A deep learning microwave imaging method fusing virtual antenna data

Abstract

The application relates to a deep learning microwave imaging method fusing virtual antenna data, comprising the following steps: a two-dimensional electromagnetic scattering model is established, and original scattering field observation data are collected under a sparse antenna configuration; the original scattering field observation data are processed by adopting a Fourier zero padding (FDZP) method, virtual scattering field data based on FDZP expansion are obtained, and a data set is further constructed; an FDZP-UNet network is constructed; the data set is input into the FDZP-UNet network, target dielectric constant prediction is output, and a high-resolution reconstructed image is further obtained. The deep learning microwave imaging method fusing virtual antenna data provided by the application comprehensively considers three performance indexes of imaging fidelity, system hardware cost and reconstruction efficiency, realizes virtual aperture expansion at a physical level through the Fourier domain zero padding method, effectively makes up for the physical information loss caused by sparse sampling, and greatly reduces the dependence on a large-scale physical antenna array.

Description

Technical Field

[0001] This invention pertains to microwave imaging and electromagnetic backscattering, and specifically relates to a deep learning microwave imaging method that integrates virtual antenna data. Background Technology

[0002] Electromagnetic backscattering imaging, a core technology in microwave imaging, reconstructs the dielectric property distribution of a target object by detecting the scattered electromagnetic waves. It has shown great application potential in fields such as medical diagnostics, industrial non-destructive testing, and geoscientific remote sensing. For microwave imaging systems, the scale of the antenna array deployment and the reconstruction capability of the imaging algorithm are key factors determining system performance, while engineering bottlenecks include spatial layout constraints, hardware deployment costs, and data acquisition time. However, due to these engineering bottlenecks, the construction of large-scale arrays often faces severe challenges in practical applications.

[0003] In practical imaging systems, image fidelity is often chosen as a core evaluation metric to measure the degree of matching between the reconstructed image and the physical features of the real target. To reduce system hardware complexity and shorten data acquisition cycles, sparse array configuration has become a key means of cost reduction. However, in practical applications, it has been found that while sparse array configuration is an effective way to reduce system complexity and data acquisition cycles, extremely sparse physical sampling leads to a severe loss of spatial spectral information, rendering traditional linear inversion methods ineffective. While complex nonlinear iterative compensation algorithms can improve reconstruction accuracy, their enormous computational overhead makes them unsuitable for real-time monitoring. This trade-off between multiple objectives has become a major technical bottleneck restricting the widespread application of low-cost, high-performance real-time microwave imaging technology. Summary of the Invention

[0004] The technical problem of this invention is to address the issues of low imaging accuracy, lack of physical information, and difficulty in real-time processing of nonlinear scattering effects caused by sparse antenna arrays in microwave imaging. This invention proposes a deep learning microwave imaging method that fuses virtual antenna data. It employs a Fourier domain zero-filling method to achieve virtual aperture expansion at the physical level, compensating for the lack of physical information caused by sparse sampling and reducing dependence on large-scale physical antenna arrays. Furthermore, the inversion process is introduced into the U-Net convolutional neural network, significantly reducing system hardware costs while improving reconstruction accuracy and imaging efficiency.

[0005] The purpose of this invention is to solve the above-mentioned problems and propose a deep learning microwave imaging method that fuses virtual antenna data. Through the synergistic effect of physical-level spectral enhancement and algorithm-level deep learning, high-performance imaging is achieved under sparse array conditions. The method includes the following steps:

[0006] S1: Establish a two-dimensional electromagnetic scattering model and collect raw scattering field observation data under a sparse antenna configuration; S2: The original scattered field observation data is processed using the Fourier zero-filling FDZP method to obtain virtual scattered field data based on FDZP extension, and then a dataset is constructed. S3: Construct the FDZP-UNet network; S4: Input the dataset into the FDZP-UNet network, output the target dielectric constant prediction, and then obtain a high-resolution reconstructed image.

[0007] Furthermore, a two-dimensional electromagnetic scattering model is used to simulate the interaction between electromagnetic waves and the target through the method of moments (MoM), obtaining the original scattered field observation data under a sparse antenna configuration. The calculation formula is as follows: ; ; ; ; In the formula, , and These represent the total electric field, the incident field, and the scattered field, respectively. Represents the Green's function. Represents angular frequency. and Let represent the permeability of the scattering medium and the background medium, respectively. This represents the difference in electrical parameters of the scatterer relative to the background medium. and These represent the dielectric constants of the scatterer and the background, respectively. This represents the position vector.

[0008] Preferably, step S2 includes the following sub-steps: 1) Perform a Fourier transform on the discrete sequence, the expression is: ; In the formula, Let M represent a discrete sequence, t represent the total length of the sequence, and t represent the time domain of the sequence. Represents the components of a frequency domain sequence; 2) Utilizing the periodicity of the rotation factor, the inverse discrete Fourier transform is rewritten in a symmetric form centered at zero frequency, as shown in the expression: ; ; In the formula, The t represents the rotation factor in the discrete Fourier transform, q and t represent the frequency domain index and time domain index, respectively, and j represents the imaginary unit; 3) In frequency domain sequences By inserting NM zeros between the high-frequency components, the constructed N-point enhanced spectrum is obtained. The expression is:

[0009] In the formula, N represents the length of the extended frequency domain sequence, and N>M; This represents the N-point enhanced frequency domain sequence obtained by extension, where u represents the frequency domain index; 4) By constructing the sequence Perform an N-point IDFT to obtain the spatial signal on the virtual antenna element. The expression is:

[0010] In the formula, and They represent Point discrete sequence and its Fourier transform, and They represent the expanded versions respectively. Point space signals and discrete Fourier transform.

[0011] Preferably, in step S3, the FDZP-UNet network includes a data preprocessing module, a core network module, and an imaging inference module. It achieves quantitative prediction of the target dielectric constant through the established nonlinear mapping model, and finally obtains the reconstructed image.

[0012] Furthermore, the data preprocessing module performs forward modeling on the dataset using the method of moments (MoM) system matrix construction and multi-aperture antenna simulation to obtain the original scattered field data. Then, it uses FDZP to perform virtual aperture expansion processing before training the model.

[0013] Preferably, the core network module is based on the U-Net convolutional neural network, adopts a symmetric encoding and decoding and skip connection structure, extracts multi-scale features of the scattering field, and then trains the U-Net sub-network with a pre-processed dataset.

[0014] Preferably, the imaging inference module inputs the preprocessed scattering field into the trained U-Net subnetwork and obtains the training result through end-to-end inference.

[0015] Furthermore, in step S3, the FDZP-UNet network also includes a loss function, expressed as: ; ; ; ; ; In the formula, , and These are the weighting coefficients for the loss of each component, which are set to 0.65, 0.25, and 0.1 respectively based on empirical experiments. For weighted root mean square error, These are the weighting coefficients; and These are the actual physical values ​​and the network-predicted values, respectively. , and Weighting factor, weight enhancement coefficient, and preset threshold; The term represents the structural similarity loss. , and These represent the local mean, variance, and covariance of the permittivity distribution plot in the physical domain, respectively. and It is the stability constant; For gradient loss, and These represent the difference operators in the horizontal and vertical directions, respectively.

[0016] Compared with the prior art, the beneficial effects of the present invention include: 1) The deep learning microwave imaging method proposed in this invention integrates virtual antenna data, taking into account three performance indicators: imaging fidelity, system hardware cost, and reconstruction efficiency. It also achieves virtual aperture expansion at the physical level through the Fourier domain zero-filling method, which effectively compensates for the lack of physical information caused by sparse sampling and greatly reduces the dependence on large-scale physical antenna arrays.

[0017] 2) The deep learning microwave imaging method proposed in this invention, which integrates virtual antenna data, uses U-Net convolutional neural network as a nonlinear inversion engine. Its multi-level convolutional layers and skip connection mechanism can deeply extract the spatial deep features of scattering data and accurately construct the complex nonlinear mapping relationship between the high-dimensional scattering field matrix and the target dielectric constant distribution.

[0018] 3) The deep learning microwave imaging method that integrates virtual antenna data proposed in this invention constructs an FDZP-UNet network that adopts an end-to-end inference mode, which avoids the cumbersome numerical calculation process of traditional iterative algorithms and greatly improves imaging efficiency.

[0019] 4) The deep learning microwave imaging method that integrates virtual antenna data proposed in this invention adapts to antenna arrays with different sparsity through the combination of FDZP preprocessing technology and U-Net network. The parameters can be adjusted according to the needs of different application scenarios, further improving the adaptability and scalability of the technology. Attached Figure Description

[0020] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0021] Figure 1 This is a schematic diagram of a two-dimensional electromagnetic scattering model according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the U-Net sub-network structure according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the FDZP-UNet network structure according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the statistical degrees of freedom results for 1000 handwritten digit models in an embodiment of the present invention; Figure 5 This is a schematic diagram showing the variation of SSIM and RMSE of imaging under different noise levels with the actual antenna in an embodiment of the present invention; Figure 6 This is a schematic diagram showing the SSIM and RMSE trends of U-Net and FDZP-UNet under different SNRs in embodiments of the present invention; Figure 7 This is a schematic diagram showing the comparative imaging effects of different inversion methods in an embodiment of the present invention. Figure 8 This is a schematic diagram of the imaging algorithm results under different SNR conditions of the virtual array in an embodiment of the present invention; Figure 9 This is a schematic diagram showing the comparison of imaging results of various inversion algorithms under different dielectric constants in an embodiment of the present invention. Detailed Implementation

[0022] like Figure 1 As shown, a deep learning-based microwave imaging method that integrates virtual antenna data achieves high-performance imaging under sparse array conditions through the synergistic effect of physical-level spectral enhancement and algorithm-level deep learning. The method includes the following steps: S1: Establish a two-dimensional electromagnetic scattering model and collect raw scattering field observation data under a sparse antenna configuration.

[0023] A two-dimensional electromagnetic scattering model is used to simulate the interaction between electromagnetic waves and the target through the method of moments (MoM), obtaining the original scattered field observation data under a sparse antenna configuration. The calculation formula is as follows: ; ; ; ; In the formula, , and These represent the total electric field, the incident field, and the scattered field, respectively. Represents the Green's function. Represents angular frequency. and Let represent the permeability of the scattering medium and the background medium, respectively. This represents the difference in electrical parameters of the scatterer relative to the background medium. and These represent the dielectric constants of the scatterer and the background, respectively. This represents the position vector.

[0024] S2: The original scattering field observation data is processed using the Fourier zero-fill FDZP method to obtain virtual scattering field data based on FDZP extension, and then a dataset is constructed.

[0025] Step S2, execute the FDZP algorithm to Point virtual antenna data extension to A point, where M is even and N>M, includes the following sub-steps: 1) Perform a Fourier transform on the discrete sequence, the expression is: ; In the formula, Let M represent a discrete sequence, t represent the total length of the sequence, and t represent the time domain of the sequence. Represents the components of a frequency domain sequence; 2) Utilizing the periodicity of the rotation factor, the inverse discrete Fourier transform is rewritten in a symmetric form centered at zero frequency, as shown in the expression: ; ; In the formula, The t represents the rotation factor in the discrete Fourier transform, q and t represent the frequency domain index and time domain index, respectively, and j represents the imaginary unit; 3) In frequency domain sequences By inserting NM zeros between the high-frequency components, the constructed N-point enhanced spectrum is obtained. The expression is: ; In the formula, N represents the length of the extended frequency domain sequence, and N>M; This represents the N-point enhanced frequency domain sequence obtained by extension, where u represents the frequency domain index; 4) By constructing the sequence Perform an N-point IDFT to obtain the spatial signal on the virtual antenna element. The expression is:

[0026] In the formula, and They represent Point discrete sequence and its Fourier transform, and They represent the expanded versions respectively. Point space signals and discrete Fourier transform.

[0027] S3: Construct the FDZP-UNet network, such as Figure 2 As shown, the FDZP-UNet network includes a data preprocessing module, a core network module, and an imaging inference module. It achieves quantitative prediction of the target dielectric constant through an established nonlinear mapping model, and finally obtains the reconstructed image.

[0028] The data preprocessing module performs forward modeling on the dataset using the method of moments (MoM) system matrix construction and multi-aperture antenna simulation to obtain the original scattered field data. Then, it uses FDZP to perform virtual aperture expansion processing before training the model.

[0029] The core network module, based on the U-Net convolutional neural network, adopts a structure of symmetric encoding and decoding and skip connections to extract multi-scale features of the scattering field, and then trains the U-Net sub-network with a pre-processed dataset.

[0030] Specifically, the symmetric encoder-decoder architecture consists of an encoder with three convolutional layers, each with two 3×3 convolutional kernels, ReLU activation, and 2×2 max pooling downsampling; a decoder with two deconvolutional layers, each with 2×2 deconvolutional upsampling, and skip connections with the corresponding encoder layers to fuse features; and an output layer of 1×1 convolution.

[0031] The imaging inference module inputs the preprocessed scattering field into the trained U-Net subnetwork and obtains the training result through end-to-end inference.

[0032] In step S3, the FDZP-UNet network also includes a loss function, expressed as: ; ; ; ; ; In the formula, , and These are the weighting coefficients for the loss of each component, which are set to 0.65, 0.25, and 0.1 respectively based on empirical experiments. For weighted root mean square error, These are the weighting coefficients; and These are the actual physical values ​​and the network-predicted values, respectively. , and Weighting factor, weight enhancement coefficient, and preset threshold; The term represents the structural similarity loss. , and These represent the local mean, variance, and covariance of the permittivity distribution plot in the physical domain, respectively. and It is the stability constant; For gradient loss, and These represent the difference operators in the horizontal and vertical directions, respectively.

[0033] S4: Input the dataset into the FDZP-UNet network, output the target dielectric constant prediction, and then obtain a high-resolution reconstructed image.

[0034] like Figure 4 As shown, to quantitatively evaluate the degrees of freedom of the random geometric feature targets in this invention, 1000 handwritten digit models were randomly selected from the MNIST test set as benchmark geometric models, and statistical analysis was performed on them. The statistical results show that, under a frequency of 800MHz, the average degrees of freedom of all test models is approximately 6. Therefore, this invention sets the minimum NOAs of the imaging system to 6.

[0035] like Figure 5 As shown, to verify the impact of real NOAs and noise on imaging performance, this invention simulated the scattering field of 10,000 handwritten character models under different physical apertures. Different levels of additive white Gaussian noise were superimposed on the original scattering data to simulate the real measurement environment. The physical aperture ranged from 6 to 20. The Gaussian white noise levels were 20 dB and 10 dB, respectively. The results showed that without noise, as NOAs increased from 6 to 20, RMSE decreased from 0.208 to 0.1182, and SSIM increased from 0.7582 to 0.9037. With 20 dB of noise added, as NOAs increased, RMSE decreased from 0.2122 to 0.1317, and SSIM increased from 0.7416 to 0.881, showing the same trend as without noise. With 10 dB of noise added, the trends of RMSE and SSIM were consistent with those without noise. Therefore, increasing the actual NOAs not only reduces RMSE but also increases SSIM.

[0036] like Figure 6As shown, to verify the technical effectiveness of FDZP-UNet, this invention interpolates and expands the scattered field data of real NOAs with different apertures to 20. The results show that the reconstruction accuracy of the scattered field after interpolation and expansion is comparable to that reconstructed with 20 real antennas. Comparing the curve fluctuations under different signal-to-noise ratios reveals that even under strong noise interference of 10dB, the overall system performance improves with increasing N, verifying the robustness and effectiveness of the proposed scheme in complex noise environments.

[0037] like Figure 7 To verify the imaging performance of FDZP-UNet, this invention selects the Born approximation and SVM for comparison. The actual NOAs values ​​are 6 and 20, and the virtual antenna N=20 represents the virtual scattered field data extended from the actual NOAs=6 to 20. Experiments show that: Figure 7 As shown in columns a, d, and g, when the actual NOAs = 6, the Born approximation and SVM inversion performance are slightly better than U-Net. Figure 7 As shown in columns c, f, and i, when the actual NOAs = 20, U-Net's nonlinear modeling advantage begins to emerge, and its reconstruction quality significantly surpasses other algorithms. Furthermore, when the FDZP algorithm is introduced to enhance sampling to a virtual scale of N = 20, as... Figure 7 As shown in columns b, e, and h, FDZP-UNet exhibits the best reconstruction performance, significantly outperforming FDZP-Born in row 2 and FDZP-SVM in row 3, achieving a reconstruction level of 20 physical antennas.

[0038] like Figure 8 As shown, to verify the imaging performance of FDZP-UNet under noisy conditions, this invention added 20dB and 10dB Gaussian white noise to the expanded virtual scattering field data, respectively, and then compared the imaging results with FDZP-Born and FDZP-SVM. The results show that in a noise-free ideal environment, FDZP-UNet exhibits the best imaging performance, followed by FDZP-SVM, while FDZP-Born's reconstruction effect is relatively weak. Although the reconstruction quality of FDZP-UNet degrades to some extent with decreasing SNR, it still significantly outperforms other comparative algorithms in terms of SSIM and RMSE values. This fully verifies that the FDZP-UNet framework has strong robustness and accuracy in noisy environments.

[0039] like Figure 9As shown, to further verify the imaging performance of FDZP-UNet at high contrast, the dielectric constant of the scatterer was set to 1.5, 3, and 7, respectively, and compared with the imaging effects of FDZP-Born and FDZP-SVM. Due to the inherent limitations of the Born approximation, the dielectric constant of the scatterer in FDZP-Born was set to 1.5. The results show that as the dielectric constant increases, the reconstruction quality of FDZP-Born deteriorates rapidly, even to the point of failing to extract the target contour. In contrast, while both FDZP-SVM and FDZP-UNet can reproduce the dielectric constant distribution, FDZP-SVM exhibits significant background artifacts and boundary distortion in high-contrast scenes. FDZP-UNet, however, can accurately map the true dielectric constant distribution under different contrast conditions, fully demonstrating the significant advantage of this patent in handling complex nonlinear scattering effects.

[0040] To quantitatively demonstrate the enhancement effect of the FDZP-UNet algorithm, from Figure 6 The experimental results extracted the SSIM and RMSE under the conditions of true NOAs=6, N=20, and true NOAs=20, and are summarized in Table 1.

[0041] Table 1

[0042] As shown in Table 1, the introduction of virtual antennas has a significant positive gain on imaging quality. Regardless of whether noise is superimposed, the two indicators of reconstruction using the FDZP-UNet method are greatly optimized compared to the original 6 antennas, and are basically on par with the 20 physical antenna array.

[0043] In Table 2, for Figure 7 The specific performance indicators of the three test samples were evaluated.

[0044] Table 2

[0045] As shown in Table 2, the changing trends of the quantitative evaluation indicators for different inversion algorithms are as follows: Figure 7 The visualization results maintained a high degree of consistency. Quantitative data further demonstrated the advantages of FDZP-UNet in reconstructing the physical aperture of sparse antennas.

[0046] To verify the imaging performance of the proposed method under noisy conditions, 20 dB and 10 dB of noise were added to the experiment. Figure 8 As shown, three typical test samples were selected to compare the reconstruction performance of three inversion algorithms—FDZP-Born, FDZP-SVM, and FDZP-UNet—under different SNRs when N=20. Table 3 presents a quantitative evaluation of their reconstruction quality.

[0047] Table 3

[0048] The quantitative evaluation metrics in Table 3 show that, under ideal noise-free conditions, FDZP-UNet exhibits the best imaging performance, followed by FDZP-SVM, while FDZP-Born shows relatively weak reconstruction results. Although the reconstruction quality of FDZP-UNet degrades to some extent with decreasing SNR, it still significantly outperforms other comparative algorithms in terms of SSIM and RMSE values. This fully validates the strong robustness and accuracy of the FDZP-UNet framework in noisy environments.

[0049] Table 4 shows the quantitative evaluation of the reconstruction quality of each algorithm at different dielectric constants.

[0050] Table 4

[0051] The results in Table 4 show that the reconstruction quality of FDZP-Born deteriorates rapidly with increasing dielectric constant, eventually failing to extract the target contour. In contrast, while both FDZP-SVM and FDZP-UNet can reproduce the dielectric constant distribution, FDZP-SVM exhibits significant background artifacts and boundary distortion in high-contrast scenes. FDZP-UNet, however, accurately maps the true dielectric constant distribution under various contrast conditions, demonstrating the significant advantage of the proposed method in handling complex nonlinear scattering effects.

[0052] As shown in Table 5, under the premise of ensuring consistent preprocessing and interpolation time, and with the relative permittivity of the scatterer being 1.5, the computational efficiency of different inversion methods in the reconstruction stage was quantitatively compared.

[0053] Table 5

[0054] The results in Table 5 show that FDZP-UNet, while maintaining high-precision imaging, exhibits better real-time processing potential and can significantly shorten the conversion cycle from raw data to images.

[0055] The above embodiments are merely preferred technical solutions of the present invention and should not be considered as limitations on the present invention. The scope of protection of the present invention should be the technical solution described in the claims, including equivalent substitutions of the technical features described in the claims. That is, equivalent substitutions and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A deep learning microwave imaging method that fuses virtual antenna data, characterized in that, High-performance imaging under sparse array conditions is achieved through the synergistic effect of physical-level spectral enhancement and algorithm-level deep learning, including the following steps: S1: Establish a two-dimensional electromagnetic scattering model and collect raw scattering field observation data under a sparse antenna configuration; S2: The original scattered field observation data is processed using the Fourier zero-filling FDZP method to obtain virtual scattered field data based on FDZP extension, and then a dataset is constructed. S3: Construct the FDZP-UNet network; S4: Input the dataset into the FDZP-UNet network, output the target dielectric constant prediction, and then obtain a high-resolution reconstructed image.

2. The deep learning microwave imaging method for fusing virtual antenna data according to claim 1, characterized in that, The two-dimensional electromagnetic scattering model uses the method of moments (MoM) to simulate the interaction between electromagnetic waves and the target, obtaining the original scattered field observation data under a sparse antenna configuration. The calculation formula is as follows: ； ； ； ； In the formula, , and These represent the total electric field, the incident field, and the scattered field, respectively. Represents the Green's function. Represents angular frequency. and Let represent the permeability of the scattering medium and the background medium, respectively. This represents the difference in electrical parameters of the scatterer relative to the background medium. and These represent the dielectric constants of the scatterer and the background, respectively. This represents the position vector.

3. The deep learning microwave imaging method for fusing virtual antenna data according to claim 1, characterized in that, Step S2 includes the following sub-steps: 1) Perform a Fourier transform on the discrete sequence, the expression is: ； In the formula, Let M represent a discrete sequence, t represent the total length of the sequence, and t represent the time domain of the sequence. Represents the components of a frequency domain sequence; 2) Utilizing the periodicity of the rotation factor, the inverse discrete Fourier transform is rewritten in a symmetric form centered at zero frequency, as shown in the expression: ； ； In the formula, The t represents the rotation factor in the discrete Fourier transform, q and t represent the frequency domain index and time domain index, respectively, and j represents the imaginary unit; 3) In frequency domain sequences By inserting NM zeros between the high-frequency components, the constructed N-point enhanced spectrum is obtained. The expression is: In the formula, N represents the length of the extended frequency domain sequence, and N>M; This represents the N-point enhanced frequency domain sequence obtained by extension, where u represents the frequency domain index; 4) By constructing the sequence Perform an N-point IDFT to obtain the spatial signal on the virtual antenna element. The expression is: In the formula, and They represent Point discrete sequence and its Fourier transform, and They represent the expanded versions respectively. Point space signals and discrete Fourier transform.

4. The deep learning microwave imaging method for fusing virtual antenna data according to claim 1, characterized in that, In step S3, the FDZP-UNet network, including a data preprocessing module, a core network module, and an imaging inference module, achieves quantitative prediction of the target dielectric constant through the established nonlinear mapping model, and finally obtains the reconstructed image.

5. The deep learning microwave imaging method for fusing virtual antenna data according to claim 4, characterized in that, The data preprocessing module performs forward modeling on the dataset using the method of moments (MoM) system matrix construction and multi-aperture antenna simulation to obtain the original scattered field data. Then, it uses FDZP to perform virtual aperture expansion processing and trains the model.

6. The deep learning microwave imaging method for fusing virtual antenna data according to claim 4, characterized in that, The core network module, based on the U-Net convolutional neural network, employs a symmetric encoding / decoding and skip connection structure and extracts multi-scale features of the scattering field to construct a U-Net sub-network, which is then trained using a pre-processed dataset.

7. The deep learning microwave imaging method for fusing virtual antenna data according to claim 4, characterized in that, The imaging inference module inputs the preprocessed scattering field into the trained U-Net subnetwork and obtains the training result through end-to-end inference.

8. The deep learning microwave imaging method for fusing virtual antenna data according to claim 1, characterized in that, In step S3, the FDZP-UNet network further includes a loss function, expressed as: ； ； ； ； ； In the formula, , and These are the weighting coefficients for the loss of each component, which are set to 0.65, 0.25, and 0.1 respectively based on empirical experiments. For weighted root mean square error, These are the weighting coefficients; and These are the actual physical values ​​and the network-predicted values, respectively. , and Weighting factor, weight enhancement coefficient, and preset threshold; The term represents the structural similarity loss. , and These represent the local mean, variance, and covariance of the permittivity distribution plot in the physical domain, respectively. and It is the stability constant; For gradient loss, and These represent the difference operators in the horizontal and vertical directions, respectively.

Images