An electromagnetic inverse scattering imaging method based on variational and residual learning

Abstract

The present invention belongs to the field of electromagnetic inverse scattering imaging. In order to improve the accuracy and efficiency of electromagnetic inverse scattering imaging, the present invention combines the variational idea and residual learning to propose a physical-assisted learning method for solving electromagnetic inverse scattering problems. The present invention first uses truncated singular value decomposition to obtain the determined part of the induced current from the scattered field. Then, the variational part of the induced current is extracted from the variational of the scattered field through the variational idea. Secondly, the present invention constructs the mapping relationship between the solved current and the fuzzy current through residual learning, so that the residual network can specifically solve the fuzzy current without solving the whole of the induced current. The method of the present invention reduces the function fitting pressure of the neural network, thereby improving the generalization ability of the network. The present invention can accurately and quickly solve complex inverse scattering imaging problems. The single inversion time is 0.07 s, and the real-time inversion imaging requirement can be realized.

Description

Technical Field

[0001] The present invention belongs to the field of electromagnetic imaging, and is a new method for electromagnetic inverse scattering imaging using variational ideas and residual neural networks. Background Art

[0002] Electromagnetic inverse scattering imaging technology can reconstruct the shape, position, and electromagnetic parameters of a scatterer using the incident field and the scattered field. This technology has played an important role in medical imaging, logging while drilling, non-destructive testing, and other fields. The electromagnetic inverse scattering problem, as the core of this technology, has always been the focus of research. However, due to the non-linearity and ill-posedness of the problem, it is difficult to solve, with slow solution speed and low solution accuracy.

[0003] The solution methods for electromagnetic inverse scattering problems are mainly divided into two categories: optimization methods based on objective functions and methods based on sample learning. According to the different electromagnetic parameters to be solved, the optimization methods based on objective functions can be divided into source-type and field-type methods. Among them, the field-type methods solve the distribution of the scatterer by solving the total electric field distribution in the region to be inverted. For example, the Born iterative method, the modified Born iterative method, and the variational Born iterative method. The source-type solution methods solve the inverse scattering problem by solving the induced current distribution in the region. For example, contrast source inversion and subspace optimization methods. However, since deterministic methods often require time-consuming optimization processes to obtain higher solution accuracy, they cannot meet real-time application scenarios.

[0004] In recent years, with the development of deep learning technology, learning-based methods have shown advantages in solving electromagnetic inverse scattering problems, such as fast solution speed and high solution accuracy. Learning-based methods refer to constructing a suitable neural network architecture and obtaining the optimal parameters of the network through training, thereby obtaining the mapping relationship between the input and the output. Among them, the direct learning method expects to construct the mapping relationship between the scattered field and the scatterer distribution through a neural network. However, due to the data dependence of the neural network, the generalization ability of the direct learning method is limited. That is to say, when the scatterer to be solved is significantly different from the scatterer distribution in the training set, the prediction ability of the network decreases significantly. The physics-assisted learning method combines physical prior knowledge with a neural network, improving the generalization ability of the method while leveraging the function fitting ability of the neural network. However, how to effectively combine physical prior knowledge with a neural network is a difficult point in such problems.

[0005] In view of the problem that the above physical-assisted learning method faces difficulties in combining physical prior knowledge with neural networks, the present invention proposes a new method for electromagnetic inverse scattering imaging using variational ideas and residual learning. The proposed method combines, for the first time, the physics-based variational idea and the learning-based residual neural network, and has higher solution accuracy and generalization ability with almost no increase in the solution time. The proposed method specifically uses the variational idea and the residual neural network to solve the ambiguous part of the current, and uses the total loss composed of multiple loss functions as the optimization target for the learnable parameters of the neural network. The present invention has higher solution accuracy and faster solution speed for electromagnetic inverse imaging problems. The present invention provides a brand-new solution method for electromagnetic inverse imaging. Summary of the Invention

[0006] The main content of the present invention aims to solve the problem of the difficulty in combining physical prior knowledge with neural networks in the field of electromagnetic inverse imaging. The present invention proposes a new physical-assisted learning method by reasonably using variational ideas and residual learning. This method has high imaging accuracy and fast imaging speed.

[0007] The technical solution of the present invention is as follows:

[0008] 1. Obtain simulated scattered field data through electromagnetic field theory

[0009] The inversion region is discretized into N grids, and scatterers with a relative permittivity of are distributed in the inversion region. The matrix forms of the total electric field in the inversion region and the scattered field received by the receiving antenna can be expressed as:

[0010]

[0011] where represents the incident field, and represent the two-dimensional Green's function matrix. represents the induced current, which is defined as:

[0012]

[0013] where represents the contrast of the scatterer. is an N×N diagonal matrix.

[0014] 2. Solve the deterministic part of the induced current by using truncated singular value decomposition

[0015] The deterministic part of the induced current can be solved by using the method of truncated singular value decomposition:

[0016]

[0017] where σ i respectively represent the i-th left singular value vector, right singular value vector, and singular value. The superscript H represents the conjugate transpose of the vector.

[0018] According to the data equation (2), the deterministic part of the induced current can be obtained from the scattered field:

[0019]

[0020] 3. Solve the variational part of the induced current using the variational idea

[0021] Taking k = 0 as an example, the main current part obtained by truncated singular value decomposition can be used to solve the corresponding scattered field through the data equation.

[0022]

[0023] The variational part of the scattered field can be obtained from the predicted scattered field and the true scattered field:

[0024]

[0025] Similar to solving the main current part, the variational part of the induced current can be solved by truncated singular value decomposition. The singular value vectors and corresponding singular values used here are the same as those for solving the main current, and there is no need to solve them again.

[0026]

[0027] 4. Solve the residual part of the induced current using a residual neural network

[0028] Build a residual module using a convolutional neural network. The convolutional neural network consists of a convolutional layer, a batch normalization layer, and an activation function. The size of the input feature map remains unchanged after encoding and decoding through max pooling and upsampling, but its value changes. The trained convolutional neural network can obtain the correction value of the induced current in the k-th round.

[0029]

[0030] 5. Construct a loss function to train the residual neural network.

[0031] The proposed method uses a convolutional neural network to correct the induced current. Therefore, there are some learnable parameters in the network that need to be determined through sample training. For example Figure 2As shown, according to the predicted induced current, the total field, the scatterer distribution, and the predicted scattered field within the region can be solved respectively by the state equation (1) and the data equation (2). The corresponding true values can be obtained by the method of moments. Therefore, according to multiple predicted values, the corresponding mean square error can be obtained:

[0032]

[0033] 6. By combining the optimized neural network and the primary current, the variational current is used to obtain the reconstructed image of the scatterer

[0034] From the obtained scattered field data, the primary current, the variational current, and the residual current are solved respectively through steps 2, 3, and 4. Adding the three together can obtain the final predicted value of the induced current.

[0035]

[0036] According to the predicted induced current, the total field distribution within the region can be obtained through Equation (1). According to the predicted induced current and the total field distribution, the inversion results of the targets within the region under N i incoming fields can be obtained.

[0037]

[0038] The feature of the present invention is that the variational idea and the residual neural network are combined for the first time to realize real-time electromagnetic inversion imaging. The present invention effectively combines reasonable prior knowledge and provides a new idea for the physically assisted learning method. The present invention first combines the variational idea to solve the variational induced current, thereby updating the primary current. In order to further solve the hidden current that cannot be extracted from the scattered field, the residual learning method is used to predict the residual part of the induced current. Combining the primary current, the variational currents solved multiple times, and the residual current, electromagnetic inversion imaging can be finally completed.

[0039] The most prominent innovation of the present invention is to achieve higher inversion accuracy without significantly increasing the solution speed. The proposed method can realize real-time electromagnetic inversion imaging, and the single inversion imaging time is 0.07 s. The present invention provides a novel solution method for electromagnetic inversion imaging technology. Description of the Drawings

[0040] Figure 1 is the experimental configuration diagram when the present invention obtains the scattered field.

[0041] Figure 2 is the flow chart of the method proposed by the present invention.

[0042] Figure 3 is the structural diagram of the convolutional neural network adopted by the present invention.

[0043] Figure 4 This is the inversion imaging result diagram of the present invention in the test set.

[0044] Figure 5 This is the structural diagram of the Austria scatterer and the imaging result of the present invention for it. Specific embodiments

[0045] The following uses specific specific examples to illustrate the implementation manners of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific implementation manners. Various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention.

[0046] The technical solution of the present invention is as follows:

[0047] 1. Obtain relevant training data including scattered fields, total fields, and true current distributions through electromagnetic field theory.

[0048] Consider the electromagnetic inverse scattering problem under the incidence of two-dimensional transverse magnetic waves. The region of interest (DOI) contains non-magnetic lossless dielectric scatterers with unknown distributions, and the background is free space. In numerical calculations, the inversion region is discretized into N grids. The matrix forms of the total electric field in the inversion region and the scattered field received by the receiving antenna can be expressed as follows:

[0049]

[0050]

[0051] Among them, represents the incident field, and represent the two-dimensional Green's function matrix. represents the induced current, which is defined as:

[0052]

[0053] Among them, represents the contrast of the scatterer. is an N×N diagonal matrix. The vector represents the relative permittivity distribution.

[0054] In numerical simulation, the size of the DOI is set to 2m × 2m. The solution frequency is set to 400 MHz. The numbers of transmitting and receiving antennas are 16 and 32 respectively, and they are evenly distributed on the circumference with a radius of 3m. The scatterer distribution used for training combines the handwritten digits and circles in the EMNIST dataset. The circles are randomly placed in the DOI. The relative permittivity of the handwritten digits and circles is randomly distributed between 1.5 and 3. In addition, the radius of the circles is randomly distributed between 0.1m and 0.5m. To improve data diversity, each sample is randomly rotated around the center by an angle distributed between -180° and 180°. The corresponding scattered field, induced current, and total field of each scatterer distribution can be solved by the method of moments to form a set of samples. 10,000 samples are generated to train the neural network.

[0055] 2. Solve the deterministic part of the induced current by using truncated singular value decomposition

[0056] The deterministic part of the induced current can be solved by the method of truncated singular value decomposition:

[0057]

[0058] where σ i represent the i-th left singular value vector, right singular value vector, and singular value respectively. The superscript H represents the conjugate transpose of the vector.

[0059] According to the data equation (2), the deterministic part of the induced current can be obtained from the scattered field:

[0060]

[0061] where L is selected as 15.

[0062] 3. Solve the variational part of the induced current by using variational ideas

[0063] The main current part obtained by truncated singular value decomposition can solve the corresponding scattered field through the data equation.

[0064]

[0065] The variational part of the scattered field can be obtained from the predicted scattered field and the true scattered field:

[0066]

[0067] Similar to solving the main current part, the variational part of the induced current can be solved by using truncated singular value decomposition.

[0068]

[0069] 4. Use a residual neural network to solve the residual part of the induced current

[0070] The universal approximation theorem proves that a neural network containing enough neurons and appropriate activation functions can approximate any function with a given accuracy. In the present invention, a convolutional neural network combined with residual learning is used to further correct the induced current, thereby solving the hidden current that cannot be directly obtained from the scattered field.

[0071] The task of the neural network is to obtain the hidden current part. Therefore, different from directly using a convolutional neural network to regress the total induced current, this work only uses the neural network to obtain the correction value of the induced current Taking k = 0 as an example, the pre-solved induced current combining the main current part and the residual part is used as the input of the network. The trained convolutional neural network can obtain the correction value of the induced current in the k-th round

[0072]

[0073] 5. Train the residual neural network using the data generated in step 1

[0074] The proposed method uses a convolutional neural network to correct the induced current. Therefore, there are some learnable parameters in the network that need to be determined by sample training. As Figure 2 shown, according to the predicted induced current, the total field, the scatterer distribution, and the predicted scattered field in the region can be solved respectively by the state equation (1) and the data equation (2). The corresponding true values can be obtained by the method of moments. Therefore, according to multiple predicted values, the corresponding mean square error can be obtained:

[0075]

[0076] In this work, the weight coefficients of each error are c1 = c3 = 1.0, c2 = 5.0, c4 = 2.5 respectively. The learnable parameters in the neural network can be updated by the gradient descent algorithm according to the loss function. In this work, the ADAM optimizer is used to optimize the learnable parameters. After 20 rounds of sample learning, the total loss function converges.

[0077] 6. Obtain the reconstructed image of the scatterer by combining the optimized neural network and the main current, variational current

[0078] From the obtained scattered field data, the main current, variational current, and residual current are solved respectively through steps 2, 3, and 4. Adding the three together can obtain the final predicted value of the induced current.

[0079]

[0080] Based on the predicted induced current, the total field distribution within the region can be obtained through Equation (1). Based on the predicted induced current and the total field distribution, the inversion results of the target within the region for N i incoming fields can be obtained.

[0081]

[0082] Implementation Example 1

[0083] First, the test set is used as Implementation Example 1. In this implementation example, handwritten fonts and a random cylinder are used as the inversion target. The scattered fields measured under the Figure 1 experimental configuration are used as the inversion data, and the proposed implementation scheme is used to complete the inversion and obtain the image of the unknown scatterer. The inversion imaging results are as Figure 4 shown. From the inversion results of 3 different profiles, it can be seen that this test example can accurately image the target based on the scattered field data.

[0084] Implementation Example 2

[0085] In this implementation example, the Austria profile, which is completely different from the training set, is used as the inversion target. The Austria profile contains two dielectric circles and a dielectric ring. The relative dielectric constants of 3 cases gradually increase. The corresponding inversion results are as Figure 5 shown. The scattered fields corresponding to the Austria profiles with three different dielectric constant distributions are used as the input data of the proposed method respectively. From the corresponding imaging results, it can be seen that the imaging effect is very close to the true parameter distribution.

[0086] The above implementation examples only illustrate the principles and effects of the present invention by way of example, and are not used to limit the present invention. Any person familiar with this technology can modify or change the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or changes completed by those with ordinary knowledge in the technical field to which the present invention pertains without departing from the spirit and technical idea disclosed by the present invention should still be covered by the claims of the present invention.

Claims

1. An electromagnetic inverse scattering imaging method based on variational and residual learning, characterized in that: It includes the following steps: Step 1: Obtain the simulated scattering field data through the electromagnetic field theory; Step 2: Solve the deterministic part of the induced current according to the scattering field by using the truncated singular value decomposition method; Step 3: Solve the variational part of the induced current by variational method through the scattering field; Step 4: Solve the residual part of the induced current by using the residual neural network; A residual module is constructed using a convolutional neural network, which consists of a convolutional layer, a batch normalization layer, and an activation function. The input and output sizes remain unchanged after encoding and decoding through max pooling and upsampling, but their values change. After training, the convolutional neural network obtains the corrected value of the induced current in the k-th round. Step 5: Construct a loss function to train the residual neural network; Step 6: Obtain the final current distribution of the scatterer from the deterministic part, variational part, and residual part of the induced current, and obtain the inversion image according to the current distribution.

2. The electromagnetic inverse scattering imaging method based on variational and residual learning according to claim 1, wherein: Scattered field data in Step 1 Obtained in the following manner: The inversion region is discretized into N grids, and there are scatterers with a relative permittivity of distributed in the inversion region. The total electric field in the inversion region and the scattered field received by the receiving antenna are respectively expressed as: Among them, represents the incident field, and represents the two-dimensional Green's function matrix, represents the induced current, which is defined as: wherein, represents the contrast of the scatterer; is an N×N diagonal matrix.

3. The electromagnetic inverse scattering imaging method based on variational and residual learning according to claim 2, characterized in that: In Step 2, the deterministic part of the induced current is obtained as follows: The deterministic part of the induced current is solved by using the truncated singular value decomposition method: wherein σ i respectively represent the i-th left singular value vector, right singular value vector, and singular value, and the superscript H represents the conjugate transpose of the vector, According to data equation (2), the determined part of the induced current is obtained from the scattered field as follows:

4. The electromagnetic inverse scattering imaging method based on variational and residual learning according to claim 3, wherein: In Step 3, the variational part of the induced current is obtained as follows: Taking k = 0 as an example, the main current part obtained by truncated singular value decomposition predicts the corresponding scattered field through the data equation (3). The variational part of the scattering field is obtained from the predicted scattering field and the true scattering field: Similar to the solution of the main current part, the variational part of the induced current is solved by using the truncated singular value decomposition method. The singular value vectors and the corresponding singular values used here are the same as those in the solution of the main current, and there is no need to solve them again; 5. The electromagnetic inverse scattering imaging method based on variational and residual learning according to claim 4, characterized in that: In Step 5, the loss function of the residual neural network is constructed as follows: According to the predicted induced current, the total field, scatterer distribution, and predicted scattering field in the region are solved by the state equation (1) and the data equation (2) respectively. The corresponding true values are obtained by the method of moments. Therefore, the mean square error is obtained according to multiple predicted values: Loss=c1Loss J +c2Loss Esca +c3Loss Etot +c4Loss χ (10) The optimized neural network can be obtained through data training according to the constructed total loss function.

6. The electromagnetic inverse scattering imaging method based on variational and residual learning according to claim 5, characterized in that: In Step 6, the inversion image is obtained as follows: The main current, variational current, and residual current are solved from the obtained scattering field data through Steps 2, 3, and 4 respectively, and the sum of the three is the final predicted value of the induced current: Based on the predicted induced current, the total field distribution within the region can be obtained through Equation (1). Based on the predicted induced current and the total field distribution, the inversion results of the target within the region under N i incomings can be obtained;

Images