A physical information embedding method for electromagnetic full-wave inverse scattering imaging

Abstract

To address the lack of interpretability and accuracy in current deep learning-based methods for electromagnetic full-wave inverse scattering imaging, this invention discloses a physical information embedding method for electromagnetic full-wave inverse scattering imaging, involving machine learning and the field of electromagnetic full-wave inverse scattering. This method employs a state-space model (Mamba network) to efficiently simulate the overall evolution of the system across space, effectively handling the complex global coupling relationships between the incident wave, the scatterer, and the scattered field. Based on this, the method embeds physical operators into the state-space model to explicitly recover the physical properties of the scatterer. This method provides a mature, reliable, and high-precision imaging approach for electromagnetic full-wave inverse scattering in fields such as underground exploration, medical imaging, and industrial non-destructive testing.

Description

Technical Field

[0001] This invention relates to the fields of machine learning and electromagnetic full-wave inverse scattering. Technical Background

[0002] Electromagnetic full-wave backscattering imaging has garnered widespread attention in fields such as underground exploration, medical imaging, and industrial non-destructive testing. Accurately reconstructing the intrinsic properties of scatterers from the electromagnetic wave scattering field is of great significance for practical applications. To this end, a series of methods based on traditional iterative methods and deep learning have been widely used. Traditional iterative methods suffer from poor stability and high computational cost. In recent years, thanks to the rapid development of artificial intelligence, deep learning-based methods have become a powerful approach, capable of processing highly nonlinear data through multi-layered neural networks and completing the inversion and reconstruction of scatterers. However, deep learning-based methods are data-driven, and their internal operation is like a black box, lacking reasonable physical and mathematical interpretation, making their reconstruction process unreliable in many fields. Furthermore, due to the lack of constraints from objective physical laws, the reconstruction capability of deep learning-based methods is closely related to the adequacy of data preparation, resulting in unstable performance of the reconstruction results. Therefore, how to efficiently process highly nonlinear data and accurately reconstruct physical properties while ensuring the interpretability and reliability of the method has become a current requirement.

[0003] Mamba, as a deep learning data processing method, has advantages such as large receptive field, long memory, real-time performance, and high precision, and has achieved good results in fields such as computer vision and natural language processing.

[0004] This invention embeds physical information into the Mamba network, enabling the Mamba to efficiently simulate the overall evolution of the system in high-dimensional space through physical constraints. It also uses bilinear interpolation to restore the induced current to high resolution, thereby obtaining more detailed physical information. It successfully preserves the interpretability of the method and achieves excellent performance in highly nonlinear electromagnetic inverse scattering problems. Summary of the Invention

[0005] The technical problem to be solved by this invention: Inspired by the above research background, this invention proposes a Mamba method with physical information. This method embeds physical constraints into the Mamba network and uses bilinear interpolation to restore the induced current to high resolution for result optimization. It can still maintain high stability, high accuracy and strong adaptive data processing capabilities even with limited computing resources.

[0006] This invention has wide applications in electromagnetic backscattering imaging (such as medical imaging, fault detection, and underground exploration). In these applications, the Mamba method can establish dependencies between data points from highly nonlinear data, thereby significantly improving computational efficiency and imaging accuracy. On the one hand, this method can accurately reconstruct the internal physical properties of the scattering body based on the scattering data; on the other hand, due to the existence of objective physical constraints, this method retains high interpretability and stability. Therefore, the Mamba method is suitable for applications requiring high precision and strong interpretability, such as medical imaging and industrial fault detection.

[0007] This method divides the scattering data of the scatterer into a fixed-size discrete grid (e.g., 64×64), effectively establishes the dependencies between each grid using a Mamba network, and further constrains the model with physical information, thereby effectively updating the scattering data dynamically. Figure 1 The diagram illustrates the specific implementation process. The technical solution of this invention is as follows: A physical information embedding method for electromagnetic full-wave backscattering imaging, the method comprising:

[0008] Step 1: First, induced current The main current is obtained by recalculating in the subspace. and secondary current The definition is as follows:

[0009] (1);

[0010] in, This represents the remaining part of the right singular vector. It is an unknown coefficient vector;

[0011] Step 2: Obtain the main current through the subspace ;

[0012] Step 3: Put The coarse dielectric constant obtained from the inversion algorithm is fused at the feature channel level and used as the input to the U-shaped Mamba network, such as... Figure 1 As shown, the U-shaped Mamba network is composed of multiple convolutional neural network blocks and Mamba network blocks; as Figure 2 As shown in -A, the convolutional neural network block, from input to output, sequentially includes: a first convolutional layer, a first normalization layer, a first activation function layer, a second convolutional layer, a second normalization layer, and a second activation function layer; as shown in Figure 1. Figure 2 As shown in -B, the Mamba network block mainly includes convolutional layers, linear mapping layers, state-space model layers, and activation functions;

[0013] Step 4: Embed physical information into the U-shaped Mamba network to recover the scattering field and physical properties of the scatterer. The physical constraint formula is as follows:

[0014] (4);

[0015] (5);

[0016] in, It is the Green's function. Indicates contrast. Represents the total electric field;

[0017] Step 5: Calculate the error between the predicted value and the true value. The loss function is expressed as follows:

[0018] (6);

[0019] (7);

[0020] (8);

[0021] (9);

[0022] in, , , , These represent current loss, scattered field loss, SSIM loss of dielectric constant, and mean square error of dielectric constant, respectively. Indicates the number of incident emitters. Represents the true value of the current. Indicates the number of receiving antennas. This represents the predicted scattering field. Represents the true scattered field, Represents the structural similarity index. This represents the predicted dielectric constant. This represents the actual dielectric constant;

[0023] Step 6: Calculate the partial derivatives of the model's predicted and true values ​​with respect to the variables in the neural network, thereby updating the weights. After iterating a certain number of times, output the final prediction result.

[0024] Furthermore, The calculation method is as follows:

[0025] (2);

[0026] in, Describes the dimension of the signal subspace. It is a singular value and satisfies , It is a left singular vector. It is a right singular vector. This represents the conjugate transpose of a left singular vector. This represents the scattered field acquired by all receivers. Let represent the dimension of the i-th signal subspace.

[0027] Furthermore, in step 2, L is set to 15.

[0028] Furthermore, in step 4, the Green's function (3);

[0029] This represents the conjugate transpose of a right singular vector.

[0030] The pseudocode flow of the entire Mamba method is shown in Appendix Table 1, where... Represents scattered field data, Represents the Green's function within the region. The region-to-receiver Green function is set to 16, and F represents the U-shaped Mamba network with physical information.

[0031] Compared to pure deep learning methods, this invention retains the powerful feature extraction capabilities of neural networks and introduces physical information to constrain the neural network, guiding its solutions and enhancing its interpretability and stability. This method utilizes the Mamba structure to potentially evolve changes in features in the global space, constructing correlations between feature data and effectively combining the physical model and the neural network, thus significantly improving the ability to process nonlinear data. Simultaneously, the Mamba-based method can establish dependencies between long datasets while selectively forgetting unimportant information, greatly alleviating computational inefficiency. In summary, the Mamba-based method offers significantly higher computational efficiency and imaging accuracy than traditional iterative methods and deep learning methods, providing a more efficient solution for processing highly nonlinear data in high-dimensional spaces. Attached Figure Description

[0032] Figure 1 This is a flowchart of the Mamba method.

[0033] Figure 2 This describes the specific structure of convolutional neural network blocks and Mamba blocks.

[0034] Figure 3 The results are from the inverse scattering imaging of the MNIST handwritten digit dataset.

[0035] Figure 4 The scattering field is recovered under physical constraints from the MNIST handwritten digit dataset.

[0036] Figure 5The image shows the backscattering imaging results of the deformed MNIST handwritten digit dataset.

[0037] Figure 6 The scattering field is recovered under physical constraints from the deformed MNIST handwritten digit dataset. Detailed Implementation

[0038] To make the technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0039] This invention constructs a Mamba network to deevolve changes in the global space, enhancing the model's global understanding ability by building interdependencies between high-dimensional features. Simultaneously, physical rules are used to constrain the Mamba model, indicating the optimal direction for the neural network's solution. Furthermore, during loss optimization, bilinear interpolation is used to compute features at a higher resolution, thereby obtaining more detailed geometric information.

[0040] In this way, the Mamba method based on embedded physical information not only retains the powerful nonlinear data processing capabilities of neural networks, but also makes the model conform to objective facts through physical constraints, thus possessing better interpretability, stability and high reconstruction accuracy.

[0041] The overall process of this invention is as follows: Figure 1 As shown, firstly, the induced current... The main current is obtained by recalculating in the subspace. and secondary current Most of the useful information is stored in In the middle. Next, The coarse dielectric constant obtained from the inversion algorithm is fused at the feature channel level and used as the input to the U-shaped Mamba network. The U-shaped Mamba network consists of multiple convolutional neural network blocks and Mamba blocks arranged in layers. A single convolutional neural network block and Mamba block, such as... Figure 2 As shown in the figure, the U-shaped Mamba network can evolve the information of each grid into the global space, thereby efficiently establishing the correlation between data. Then, physical information is further embedded in the U-shaped Mamba network to recover the scattering field and physical properties of the scatterer. This approach not only enhances its interpretability but also helps the neural network find better solutions. Finally, the induced current, scattering field, and dielectric constant predicted by the entire model are used as outputs. The specific pseudocode of the model is shown in Table 1.

[0042] During the experiment, the Mamba method based on embedded physical information updated the weights through current loss, scattering field loss, and dielectric constant loss. The update process includes the following steps:

[0043] Step 1 (Prepare Data): Collect training data and preprocess it.

[0044] Step 2 (Parameter Initialization): Initialize the step size, initial learning rate, etc. of the neural network model.

[0045] Step 3 (Forward Propagation): Input the scattering data of the samples into the model, build the dependencies between the data through the Mamba network, use physical constraints to specify the solution of the model, and finally output the predicted value of the model.

[0046] Step 4 (backpropagation): Calculate the error between the predicted value and the actual value.

[0047] Step 5 (Update weights using loss function): The weights are updated by taking the partial derivative of the loss between the model's predicted and true values ​​with respect to the variables in the neural network. After a certain number of iterations, the final prediction result is output.

[0048] The experiments performed inverse scattering imaging tasks on the MNIST handwritten digit dataset, a modified MNIST handwritten digit dataset, and an enhanced EMNIST dataset. Comparative experiments were conducted with traditional inversion methods (BP), iterative algorithmic subspace optimization (SOM), neural network methods (Unet), and subspace expansion-based methods (SOM-Net). Evaluation metrics included structural similarity (SSIM), root mean square error (RMSE), and peak signal-to-noise ratio (PSNR). The calculation methods for these metrics are as follows:

[0049] (10);

[0050] Where u represents the average value of the image, Represents the difference values ​​of the image. Representing an image covariance, It is a constant value.

[0051] (11);

[0052] (12);

[0053] Where a and b represent the dimensions of the image. Represents the raw pixel values ​​of the image. This represents the reconstructed value of the image, where MAX represents the maximum pixel value in the image.

[0054] Specific experimental results are shown in Appendices 2 to 10, and performance comparisons are shown in... Figures 3 to 6 The results show that, in different datasets, the Mamba-SOM method of this invention has better stability and higher accuracy than traditional inversion methods, subspace optimization methods, neural network methods, and subspace expansion-based methods.

[0055] Table 1. Pseudocode flow of the entire Mamba Method

[0056]

[0057] Table 2. SSIM index of random test samples in the MNIST dataset.

[0058]

[0059] Table 3 RMSE metrics for random test samples in the MNIST dataset

[0060]

[0061] Table 4. PSNR metrics for random test samples in the MNIST dataset.

[0062]

[0063] Table 5. SSIM index of random test samples in the modified MNIST dataset.

[0064]

[0065] Table 6. RMSE index of random test samples in the modified MNIST dataset

[0066]

[0067] Table 7. PSNR index of random test samples in the modified MNIST dataset

[0068]

[0069] Table 8. SSIM of test samples from the Emnist dataset with interfering data.

[0070]

[0071] Table 9. RMSE of test samples in the Emnist dataset with interfering data

[0072]

[0073] Table 10 PSNR of test samples in the Emnist dataset with interfering data

[0074]

Claims

1. A method for embedding physical information for electromagnetic full-wave backscattering imaging, the method comprising: Step 1: First, the induced current is recalculated in the subspace to get the primary current and the secondary current defined as follows: （1）； in, This represents the remaining part of the right singular vector. It is an unknown coefficient vector; Step 2: Obtain the main current through the subspace ; Step 3: Put The coarse dielectric constant obtained by the inversion algorithm is fused at the feature channel level as the input of the U-shaped Mamba network. The U-shaped Mamba network is composed of multiple convolutional neural network blocks and Mamba network blocks. The convolutional neural network block includes, from input to output, the following layers in sequence: first convolutional layer, first normalization layer, first activation function layer, second convolutional layer, second normalization layer, and second activation function layer. The Mamba network block mainly includes convolutional layers, linear mapping layers, state space model layers, and activation functions. Step 4: Embed physical information into the U-shaped Mamba network to recover the scattering field and physical properties of the scatterer. The physical constraint formula is as follows: （4）； （5）； in, It is the Green's function. Indicates contrast. Represents the total electric field; Step 5: Calculate the error between the predicted value and the true value. The loss function is expressed as follows: （6）； （7）； （8）； （9）； in, , , , These represent current loss, scattered field loss, SSIM loss of dielectric constant, and mean square error of dielectric constant, respectively. Indicates the number of incident emitters. Represents the true value of the current. Indicates the number of receiving antennas. This represents the predicted scattering field. Represents the true scattered field, Represents the structural similarity index. This represents the predicted dielectric constant. This represents the actual dielectric constant; Step 6: Calculate the partial derivatives of the model's predicted and true values ​​with respect to the variables in the neural network, thereby updating the weights. After iterating a certain number of times, output the final prediction result.

2. The physical information embedding method for electromagnetic full-wave backscattering imaging as described in claim 1, characterized in that, In step 2 The calculation method is as follows: （2）； in, Describes the dimension of the signal subspace. It is a singular value and satisfies , It is a left singular vector. It is a right singular vector. This represents the conjugate transpose of a left singular vector. This represents the scattered field acquired by all receivers. Let represent the dimension of the i-th signal subspace.

3. The physical information embedding method for electromagnetic full-wave backscattering imaging as described in claim 1, characterized in that, Green function in step 4 (3); This represents the conjugate transpose of a right singular vector.

4. The physical information embedding method for electromagnetic full-wave backscattering imaging as described in claim 2, characterized in that, In step 2, L is set to 15.

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