An electromagnetic inverse scattering imaging method based on the Deep U-Net model

Abstract

The present invention discloses an electromagnetic inverse scattering imaging method based on a DeepU-Net model, including Step 1: preprocessing the scattered field to obtain a pre-imaging result; Step 2: calculating an initial value of a weighting coefficient by using the pre-imaging result; Step 3: training an inverse scattering imaging model; Step 4: testing the training result by using test data to judge the weight value; Step 5: outputting an imaging result by using the trained model to test the electromagnetic inverse scattering model; this method is implemented by using a U-Net network integrating a TV loss function regular term. On the one hand, the addition of the TV loss function improves the ability of the model to cope with the "artifacts" existing in the preprocessed data, and improves the imaging ability of the model in the case of high noise and strong scatterers. On the other hand, the addition of the regular term enables good inversion results to be generated with less training data and has strong generalization ability, and has the characteristics of good imaging effect, short training time and strong generalization ability.

Description

Technical Field

[0001] The present invention relates to the technical field of electronic information microwave imaging, and particularly relates to an electromagnetic inverse scattering imaging method based on a Deep U-Net model. Background Art

[0002] Nonlinear electromagnetic inverse scattering is a super-resolution imaging technology. By establishing the functional relationship between the target area and the scattered field based on the scattered field data received by the receiving antenna, relevant information such as the position, shape, and material of the scatterer medium in the target area can be solved. Compared with traditional tomography, a more detailed and specific interaction process between the scene and electromagnetic waves is considered during the imaging process, making it have a wider range of application values. For example, in the field of non-destructive detection, it is used to detect possible cracks, corrosion, or the absence, displacement, and shrinkage of units in some periodic structures in the target object; in the field of petrochemical engineering, it is used for unknown oil and gas exploration; in the medical field, it is used to assist in the early detection and diagnosis of diseases. However, the inherent nonlinearity, ill-posedness, and high computational cost of the electromagnetic inverse scattering problem make it impossible to accurately invert the scatterer information or the inversion takes a long time in many situations, and the accuracy, stability, and efficiency of the inversion need to be improved. How to quickly, efficiently, and accurately perform inverse scattering imaging on the target and model the electrical parameters of the target becomes crucial.

[0003] The solution of electromagnetic inverse scattering can be divided into two categories: qualitative imaging and quantitative imaging. Qualitative imaging means starting from the known scattered field and qualitatively solving the shape and position information of the target scatterer without obtaining the electromagnetic parameter information of the scatterer (such as relative permittivity, conductivity, permeability, etc.). Quantitative imaging, on the basis of solving the shape and position information of the unknown scatterer, further obtains the electromagnetic parameter information of the unknown scatterer. Therefore, the quantitative solution algorithm has more parameters to be solved than the qualitative solution algorithm, and the solution difficulty is greater.

[0004] The key to quantitatively solving the non - linear electromagnetic inverse scattering problem lies in dealing with its ill - posedness and non - linearity. Thus, traditional inversion algorithms can be divided into two major categories: non - iterative methods and iterative methods. Non - iterative methods linearize the non - linear problem through field approximation to simplify the solution difficulty. They mainly include the Born Approximation (BA), Rytov Approximation (RA), and Back Propagation (BP) algorithms. The Born Approximation approximates the total field in the scatterer as the incident field, making the relationship between the induced current and the scatterer parameters linear. This method has a simple idea and low computational complexity. However, this approximation is only applicable when the scatterer parameters are not very different from the background parameters and the electrical size of the scatterer is small. Otherwise, if the scattering intensity of the target is very high, it will lead to a large deviation between the approximate result and the true value, making the result highly distorted. The Rytov Approximation can be regarded as an extension of the Born Approximation in the high - frequency case. By introducing phase information, the total field is approximated as the form of the incident field strength multiplied by the phase difference. When the volume of the object to be measured is small and its electrical parameters are not very different from the background, the two methods can obtain similar results. The Back Propagation algorithm is based on calculating the Green's operator of the scattered field and assumes a linear relationship between the induced current and the scattered field, thereby calculating the total field and the distribution of scatterer electrical parameters. The approximation method is more effective in the inverse solution process of weak scatterer targets (small electrical size, scattering intensity not very different from background parameters). However, when the target electrical size is large or the scattering intensity is high, due to the multiple scattering in the scatterer that cannot be ignored, the non - linear relationship between the induced current and the scattered field is significantly enhanced, and the inverse scattering imaging method based on the approximation method is no longer applicable.

[0005] Iterative methods mainly include the Born Iterative Method (BIM), the Distorted Born Iterative Method (DBIM), the Contrast Source Inversion (CSI), the Subspace-based Optimization Method (SOM), etc., which provide reliable ways for the inversion calculation of electrically large-sized or strongly scattering extended targets. Among them, the Born iteration and the distorted Born iteration use the idea of modified gradient to perform multiple iterations on the Born approximation. Although their application scope has been greatly improved compared with the Born approximation, limited by the approximate operation, they still cannot handle all inversion cases. The iterative methods of conjugate gradient regard inverse scattering as an optimization problem. The biggest difference between these methods and the approximation method is that they no longer use the incident field to replace the total field in the target area, but through multiple iterations, the calculated value gradually approaches the real situation, and then a more accurate solution is obtained. This type of method includes the contrast source inversion method and the subspace optimization method. Since the calculation process does not involve approximation, theoretically all inverse scattering cases can be solved, but this type of method is very dependent on the initial value, and inappropriate initial values may cause the operation result to fall into the local optimal trap. In addition, compared with non-iterative methods, almost all iterative methods have problems such as high computational complexity, large computational space requirements, and long time consumption, which also makes it difficult to meet the requirements of real-time inversion in practical applications.

[0006] After being specifically trained with a large amount of data sets, machine learning methods can solve inverse problems in real time. Due to its advantages of high efficiency and high precision in solving electromagnetic inverse scattering problems, it has received extensive attention from researchers in recent years. Professor Chen Xudong and others applied the semantic segmentation network U-Net to solve the nonlinear electromagnetic inverse scattering problem in the literature "Wei Z, Chen X. Deep-learning schemes for full-wave nonlinear inverse scattering problems[J]. IEEE Transactions on Geoscience And Remote Sensing, 2019; 57(4): 1849-1859". By comparing the results of the U-Net direct inversion algorithm, the BP approximation + U-Net algorithm, and the SOM + U-Net algorithm, etc., it fully demonstrated the effectiveness of the U-Net neural network in solving electromagnetic inverse scattering problems; Professor Li Lianlin and others faced the problem that currently commonly used deep neural networks only use real-domain data and cannot be directly applied to complex-domain problems in the literature "Li L, Wang L G, Teixeira F L, et al. DeepNIS: deep neural network for nonlinear electromagnetic inverse scattering[J]. IEEE Transactions on Antennas and Propagation, 2019, 67(3): 1819-1825.", and proposed the DeepNIS network.DeepNIS is composed of multiple complex convolutional neural network modules connected in series. Its structure is similar to the iterative solution of the nonlinear electromagnetic inverse scattering problem. However, the difference is that once the DeepNIS network is trained, the solution speed is much faster than the existing iterative solution algorithms for nonlinear electromagnetic inverse scattering. Liu Che and others, in the literature "C. Liu, H. Zhang, L. Li and T. J. Cui. Towards intelligent electromagnetic inverse scattering using deep learning techniques and information metasurfaces[J]. IEEE Journal of Microwaves, 2023(1):509-522", extended the typical contrast source inversion (CSI) algorithm through a generative adversarial network (GAN), and proposed a new unsupervised deep learning method for solving inverse scattering based on physical information, abbreviated as CSI-GAN. This method relies on the supervision of physical laws rather than a labeled training dataset. Benefiting from the highly nonlinear fitting ability of machine learning, the solution of electromagnetic inverse scattering problems based on neural networks shows the potential to surpass traditional algorithms.

[0007] However, when the above methods are used, the following problems still need to be further solved:

[0008] 1. The above methods require a large amount of training data to train the model during implementation, with a long training time and difficult preparation of the dataset;

[0009] 2. The existing electromagnetic inverse scattering solution methods have poor imaging effects when dealing with the inverse scattering imaging of strong scatterers, with large "artifacts";

[0010] 3. The existing electromagnetic inverse scattering solution methods have poor imaging effects when dealing with high-noise data;

[0011] Therefore, there is an urgent need to design a new electromagnetic inverse scattering imaging method to solve the problems of the existing methods, such as the need for a large amount of data and the limitations in dealing with high-noise and strong-scatterer situations. Summary of the Invention

[0012] In view of the above problems, the present invention aims to provide an electromagnetic inverse scattering imaging method based on the Deep U-Net model. By exploring the incorporation of physical information into the learning and training process on the basis of existing deep learning methods, that is, by adding a TV loss function regularization term to the loss function and utilizing its "delineation" ability for object contours to assist imaging, accurate inverse imaging in the presence of strong scatterers and high-noise environments is achieved, improving the imaging ability of existing methods, and having the characteristics of good imaging effect, short training time, and strong generalization ability.

[0013] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0014] An electromagnetic inverse scattering imaging method based on the Deep U-Net model, comprising

[0015] Step 1: Preprocess the scattered field, generate a pre-imaging result using the BP method, and randomly assign the result as training data and test data;

[0016] Step 2: Calculate the initial value of the weighting coefficient using the pre-imaging result;

[0017] Step 3: Use the training data in Step 1 and the preprocessing result in Step 2 to train a U-Net electromagnetic inverse scattering solver incorporating the TV loss function;

[0018] Step 4: Use the test data to test the training result, determine whether the weight value is optimal. In the non-optimal case, modify the test weight and repeat Steps 3 and 4 to obtain the final model M for solving the electromagnetic inverse scattering problem IPS ;

[0019] Step 5: Use the trained model to output the imaging result and test the electromagnetic inverse scattering model.

[0020] Preferably, the specific process of preprocessing the scattered field in Step 1, generating a pre-imaging result using the BP method, and randomly assigning the result as training data and test data includes

[0021] Step 1.1: Process the MNIST handwritten digit dataset, randomly select 2000 images from it, extract the grayscale value of each image, assign its relative permittivity as 1 and use it as the background part when the grayscale value is less than 1 / 3 of the maximum value, and randomly assign its relative permittivity as [1, 5] and use it as the scatterer part when the grayscale value is greater than 1 / 3 of the maximum value;

[0022] Step 1.2: Use the method of moments, pulse basis functions, and delta testing functions to discretize the target area with a size of 5.6λ0×5.6λ0 into 64×64 pixels;

[0023] Step 1.3: Adopt the formula

[0024]

[0025] wherein, is the scattered field, k is the wave number, is the two-dimensional scalar Green's function in free space, which can be further expressed as where is the Hankel function of the second kind of order 0, and χ(r') is the scattering intensity of the scatterer, which is calculated from the relative permittivity, is the total field in the target area;

[0026] The scattered field data is obtained by solving with the method of moments to complete the numerical simulation;

[0027] Step 1.4: Add Gaussian noise with a mean of 0 and a variance following a uniform distribution of (0, 0.1) with a probability of 0.15 to obtain a scattered field with a specific signal-to-noise ratio;

[0028] Step 1.5: Preprocess the scattered field data obtained in Step 1.5 using the BP method;

[0029] Step 1.6: Randomly divide the preprocessing result into 1000 training data sets and 1000 test data sets to complete the preparation of the training data.

[0030] Preferably, the specific process of calculating the initial value of the weighting coefficient using the pre-imaging result described in Step 2 includes

[0031] Using the preprocessing result obtained in Step 1, through the formula

[0032]

[0033] Calculate the initial weight value of the regularization term;

[0034] where x is the pixel matrix of the data set, x i,j-1 , x i,j , x i+1,j is each pixel unit.

[0035] Preferably, the process of training the U-Net electromagnetic inverse scattering solver incorporating the TV loss function described in Step 3 includes

[0036] Step 3.1: Select the deep learning segmentation method Deep U-Net as the segmentation framework of the U-Net electromagnetic inverse scattering solver;

[0037] Among them, this framework adopts hierarchical feature representation and symmetric encoding and decoding paths, including a 6-layer convolutional network structure, and the maximum number of channels is set to 256;

[0038] Step 3.2: Use a contrast-based function and the TV loss function based on the compressed sensing theory whose sum \(L = L contrast +\beta L TV as the total loss for training to constrain the training process;

[0039] where \(x\) is the pixel matrix of the dataset, \(x i,j-1 ,x i,j ,x i+1,j is each pixel unit, and \(\beta\) is the regularization term weight;

[0040] Step 3.3: Use the training data obtained in Step 1 for training, and the data batch size is 300;

[0041] Step 3.4: Set the initial learning rate to \(1\times10 -5 , and the learning rate is halved every 20 iterations. Training is terminated after 150 iterations to obtain the model \(M\) for solving the electromagnetic inverse scattering problem IPS .

[0042] Preferably, the specific process of using the test data to test the training result and determining whether the weight value is optimal in Step 4 includes

[0043] Step 4.1: Use the trained model to test the test dataset. By sampling regularly within the interval near the initial value, test each sampling value, and count the MSE and SSIM values of 1000 samples to determine whether the weight parameter \(\beta\) is optimal. When \(\beta\) is optimal, the test result has the smallest MSE and the largest SSIM value;

[0044] Step 4.2: Determine the optimal \(\beta\) to obtain the final model \(M\) for solving the electromagnetic inverse scattering problem IPS .

[0045] Preferably, the specific process of using the trained model to output the imaging result and test the electromagnetic inverse scattering model in Step 5 includes using the model \(M\) for solving the electromagnetic inverse scattering problem obtained by optimizing in Step 4 IPS to test the input test data and output the result for simulation analysis.

[0046] The beneficial effects of the present invention are: The present invention discloses an electromagnetic inverse scattering imaging method based on the DeepU-Net model. Compared with the prior art, the improvements of the present invention are as follows:

[0047] The present invention proposes an electromagnetic inverse scattering imaging method based on the DeepU-Net model, including: Step 1: Preprocess the scattered field obtained from experiments or electromagnetic computational simulations, generate a pre-imaging result using the BP method, and randomly assign the result as training data and test data; Step 2: Calculate the initial value of the weighting coefficient using the pre-imaging result; Step 3: Train the inverse scattering imaging model; Step 4: Test the training result using the test data, determine whether the weight value is optimal, and modify the test weight and repeat Steps 3 and 4 in the case of non-optimal; Step 5: Use the trained model to output the imaging result and test the electromagnetic inverse scattering model; When in use:

[0048] 1. It has a shorter training time; In the training process of existing models, 3000 - 5000 data are mostly required for training, and some complex models require more than 5000 training samples. The present invention only needs 1000 samples of pre-imaging of scatterers to complete the training within ten minutes, shortening the training time required and reducing the workload of data set preparation;

[0049] 2. It has a better imaging effect; By adding a regularization term, the present invention can better handle the "artifacts" existing in the imaging process. Therefore, the present invention performs well in dealing with the inverse scattering imaging of strong scatterers and the inverse scattering imaging tasks in high-noise situations;

[0050] 3. It has a wider application scenario; By adding a regularization term, the present invention can handle multiple imaging problems under the condition of training with a single data set, performs well in dealing with simulation data and experimental data, has a strong generalization ability, and has the advantages of good imaging effect, short training time, and strong generalization ability. Description of the Drawings

[0051] Figure 1 It is a flowchart of the overall implementation of the present invention.

[0052] Figure 2 It is a statistical result graph of the final test of the present invention, and the statistics are carried out on the MNIST handwritten digit test data set, the MNIST handwritten digit training data set, and the polygon test data set respectively.

[0053] Figure 3 It is a visualization graph of the inversion result of the present invention for MNIST handwritten digits.

[0054] Figure 4 It is a visualization graph of the inversion result of the present invention for polygons.

[0055] Figure 5 It is a visualization graph of the inversion result of the present invention for the Austria pattern.

[0056] Figure 6This is the visualization graph of the inversion result of the experimental data for the present invention. Specific Embodiment

[0057] To enable those of ordinary skill in the art to better understand the technical solution of the present invention, the technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0058] Example 1: Refer to the Figure 1-6 An electromagnetic inverse scattering imaging method based on the Deep U-Net model shown, including

[0059] Step 1: Preprocess the scattered field obtained from experiments or electromagnetic computational simulations, and use the BP method to generate a pre-imaging result. Randomly assign the pre-imaging result as training data and test data, specifically including:

[0060] Step 1.1: Process the MNIST handwritten digit dataset, randomly select 2000 images from it, extract the grayscale value of each image. When the grayscale value is less than 1 / 3 of the maximum value, assign its relative permittivity as 1 and use it as the background part. When the grayscale value is greater than 1 / 3 of the maximum value, randomly assign its relative permittivity as [1, 5] and use it as the scatterer part;

[0061] Step 1.2: Use the method of moments, pulse basis functions, and delta testing functions to discretize the scatterer part DOI with a size of 5.6λ0×5.6λ0 into 64×64 pixels, where λ0 = 7.5 cm;

[0062] Step 1.3: Use the formula

[0063]

[0064] where is the scattered field, k is the wave number, is the two-dimensional scalar Green's function in free space, which can be further expressed as where is the Hankel function of the second kind of order 0, χ(r') is the scattering intensity of the scatterer, calculated from the relative permittivity, is the total field within the target area;

[0065] Solve for the scattered field data with the help of the method of moments to complete the numerical simulation;

[0066] Step 14: With a probability of 0.15, add Gaussian noise with a mean of 0 and a variance following a uniform distribution of (0, 0.1); obtain a scattered field with a specific signal-to-noise ratio;

[0067] That is, the scattered far-field solution of the handwritten digit scatterer is obtained through Step 1.5; the noise measurement of the image is obtained by adding Gaussian noise to the scattered field with a specific signal-to-noise ratio; by adding noise, the training data is made more complex to enhance the model and ensure that a model with strong domain generalization ability is obtained through training;

[0068] Step 1.5: Use the BP method to preprocess the scattered field data obtained in Step 1.5;

[0069] Step 1.6: Randomly divide the preprocessing result into 1000 training data sets and 1000 test data sets;

[0070] After the above preprocessing operations, the preparation of the training data is achieved;

[0071] Step 2: Use the preprocessing result obtained in Step 1 to calculate the initial weight of the regularization term through the formula

[0072]

[0073] where x is the pixel matrix of the data set, x i,j-1 , x i,j , x i+1,j is each pixel unit, and calculate the initial weight of the regularization term;

[0074] Step 3: Use the training data prepared in Step 1 and the preprocessing result generated in Step 2 to train the U-Net electromagnetic inverse scattering solver incorporating the TV loss function; specifically

[0075] Step 3.1: Select the deep learning segmentation method Deep U-Net as the segmentation framework of the U-Net electromagnetic inverse scattering solver. This framework adopts hierarchical feature representation and symmetric encoding and decoding paths, including a 6-layer convolutional network structure, and the maximum number of channels is set to 256;

[0076] Step 3.2: Use the contrast-based function the TV loss function based on the compressed sensing theory and L = L contrast +βL TV as the total loss of training to constrain the training process;

[0077] where x is the pixel matrix of the data set, x i,j-1 , x i,j , x i+1,j is each pixel unit, and β is the regularization term weight;

[0078] Step 3.3: Use the training data obtained in Step 1 for training, and the data batch size is 300;

[0079] Step 3.4: Set the initial learning rate to 1×10 -5 , halve it every 20 training times, and terminate the training process after 1000 iterations to obtain the model M for solving the electromagnetic inverse scattering problem IPS ;

[0080] Step 4: Optimize the trained electromagnetic inverse scattering solver; specifically

[0081] Step 4.1: Use the trained model M IPS to test the test data set. By sampling according to a certain rule in the interval near the initial value and testing each sampling value, count the MSE and SSIM values of 1000 samples to judge whether the weight parameter β is optimal. When β is optimal, the test result has the smallest MSE and the largest SSIM value;

[0082] Step 4.2: Determine the optimal β to obtain the final model M for solving the electromagnetic inverse scattering problem IPS ;

[0083] Step 5: Test the trained electromagnetic inverse scattering solver; specifically

[0084] Use the model M for solving the electromagnetic inverse scattering problem optimized in Step 4 IPS to test the input test data and output the result for simulation analysis.

[0085] Example 2: Different from Example 1, to verify the effectiveness of the electromagnetic inverse scattering imaging method based on the Deep U-Net model described in Example 1 above, this simulation example is designed to verify the above method:

[0086] 1. Simulation conditions

[0087] This invention is trained using MATLAB 2022b on a workstation with 1.67TB of memory, a 2.1GHz CPU, and an NVIDIA RTX 6000 graphics card;

[0088] The test data set used in the experiment is the MNIST handwritten digit data set, which was collected by Yann LeCun. It is a large handwritten digit database and is usually used to train various image processing systems and is also widely used for training and testing in the field of machine learning. The MNIST data set contains 70,000 handwritten digit images. The images are grayscale, 28x28 pixels, and centered to reduce preprocessing and speed up operation.

[0089] 2. Simulation content

[0090] Test the accuracy and domain generalization performance of this invention for electromagnetic inverse scattering imaging;

[0091] To verify the improvement of the model domain generalization ability of the present invention through data augmentation, a polygon model and an MSE / SSIM evaluation method similar to those mentioned by Professor Liu Zicheng in the literature "Liu Z, Roy M, Prasad D K, et al. Physics-guided loss functions improve deep learning performance in inverse scattering[J]. IEEE Transactions on Computational Imaging, 2022, 8: 236-245." are adopted as evaluation indicators. For the MNIST training dataset, the MNIST test dataset, and the polygon test dataset, the deviations between the predicted results and the true results are respectively counted, and the comparison results are shown in Table 1;

[0092] Visualize the predicted results of the present invention under different noise conditions on the handwritten digit dataset and the polygon dataset. The comparison chart of the visualization results is as Figure 3 , Figure 4 shown.

[0093] Table 1: Performance verification results of the inverse scattering model

[0094] MNIST Train MNIST Test Polygon test MSE Mean 0.0766 0.0859 0.2969 MSE Median 0.0500 0.0500 0.0800 SSIM Mean 0.8483 0.8461 0.8336 SSIM Median 0.8600 0.8500 0.8600

[0095] To verify the ability of the present invention in dealing with complex targets and strong scatterers, the Austrian ring pattern used in the literature "Wei Z, Chen X. Deep-learning schemes for full-wave nonlinear inverse scattering problems[J]. IEEE Transactions on Geoscience And Remote Sensing, 2019; 57(4): 1849-1859" is selected for testing. The test results are as Figure 5 shown; the electrical parameters of the ring are set to increase from 1.5 to 5 with a step size of 0.5. It can be found through testing that the shape of the scatterer can be well restored when the electrical parameters are small. As the electrical parameters gradually increase, artifacts appear around the scatterer, but the shape of the scatterer can still be distinguished. As the electrical parameters increase, the scattering ability improves, and the deterioration of the inversion result is inevitable. However, compared with other methods, the reconstruction ability of the present invention for strong scatterers has been greatly improved.

[0096] To verify the generalization ability of the present invention, experimental data was selected for testing. The experimental data was chosen as the "FoamDielExt" experimental data provided by the Fresnel Institute in Marseille, France in "Geffrin J M, Sabouroux P, Eyraud C. Free space experimental scattering database continuation: experimental set-up and measurement precision[J]. Inverse Problems, 2005, 21(6): S117." The inversion results are as follows Figure 6 shown, where Figure 6 (a) is the true scatterer, Figure 6 (b) is the pre-imaging result by the BP method, Figure 6 (c) is the inversion result without adding the regularization term, Figure 6 (d) is the inversion result with the regularization term added. It can be found from the pictures that after adding the regularization term, the inversion ability has been greatly improved, making the electrical parameters closer to the true values and the contours clearer.

[0097] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. The above embodiments and the descriptions in the specification only illustrate the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed. The scope of the present invention claimed is defined by the appended claims and their equivalents.

Claims

1. An electromagnetic inverse scattering imaging method based on the Deep U-Net model, characterized in that: Including Step 1: Preprocess the scattered field, generate a pre-imaging result using the BP method, and randomly assign the result as training data and test data; Step 2: Calculate the initial value of the weighting coefficient using the pre-imaging result; Step 3: Use the training data in Step 1 and the preprocessing result in Step 2 to train a U-Net electromagnetic inverse scattering solver incorporating a TV loss function; Step 4: Use the test data to test the training results, determine whether the weight value is optimal. In the case of non-optimal, modify the test weights and repeat Steps 3 and 4 to obtain the final model for solving the electromagnetic inverse scattering problem ; Step 5: Use the trained model to output an imaging result and test the electromagnetic inverse scattering model; The process of training the U-Net electromagnetic inverse scattering solver incorporating a TV loss function described in Step 3 includes: Step 3.1: Select the deep learning segmentation method Deep U-Net as the segmentation framework for the U-Net electromagnetic inverse scattering solver; Among them, this framework adopts a hierarchical feature representation and a symmetric encoding-decoding path, including a 6-layer convolutional network structure, and the maximum number of channels is set to 256; Step 3.2: Use the sum of a contrast-based function and a TV loss function based on the compressive sensing theory as the total loss for training to constrain the training process; ​ Among them, is the pixel matrix of the data set, is each pixel unit, is the regularization term weight; Step 3.3: Use the training data obtained in Step 1 for training, and the data batch size is 300; Step 3.4: Set the initial learning rate to , and halve the learning rate every 20 iterations. Terminate the training after 150 iterations to obtain a model for solving the electromagnetic inverse scattering problem .

2. The electromagnetic inverse scattering imaging method based on the Deep U-Net model according to claim 1, characterized in that: The specific process of preprocessing the scattered field described in Step 1, generating a pre-imaging result using the BP method, and randomly assigning the result as training data and test data includes Step 1.1: Process the MNIST handwritten digit dataset, randomly select 2000 images from it, extract the grayscale value of each image, when the grayscale value is less than 1 / 3 of the maximum value, assign its relative permittivity as 1 and use it as the background part, when the grayscale value is greater than 1 / 3 of the maximum value, randomly assign its relative permittivity to [1, 5] and use it as the scatterer part; Step 1.2: Using the method of moments, pulse basis functions, and delta testing functions, discretize the target area with a size of into 64×64 pixels; Step 1.3: Use the formula Among them, is the scattered field, k is the wave number, is the two-dimensional scalar Green's function in free space, which can be further expressed as , where is the Hankel function of the second kind of order 0, is the scattering intensity of the scatterer, which is calculated from the relative permittivity, is the total field in the target area; Solve to obtain the scattered field data by the method of moments to complete the numerical simulation; Step 1.4: With a probability of 0.15, add Gaussian noise with a mean of 0 and a variance following a uniform distribution of (0, 0.1) to obtain a scattered field with a specific signal-to-noise ratio; Step 1.5: Preprocess the scattered field data obtained in Step 1.5 using the BP method; Step 1.6: Randomly divide the preprocessing result into 1000 training data sets and 1000 test data sets to complete the preparation of the training data.

3. An electromagnetic inverse scattering imaging method based on the Deep U-Net model according to claim 1, characterized in that: The specific process of calculating the initial value of the weighting coefficient using the pre-imaging result described in Step 2 includes Using the preprocessing result obtained in Step 1, through the formula Calculate the initial weight value of the regularization term; Among them, is the pixel matrix of the data set, is each pixel unit.

4. The electromagnetic inverse scattering imaging method based on the Deep U-Net model according to claim 1, wherein: The specific process of using the test data to test the training result and judge whether the weight value is optimal described in Step 4 includes Step 4.1: Use the trained model to test the test data set, sample regularly in the interval near the initial value, test each sampled value, and count the MSE and SSIM values of 1000 samples to judge whether the weight parameter β is optimal. When β is optimal, the test result has the smallest MSE and the largest SSIM value; Step 4.2: Determine the optimal β to obtain the final model for solving the electromagnetic inverse scattering problem .

5. The electromagnetic inverse scattering imaging method based on the Deep U-Net model according to claim 1, characterized in that: The specific process of using the trained model to output an imaging result and test the electromagnetic inverse scattering model described in Step 5 includes The model for solving the electromagnetic inverse scattering problem optimized by using Step 4 Test the input test data and output the simulation analysis of the results.

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