An electromagnetic inverse scattering imaging method based on a multi-scale coordinate attention mechanism neural network

Abstract

The present application relates to the technical field of electromagnetic calculation, in particular to a kind of electromagnetic inverse scattering imaging method based on multi-scale coordinate attention mechanism neural network. Including step 1: scattering field data is acquired using transmitting and receiving antenna and initial rough image is generated by back propagation algorithm;Step 2: neural network model is constructed, which is composed of input layer, multi-scale feature extraction module, adaptive fusion module, coordinate attention module and output layer;Step 3: the cost function of the combination of normalized mean square error and regularization constraint is used to optimize network parameters;Step 4: scattering body reconstruction is carried out by training multi-scale coordinate attention mechanism neural network;The present application makes full use of the prior information of scattering field data and rough image, improves the reconstruction accuracy of high-contrast scattering body edge and details through multi-scale feature fusion and coordinate attention mechanism, and has the advantages of good imaging effect, strong generalization ability and high precision.

Description

Technical Field

[0001] The present invention relates to the field of electromagnetic computing technology, and in particular to an electromagnetic inverse scattering imaging method based on a multi-scale coordinate attention mechanism neural network. Background Art

[0002] Electromagnetic inverse scattering imaging is a technique that reconstructs the spatial distribution of electromagnetic parameters such as the dielectric constant and conductivity of a target object by measuring the scattered field data generated by the object under external electromagnetic excitation. Essentially, it solves the inverse problem of the nonlinear Maxwell equations. Specifically, given known incident and scattered field observations, the technique analyzes the scattered waves generated by electromagnetic waves encountering objects with different dielectrics to infer information such as the scatterer's geometry and physical parameters. This technique has found widespread application in medical imaging, geophysical exploration, industrial nondestructive testing, public safety, and military detection.

[0003] The actual electromagnetic inverse scattering problem is a very complex nonlinear problem, and the existence, uniqueness and stability of its solution are often not met simultaneously.

[0004] Traditional methods for solving inverse scattering problems can generally be divided into iterative and non-iterative methods. Non-iterative methods, such as the Born approximation, Rytov approximation, and backpropagation, transform nonlinear problems into linear problems through specific approximations. Iterative methods, such as the Newton method, the Born iteration method, the distorted Born iteration method, the contrast source inversion algorithm, and the subspace optimization algorithm, transform the inverse scattering problem into an optimization problem and determine the optimal solution by minimizing the objective function through an iterative process.

[0005] To address the ill-posedness of electromagnetic inverse scattering problems, regularization methods such as Tikhonov regularization, total variation (TV) regularization, and multiplicative regularization are often employed. Non-iterative methods can quickly approximate solutions for weak scatterers, but the accuracy of the approximation decreases significantly for strong or complex scatterers. Iterative methods, while reliable, are prone to falling into local optima and are computationally expensive.

[0006] In recent years, with the rapid development of deep learning technology, deep learning-based methods have provided new approaches to solving electromagnetic inverse scattering problems. In the paper “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”, Chen Xudong et al. introduced three U-Net-based training schemes for direct inversion, backpropagation, and dominant current, respectively. In the paper “Li L, Wang LG, Teixeira FL, et al. DeepNIS: deep neural network for nonlinear electromagnetic inverse scattering[J]. IEEE Transactions on Antennas and Propagation, 2019, 67(3): 1819-1825”, Li Lianlin et al. proposed a DeepNIS method based on a deep neural network, which uses a cascade of multi-layer complex-valued residual convolutional neural network modules to solve the high-contrast inverse scattering problem. These methods utilize the powerful nonlinear fitting capabilities of neural networks to learn the complex mapping relationship between scattered field data and scatterer properties, thereby improving the accuracy and efficiency of imaging to a certain extent.

[0007] However, the above method still has the following problems:

[0008] 1. Insufficient utilization of prior information: Most networks only use raw scattered field data as input, ignoring the initial structure contained in the rough reconstructed images generated by traditional methods. This leads to a sharp drop in the model's generalization ability in pathological scenarios such as strong scattering or limited angle measurement.

[0009] 2. Inadequate multi-scale feature modeling capabilities: In electromagnetic inverse scattering imaging, target contours are dominated by low-frequency scattered waves, while microstructures rely on high-frequency components. Existing single-scale neural networks struggle to collaboratively capture these cross-scale features, resulting in an imbalance between global morphology and local details in the reconstructed image.

[0010] 3. Poor imaging of high-contrast scatterers: Existing methods are prone to distortion or artifacts when reconstructing high-contrast scatterers due to the influence of multiple scattering effects;

[0011] Therefore, a new electromagnetic inverse scattering imaging method is urgently needed to solve the problems of insufficient utilization of prior information, insufficient multi-scale feature modeling capabilities, and poor imaging effect of high-contrast scatterers in the above-mentioned existing methods. Summary of the Invention

[0012] In order to solve the technical problems existing in the background technology, the present invention provides an electromagnetic inverse scattering imaging method based on a multi-scale coordinate attention mechanism neural network. This method fully utilizes prior information on the basis of existing deep neural networks, takes scattered field data and rough images reconstructed by traditional methods as network input, captures cross-scale features through a multi-scale feature extraction module, and at the same time adds a coordinate attention mechanism to make the network pay more attention to the edges and internal change areas of the scatterer, thereby achieving accurate reconstruction of high-contrast scatterers, improving the imaging capabilities of existing methods, and having the characteristics of good imaging effect, strong generalization ability and high imaging accuracy.

[0013] The technical solution adopted by the present invention to solve its technical problem is:

[0014] An electromagnetic inverse scattering imaging method based on a multi-scale coordinate attention mechanism neural network includes the following steps:

[0015] Step S1. Build the experimental scene and place transmit antennas and The receiving antennas are used to obtain the scattered field data of the target scatterer, and the obtained scattered field is The matrix is ​​then used to obtain the initial rough image using the back propagation algorithm;

[0016] Step S2. Based on the MNIST handwritten digital image, take it as the target scatterer and use the moment method to obtain the target scattering field. The target scatterer scattered field data matrix is ​​obtained, and then the back propagation algorithm is used to obtain the initial rough image of the MNIST handwritten digits to construct the data set;

[0017] Step S3. Using the scattered field data matrix and the initial rough image as the input values ​​of the neural network and the real MNIST handwritten images as labels, a neural network prediction model based on the multi-scale coordinate attention mechanism is constructed. The network consists of an input layer, a multi-scale feature extraction module, an adaptive fusion module, a coordinate attention module, and an output layer.

[0018] The input layer encodes the scattered field data and the initial imaging image separately, extracts and encodes the features using a convolutional neural network (CNN), and then normalizes them before sending them to the multi-scale feature extraction module for processing.

[0019] The multi-scale feature extraction module includes multiple convolution operations. The size and parameters of the convolution kernel are determined according to the complexity of the channel and spatial information in the feature vector. By adjusting the convolution kernel size and step size, features of different scales are obtained. These features of different scales are spliced ​​in the channel dimension to further enrich the feature information.

[0020] The adaptive fusion module calculates the cosine similarity between the scattered field data and the multi-scale features of the initial imaging image. Based on the calculated cosine similarity, the Softmax function is used to generate adaptive fusion weights to weightedly fuse the multi-scale features.

[0021] The coordinate attention module performs coordinate attention operations based on weighted fusion of multi-scale features. To better highlight the boundaries of scatterers and the accuracy of internal structural changes, the average pooling and maximum pooling in the coordinate attention operation are replaced by only maximum pooling, thereby improving the model's ability to focus on key edge features.

[0022] Next, the cost function is used to calculate the network error and perform regression to further optimize the network parameters. After multiple iterations, a neural network prediction model based on the multi-scale coordinate attention mechanism is finally established.

[0023] The output layer uses transposed convolution to achieve high-resolution reconstruction or is combined with a fully connected layer for classification;

[0024] Step S4: Input the actual target scatterer initial image and the corresponding scattering field matrix into the prediction model to obtain the actual predicted imaging result.

[0025] Furthermore, step S1 includes:

[0026] With the center of the imaging area where the target scatterer is located as the center of the circle, Place on the circumference transmit antennas and receiving antennas, where The transmitting antenna first transmits electromagnetic waves, which are then absorbed and scattered by the scatterer. The receiving antenna receives the The matrix is ​​then obtained using the back propagation algorithm The initial rough image of pixels, where .

[0027] Furthermore, step S2 includes:

[0028] First, the MNIST handwritten digit images are preprocessed, 5000 images are randomly selected and transformed into The digital part of each picture is used as the scatterer, the area with gray value less than 1 / 4 of the maximum value is used as the background area, the relative dielectric constant is assigned to 1, and the rest of the image is used as the scatterer to be measured, and the relative dielectric constant is randomly assigned to , take these images as real label data;

[0029] Then, the target imaging area is discretized into Pixels, numerical simulation was performed using the Lippmann-Schwinger equation and the moment method to obtain the scattered field data of 5000 handwritten digits;

[0030] The obtained scattered field data were processed using the back propagation algorithm to obtain 5000 rough initial imaging images;

[0031] Finally, the processed results are randomly divided into 3500 training data sets and 1500 test data sets in a ratio of 7:3, and the rough imaging images and scattered field data are matched to complete the preparation of the data set.

[0032] Furthermore, the cost function is:

[0033]

[0034] in, is the iteration parameter, yes The predicted contrast value for the position, is the contrast value of the real scatterer, is the regularization parameter and , the first term of the cost function quantifies the difference between the true value and the predicted value through the normalized mean square error, and the second term is the regularization constraint.

[0035] Furthermore, the actual predicted imaging result obtained in step S4 is a relative dielectric constant distribution map.

[0036] Beneficial effects of the present invention:

[0037] (1) This paper proposes to use a multi-scale coordinate attention mechanism neural network to solve the problem of high-contrast inverse scattering imaging. The proposed method takes the scattered field data and the rough image generated by the traditional method as input, makes full use of the prior information, and makes the imaging more accurate, thereby improving the precision and effectiveness of imaging.

[0038] (2) The present invention uses a multi-scale feature extraction module to capture features of different scales, which can better learn the different features of high-contrast scatterers. At the same time, a coordinate attention mechanism is added to focus the attention of the neural network on the edges and internal structure change areas of the target scatterer, further improving the accuracy of the scatterer reconstructed image. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] The present invention will be further described below with reference to the accompanying drawings and examples.

[0040] Figure 1 This is a flow chart of the electromagnetic inverse scattering imaging method based on a multi-scale coordinate attention mechanism neural network proposed in the present invention;

[0041] Figure 2 This is a schematic diagram of a multi-scale feature extraction module in a deep neural network of an electromagnetic inverse scattering imaging method based on a multi-scale coordinate attention mechanism neural network proposed in the present invention;

[0042] Figure 3 This is a schematic diagram of the coordinate attention mechanism in the deep neural network of the electromagnetic inverse scattering imaging method based on the multi-scale coordinate attention mechanism neural network proposed in the present invention;

[0043] Figure 4 This is a graph showing the result of reconstructing the relative permittivity of handwritten digits in the electromagnetic inverse scattering imaging method based on the multi-scale coordinate attention mechanism neural network proposed in the present invention;

[0044] Figure 5 This is a graph showing the results of reconstructing the relative dielectric constant using the Austrian ring pattern in the electromagnetic inverse scattering imaging method based on the multi-scale coordinate attention mechanism neural network proposed in the present invention;

[0045] Figure 6 This is a graph showing the result of reconstructing the relative dielectric constant from the Fresnel Institute's measured data in the electromagnetic inverse scattering imaging method based on a multi-scale coordinate attention mechanism neural network proposed in this invention. DETAILED DESCRIPTION

[0046] The present invention will be further described in detail below with reference to the accompanying drawings.

[0047] An electromagnetic inverse scattering imaging method based on a multi-scale coordinate attention mechanism neural network includes the following steps:

[0048] Step S1. Build the experimental scene, with the center of the area of ​​interest as the center and the radius as R, and place transmit antennas and The receiving antennas are used to obtain the scattered field data of the target scatterer, and the obtained scattered field is The matrix is ​​then processed using the back propagation algorithm to obtain the initial rough image.

[0049] Step S2. Based on the MNIST handwritten digital image, it is transformed into a target scatterer through binarization, and the target scattering field is obtained using the moment method. The target scatterer scattered field data matrix is ​​obtained, and then the back propagation algorithm is used to obtain the initial rough image of the MNIST handwritten digits, which corresponds to the scatterer of the target scatterer, thereby constructing the data set.

[0050] Step S3. Based on the scattered field data matrix and the initial rough image as the input values ​​of the neural network, and the real MNIST handwritten image after binarization as the label, a neural network prediction model based on the multi-scale coordinate attention mechanism is constructed. The network consists of an input layer, a multi-scale feature extraction module, an adaptive fusion module, a coordinate attention module and an output layer.

[0051] In the input layer, the scattered field data and the initial imaging image are feature encoded respectively, and the features are extracted and encoded using a convolutional neural network (CNN). After that, they are normalized and sent to the multi-scale feature extraction module for processing.

[0052] The multi-scale feature extraction module contains multiple convolution operations. The size and parameters of the convolution kernel are determined according to the complexity of the channel and spatial information in the feature vector. By adjusting the convolution kernel size and step size, features of different scales are obtained. These features of different scales are spliced ​​in the channel dimension to further enrich the feature information.

[0053] The adaptive fusion module calculates the cosine similarity between the scattered field data and the multi-scale features of the initial imaging image. Based on the calculated cosine similarity, the Softmax function is used to generate adaptive fusion weights to weightedly fuse the multi-scale features.

[0054] The coordinate attention module performs coordinate attention operations based on weighted fusion of multi-scale features. To better highlight the boundaries of scatterers and the accuracy of internal structural change areas, the average pooling and maximum pooling in the coordinate attention operation are replaced by only maximum pooling, thereby improving the model's ability to focus on key edge features.

[0055] Next, the cost function is used to calculate the network error and perform regression to further optimize the network parameters. After multiple iterations, a neural network prediction model based on the multi-scale coordinate attention mechanism is finally established.

[0056] The output layer uses transposed convolution to achieve high-resolution reconstruction for tasks such as scene reconstruction and target detection, or combines it with a fully connected layer for classification.

[0057] Step S4: Input the actual target scatterer initial image and the corresponding scattering field matrix into the prediction model to obtain the actual predicted imaging result.

[0058] Furthermore, step S1 includes:

[0059] With the center of the imaging area where the target scatterer is located as the center of the circle, Place on the circumference transmit antennas and receiving antennas, where The transmitting antenna first transmits electromagnetic waves, which are then absorbed and scattered by the scatterer. The receiving antenna receives the The matrix is ​​then obtained using the back propagation algorithm The initial coarse image of pixels, where .

[0060] Furthermore, step S2 includes:

[0061] First, the MNIST handwritten digit images are preprocessed, 5000 images are randomly selected and transformed into The digital part of each picture is used as the scatterer, the area with gray value less than 1 / 4 of the maximum value is used as the background area, the relative dielectric constant is assigned to 1, and the rest of the image is used as the scatterer to be measured, and the relative dielectric constant is randomly assigned to , and use these images as real label data.

[0062] Then, the target imaging area is discretized into pixels, using the Lippmann-Schwinger equation:

[0063]

[0064]

[0065] Among them, and are the coordinates within the region, is the incident electric field produced by the transmitting antenna, It is the total electric field composed of the incident field and the scattered field. is the wave number, is the Green's function of free space in the two-dimensional transverse magnetic case, ,in is the zero-order Hankel function of the second kind, is the induced current (also called contrast source), , where contrast ,in represents the relative permittivity of the unknown scatterer.

[0066] Numerical simulations were performed using the Lippmann-Schwinger equation and the moment method to obtain the scattered field data of 5000 handwritten digits.

[0067] The obtained scattered field data were processed using the back propagation algorithm to obtain 5000 rough initial imaging images.

[0068] Finally, the processed results are randomly divided into 3500 training data sets and 1500 test data sets in a ratio of 7:3, and the rough imaging images and scattered field data are matched to complete the preparation of the data set.

[0069] Furthermore, the neural network prediction model based on the multi-scale coordinate attention mechanism constructed in step S3 is composed of an input layer, a multi-scale feature extraction module, an adaptive fusion module, a coordinate attention module and an output layer.

[0070] The input layer encodes the scattered field data and the initial image separately. Using different convolutional layers of the convolutional neural network, the convolution kernel size and step size are adjusted to extract features from the different data. The scattered field data features are then concatenated with the initial image features along the channel dimension to further enrich the feature information. The data is then fed into the multi-scale feature extraction module for processing.

[0071] The multi-scale feature extraction module includes multiple convolution operations. The size and parameters of the convolution kernel are determined according to the complexity of the channel and spatial information in the feature vector. Features of different scales are obtained by adjusting the convolution kernel size and step size. These features of different scales are spliced ​​in the channel dimension to further enrich the feature information.

[0072] The adaptive fusion module calculates the cosine similarity between the scattered field data and the multi-scale features of the initial imaging image, generates adaptive fusion weights through the Softmax function based on the calculated cosine similarity, and weightedly fuses the multi-scale features.

[0073] The coordinate attention module performs a coordinate attention operation based on the above-mentioned fused feature vector. In order to further highlight the boundaries of the scatterer and the accuracy of the internal structure change area, the average pooling and maximum pooling in the coordinate attention operation are replaced by only maximum pooling, thereby improving the model's ability to focus on key edge features.

[0074] Next, the cost function is used to calculate the network error and perform regression to further optimize the network parameters. After multiple iterations, a neural network prediction model based on the multi-scale coordinate attention mechanism is finally established.

[0075] Furthermore, the cost function is:

[0076]

[0077] in, is the iteration parameter, yes The predicted contrast value for the position, is the contrast value of the real scatterer, is the regularization parameter and , the first term of the cost function quantifies the difference between the true value and the predicted value through the normalized mean square error, and the second term is the regularization constraint.

[0078] Furthermore, the actual predicted imaging result obtained in step S4 is a relative dielectric constant distribution map.

[0079] The present invention will be further described below with reference to the accompanying drawings:

[0080] like Figure 1 As shown, an electromagnetic inverse scattering imaging method based on a multi-scale coordinate attention mechanism neural network includes the following steps:

[0081] Step S1. Take the center of the imaging area where the target scatterer is located as the center of the circle, and Place on the circumference transmit antennas and receiving antennas, where The transmitting antenna first transmits electromagnetic waves, which are then absorbed and scattered by the scatterer. The receiving antenna receives the The matrix is ​​then obtained using the back propagation algorithm The initial coarse image of pixels, where .

[0082] Step S2. Preprocess the MNIST handwritten digit images, randomly select 5000 images from them, and transform them into The digital part of each picture is used as the scatterer, the area with gray value less than 1 / 4 of the maximum value is used as the background area, the relative dielectric constant is assigned to 1, and the rest of the image is used as the scatterer to be measured, and the relative dielectric constant is randomly assigned to , and use these images as real label data.

[0083] Step S3. Numerical simulation is performed using the Lippmann-Schwinger equation and the moment method to obtain scattered field data of 5,000 handwritten digits.

[0084] Step S4. Process the scattered field data obtained above using the backpropagation algorithm to obtain 5000 rough initial imaging images. Finally, randomly divide the processed results into a training dataset of 3500 images and a test dataset of 1500 images in a 7:3 ratio. Align the rough imaging images with the scattered field data to complete the dataset preparation.

[0085] Step S5. Use the above-mentioned scattering field data and the initial imaging image as the input of the multi-scale coordinate attention mechanism neural network to construct a multi-scale coordinate attention mechanism neural network prediction model. The neural network of the prediction model consists of an input layer, a multi-scale feature extraction module, an adaptive fusion module, a coordinate attention module and an output layer.

[0086] The input layer performs feature encoding on the scattered field data and the initial imaging image respectively, and uses different convolutional layers of the convolutional neural network to split the encoding of the scattered field data into two channels, the real part and the imaginary part, and pass Convolution (64 kernels, stride 1, padding 1), then we get The size of the tensor is then passed through the batch normalization layer and the Leaky-ReLU activation function. For the encoding of the initial image, a similar operation is performed, which is single channel, passing it through Convolution (64 kernels, stride 1, padding 1), followed by batch normalization layer and Leaky-ReLU activation function. The features of the scattered field data and the features of the initial imaging image are spliced ​​in the channel dimension. The tensors of size are added element by element, and then Convolution (64 kernels) is used to unify the feature dimensions and further enrich the feature information. The data is then sent to the multi-scale feature extraction module for processing.

[0087] The multi-scale feature extraction module has a specific structure as follows Figure 2 As shown in the figure, it contains multiple convolution operations. The size and parameters of the convolution kernel are determined according to the complexity of the channel and spatial information in the feature vector. Features of different scales are obtained by adjusting the size and step size of the convolution kernel. Specifically, the original features are divided into three branches: large scale, medium scale and small scale. The large scale branch adopts Convolution (64 kernels, stride 1, padding 4) yields A tensor of size, then passed Pooling, step size is 2, void rate is 2, the output is A tensor of size; the mesoscale branch uses Convolution (32 kernels, stride 1, padding 2) yields A tensor of size, then passed Pooling, the output is A tensor of size, finally used Convolution (64 kernels) yields Tensor of size; small-scale branches adopt Convolution (16 kernels, stride 1, padding 1) yields A tensor of size, then passed Pooling, the output is A tensor of size, finally used Convolution (64 kernels) yields These features of different scales are concatenated in the channel dimension to obtain The size of the tensor further enriches the feature information.

[0088] The adaptive fusion module calculates the cosine similarity between the scattered field data and the multi-scale features of the initial imaging image, generates adaptive fusion weights through the Softmax function based on the calculated cosine similarity, and weightedly fuses the multi-scale features.

[0089] The coordinate attention module has the following specific structure: Figure 3 As shown in the figure, the coordinate attention operation is performed on the basis of the above fused feature vector. In order to highlight the accuracy of the boundary of the scatterer and the internal structure change area, the average pooling and maximum pooling in the coordinate attention operation are replaced by only the maximum pooling. Specifically, the global maximum pooling operation is first performed on the feature vector along the X axis to obtain A tensor of size, then pooled along the Y axis to obtain The two tensors are concatenated to generate attention weights, and are multiplied element-by-element with the original feature vector to improve the model's ability to focus on key edge features.

[0090] The output layer, for the scene reconstruction task, uses Transposed convolution (64 kernels, step size 2), and then by using Transposed convolution (1 kernel, stride 2) output A tensor of size , achieving high-resolution reconstruction.

[0091] Step S6. Use the cost function to calculate the network error and perform regression to further optimize the network parameters. After multiple iterations, a neural network prediction model based on the multi-scale coordinate attention mechanism is finally established.

[0092] The cost function is:

[0093]

[0094] in, is the iteration parameter, yes The predicted contrast value for the position, is the contrast value of the real scatterer, is the regularization parameter and , the first term of the cost function quantifies the direct difference between the true value and the predicted value through the normalized mean square error, and the second term is the regularization constraint;

[0095] Step S7. Input the scattering field data of the actual target scatterer and the initial rough image into the multi-scale coordinate attention mechanism neural network prediction model, and obtain the output result as a relative dielectric constant distribution map.

[0096] In order to further illustrate the technical solution of the present invention, the following specific examples are given:

[0097] Specific examples:

[0098] Step S1. Label data generation: Randomly extract 5000 images from the MNIST handwritten digit dataset and transform them into The digital part of each picture is used as the scatterer, the area with gray value less than 1 / 4 of the maximum value is used as the background area, the relative dielectric constant is assigned to 1, and the rest of the image is used as the scatterer to be measured, and the relative dielectric constant is randomly assigned to , and use these images as label data.

[0099] Step S2. Input data generation: Set the imaging area size to In a square area, 16 transmitting antennas and 28 receiving antennas are evenly placed in the The center of the circle is 3 meters. The operating frequency of the transmitting antenna is 400 MHz. The 16 transmitting antennas transmit transverse magnetic waves in turn, which are then collected by the 28 receiving antennas to obtain The scattered field matrix is ​​generated by the back propagation algorithm The data generation steps are repeated for the above 5000 samples to obtain 5000 scattering field matrices and 5000 initial rough images, which are used as the input of the multi-scale coordinate attention mechanism neural network prediction model.

[0100] Step S3. Training the multi-scale coordinate attention mechanism neural network prediction model: 5000 training samples were allocated in a 7:3 ratio, with 3500 samples used as the training set and 1500 as the test set. Training was performed using PyTorch on a workstation equipped with an Intel Core i9-10920X @ 3.5GHz processor and an NVIDIA RTX3080 GPU. The maximum learning rate was set to 0.0005, and a ramp-up-then-down learning strategy was adopted. The learning rate started at a low value, gradually increased to the maximum learning rate, and then gradually decreased. Training was stopped after 50 iterations to obtain the multi-scale coordinate attention mechanism neural network prediction model.

[0101] Step S4. Based on the results of the multi-scale coordinate attention mechanism neural network prediction model: the scattered field data of the actual target scatterer and the initial rough image data are input into the trained multi-scale coordinate attention mechanism neural network prediction model, and the output is the predicted target scatterer dielectric constant distribution map.

[0102] Through the process of specific example 1, such as Figure 4 、 Figure 5 、 Figure 6 As shown, three example results are obtained to illustrate the advantages of the present invention.

[0103] Example result 1:

[0104] In order to verify that the multi-scale coordinate attention mechanism neural network proposed in the present invention has significantly improved imaging accuracy compared with the traditional U-Net model and the back propagation algorithm, the traditional U-Net is trained according to the above experimental configuration, and the prediction results of the present invention are compared with those of the traditional U-Net and the back propagation algorithm.

[0105] Three images are randomly selected from the above test set as examples to compare the multi-scale coordinate attention mechanism neural network proposed in this invention with the traditional U-Net model and the back propagation algorithm. The imaging results are compared. Figure 4 As shown in Figure 2, it can be seen that the reconstruction of strong scatterers and weak scatterers by the present invention is superior to the traditional U-Net model and back propagation algorithm. Figure 4 The scale on the right side of the diagram represents the range of relative permittivity.

[0106] Taking the normalized mean square error and structural similarity as indicators, the results of 1,500 predicted target scatterers were analyzed. The normalized mean square errors of the multi-scale coordinate attention mechanism neural network proposed in the present invention, the traditional U-Net model and the back-propagation algorithm were 0.072, 0.147 and 0.604, respectively, and the structural similarities were 0.887, 0.723 and 0.325, respectively. It can be seen that the multi-scale coordinate attention mechanism neural network proposed in the present invention is significantly superior to the traditional U-Net model and the back-propagation method in terms of normalized mean square error and structural similarity.

[0107] Example result 2:

[0108] In order to verify the generalization performance of the present invention and its ability to handle complex targets, a multi-scale coordinate attention mechanism neural network is used to predict the Austrian ring pattern, and the relative dielectric constant of the ring is set to 3. The prediction results are as follows Figure 5 As shown, it can be seen that the multi-scale coordinate attention mechanism neural network proposed in the present invention has good generalization performance, and the imaging results are better than the traditional U-Net model and back propagation method.

[0109] Example result 3:

[0110] In order to further verify the present application, the measured data of Fresnel Institute is predicted using the multi-scale coordinate attention mechanism neural network, and the result is as shown in Figure 6 The result shows that the reconstruction of the present application for real world scatterers is obviously better than the traditional U-Net model and the back propagation method.

[0111] With the above ideal embodiments according to the present application as inspiration, through the above description, relevant personnel can certainly make various changes and modifications without deviating from the technical idea of the present application. The technical scope of the present application is not limited to the content in the specification.

Claims

1. An electromagnetic inverse scattering imaging method based on a multi-scale coordinate attention mechanism neural network, It is characterized by: The following steps are involved: Step S1. Build the experimental scene and place transmit antennas and The receiving antennas are used to obtain the scattered field data of the target scatterer, and the obtained scattered field is The matrix is ​​then used to obtain the initial rough image using the back propagation algorithm; Step S2. Based on the MNIST handwritten digital image, take it as the target scatterer and use the moment method to obtain the target scattering field. The target scatterer scattered field data matrix is ​​obtained, and then the back propagation algorithm is used to obtain the initial rough image of the MNIST handwritten digits to construct the data set; Step S3. Using the scattered field data matrix and the initial rough image as the input values ​​of the neural network and the real MNIST handwritten images as labels, a neural network prediction model based on the multi-scale coordinate attention mechanism is constructed. The network consists of an input layer, a multi-scale feature extraction module, an adaptive fusion module, a coordinate attention module, and an output layer. The input layer performs feature encoding on the scattered field data and the initial imaging image, extracts and encodes the features using a convolutional neural network (CNN), then normalizes them and sends them to the multi-scale feature extraction module for processing; The multi-scale feature extraction module includes multiple convolution operations. The size and parameters of the convolution kernel are determined according to the complexity of the channel and spatial information in the feature vector. By adjusting the convolution kernel size and step size, features of different scales are obtained. These features of different scales are spliced ​​in the channel dimension to further enrich the feature information. The adaptive fusion module calculates the cosine similarity between the scattered field data and the multi-scale features of the initial imaging image, generates adaptive fusion weights through the Softmax function based on the calculated cosine similarity, and weightedly fuses the multi-scale features; The coordinate attention module performs coordinate attention operations based on weighted fusion of multi-scale features. To better highlight the boundaries of scatterers and the accuracy of internal structural change areas, the average pooling and maximum pooling in the coordinate attention operation are replaced by only maximum pooling, thereby improving the model's ability to focus on key edge features. Next, the cost function is used to calculate the network error and perform regression to further optimize the network parameters. After multiple iterations, a neural network prediction model based on the multi-scale coordinate attention mechanism is finally established. The output layer uses transposed convolution to achieve high-resolution reconstruction, or is combined with a fully connected layer for classification; Step S4: Input the actual target scatterer initial image and the corresponding scattering field matrix into the prediction model to obtain the actual predicted imaging result.

2. The electromagnetic inverse scattering imaging method based on a multi-scale coordinate attention mechanism neural network according to claim 1, characterized in that: The step S1 comprises: With the center of the imaging area where the target scatterer is located as the center of the circle, Place on the circumference transmit antennas and receiving antennas, where The transmitting antenna first transmits electromagnetic waves, which are then absorbed and scattered by the scatterer. The receiving antenna receives the The matrix is ​​then obtained using the back propagation algorithm The initial coarse image of pixels, where .

3. The electromagnetic inverse scattering imaging method based on a multi-scale coordinate attention mechanism neural network according to claim 1, characterized in that: The step S2 comprises: First, the MNIST handwritten digit images are preprocessed, 5000 images are randomly selected from them, and they are transformed into The digital part of each picture is used as the scatterer, the area with gray value less than 1 / 4 of the maximum value is used as the background area, the relative dielectric constant is assigned to 1, and the rest of the image is used as the scatterer to be tested, and the relative dielectric constant is randomly assigned to , take these images as real label data; Then, the target imaging area is discretized into Pixels, numerical simulation was performed using the Lippmann-Schwinger equation and the moment method to obtain the scattered field data of 5000 handwritten digits; The obtained scattered field data were processed using the back propagation algorithm to obtain 5000 rough initial imaging images; Finally, the processed results are randomly divided into 3500 training data sets and 1500 test data sets in a ratio of 7:3, and the rough imaging images and scattered field data are matched to complete the preparation of the data set.

4. The electromagnetic inverse scattering imaging method based on a multi-scale coordinate attention mechanism neural network according to claim 1, characterized in that: The cost function is: ； in, is the iteration parameter, yes The predicted contrast value for the position, is the contrast value of the real scatterer, is the regularization parameter and , the first term of the cost function quantifies the difference between the true value and the predicted value through the normalized mean square error, and the second term is the regularization constraint.

5. The electromagnetic inverse scattering imaging method based on a multi-scale coordinate attention mechanism neural network according to any one of claims 1 to 4, characterized in that: The actual predicted imaging result obtained in step S4 is a relative dielectric constant distribution map.

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