 3 As shown in Table 1 below.

[0079]

[0080] In the EVS configuration, mmUSAR consistently outperforms the baseline methods at all sparsity rates. At SR=0.25, mmUSAR achieves the lowest IE (11.64) and highest IC (10.33), significantly outperforming the next best method, ComDecoder. While methods such as ISTA and ADMM provide some noise suppression, they are unable to effectively remove background artifacts, resulting in higher IE values. Untrained neural network methods (CCN and ComDecoder) show promising artifact suppression but still exhibit blurring of target outlines. As the sparsity rate increases to 0.375 and 0.5, the performance difference narrows, but mmUSAR still maintains its lead, demonstrating its robustness.

[0081] The result of RHS sparse trajectory configuration is as follows Figure 4 and as shown in Table 2 below.

[0082]

[0083] In the RHS configuration, mmUSAR once again stands out, consistently outperforming the baseline methods at all sparsity rates. At SR=0.25, mmUSAR achieves the lowest IE (11.55) and highest IC (11.28). Despite the absence of artifact issues in the RHS configuration, all methods produce clear imaging results, and mmUSAR continues to provide the clearest structural details. As the sparsity rate decreases, the performance gap between mmUSAR and other methods narrows, but mmUSAR still achieves the best trade-off between noise reduction and detail preservation.

[0084] In both experimental settings, the superior performance of mmUSAR is attributed to its network structure prior and regularization ability of structured sparse features, which enables it to adapt to different sparse trajectory configurations and effectively suppress noise and artifacts. The results confirm that mmUSAR outperforms traditional model-based algorithms (such as RMA, ISTA and ADMM) and neural network-based methods (such as CCN and ComDecoder) in radar image reconstruction.

[0085] Experimental results show that the present invention reduces scanning time and data acquisition by 75% through sparse trajectory configuration, and provides high-fidelity SAR imaging results through neural network methods and structured sparse constraints. The method does not require the use of supervised data training in advance, and directly performs unsupervised sparse imaging on single-shot acquisition data.

[0086] It should be noted that, in the above method, steps, parameters, models, etc. not described here belong to the prior art and are well known to those skilled in the art. Therefore, they will not be described in detail.

[0087] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit it. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A sparse trajectory SAR imaging method based on an untrained complex-valued neural network, characterized in that: The steps include: S1. Construct the basic mathematical model and optimization objectives of sparse SAR imaging; S2, setting the sparse rate r and selecting the sparse trajectory configuration, and determining the trajectory index of the synthetic aperture radar; S3, controlling the radar system according to the sparse trajectory configuration and trajectory index in step S2 to collect the echo signal s; S4, filling the obtained echo signal s into a preset zero matrix to generate a sparse signal s′, and generating a mask matrix M based on the sampling position; S5, reconstructing the optimization target of sparse SAR imaging under sparse trajectory according to the sparse signal s' and the mask matrix M; S6. Build a complex-valued neural network F based on U-Net θ , θ is the parameter of the complex-valued neural network. The input of the network is a fixed value z, which is sampled from complex random variables that obey an independent uniform distribution U(0,1) and has the same size as the image. S7. The optimization objective is restated as: S8, by minimizing the above objectives, continuously adjust the network parameters θ, and when the optimal parameters are obtained After that, the network output This is the optimal SAR imaging result.

2. The sparse trajectory SAR imaging method based on an untrained complex-valued neural network according to claim 1, characterized in that: In step S7, According to the frequency domain SAR imaging method, the observation approximation operator O(·) of the observation matrix Φ is obtained by azimuth-range decoupling; the mapping relationship between the reconstructed echo signal s, the observation matrix Φ and the scattering coefficient σ is approximately as follows: Introducing the structured sparse regularization term L SS in, represents the convolution operation, is a Gaussian kernel function, the kernel size is set to 3×3, and Υ is an arbitrary small positive number used to avoid the denominator being zero; the final optimization goal is:

3. The sparse trajectory SAR imaging method based on an untrained complex-valued neural network according to claim 2, characterized in that: In step S8, the learning rate of the network is set to 9e-4, AdamW is used as the optimizer, the iteration number is 1000 rounds, the loss function is minimized in an iterative manner, and the network parameter θ is updated during the optimization process. When the iteration is terminated, the network output This is the SAR imaging result.

4. The sparse trajectory SAR imaging method based on an untrained complex-valued neural network according to claim 1, characterized in that: In step S1, the imaging scene is represented by a discretized pixel grid, and the matrix form of the echo signal is used respectively. and the matrix form of the target scattering coefficient To describe the relationship between the radar echo signal and the reflectivity function; the observation matrix The relationship between radar echo and target scattering coefficient is established, and its mathematical model is expressed as: s=Φσ+∈ Among them, ∈ is white Gaussian noise in complex form; The approximate target scattering coefficient is estimated by optimizing the following objective Among them, the first is a fidelity term that ensures the accuracy of data fitting; the second term |σ|1 is a regularization term that encourages the sparsity of the solution; the parameter λ plays a trade-off between fitting the data and promoting sparsity.

5. The sparse trajectory SAR imaging method based on an untrained complex-valued neural network according to claim 1, characterized in that: In step S2, before starting the SAR device, first, the configuration of the sparse trajectory is selected as EVS configuration or RHS configuration according to the specific scenario; then, the sparse rate r is set according to the total number of vertical sampling points N V Calculate the number of sparse trajectories l = N that need to be collected V ×r, calculate l sparse trajectories in N according to the sparse trajectory configuration V The corresponding index I={i1,i2,…,i l }, if it is EVS configuration, the index is evenly distributed among l sampling points; if it is RHS configuration, you only need to determine the starting point of the index.

6. The sparse trajectory SAR imaging method based on an untrained complex-valued neural network according to claim 1, characterized in that: In step S4, the zero matrix is represents a fully sampled grid; according to index I, the value of the echo signal s is inserted into the zero matrix G to form a sparse signal s'; The mask matrix is ​​defined as: The mask matrix M records the positions of the sampling indices.

7. The sparse trajectory SAR imaging method based on an untrained complex-valued neural network according to claim 1, characterized in that: In step S5, the optimization goal is: Where ⊙ represents the Hadamard product, and (s'-Φσ)⊙M ensures that only sampled points are used for error calculation.

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