Electrical impedance imaging method and device and storage medium

Abstract

The invention discloses an electrical impedance tomography method, which integrates a physical model and deep learning to construct a deep learning framework with physical constraints so as to improve physical consistency and reconstruction precision. According to the method, a neural network based on an encoder-decoder structure is adopted, and measured boundary voltage is used as input to predict conductivity distribution of a target object; in order to improve the performance of the neural network, a physical Jacobian matrix is introduced, and the sensitivity of boundary voltage to conductivity is described; and constructing a physical regularization loss function, comparing a physically calculated Jacobi matrix with a neural network predicted Jacobi matrix, and combining a final total loss function with data error loss and physical consistency loss. According to the method, data driving model training is guided through physical constraints, combination of physical information and deep learning is achieved, the precision of electrical impedance reconstruction and the generalization ability of the model are remarkably improved, and a new solution thought is provided for the fields of medicine, flexible electronics, environment monitoring and the like.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of electrical impedance reconstruction, and particularly relates to an electrical impedance imaging method and device based on data driving and physical model fusion and a storage medium. BACKGROUND

[0002] Electrical Impedance Tomography (EIT) is an imaging technology based on boundary voltage measurement and current injection to reconstruct the conductivity distribution inside the target region, which is widely applied in medical imaging, industrial detection, tactile imaging and other fields. The core problem of EIT is to infer the conductivity distribution inside the target region from the boundary voltage data, which is a highly nonlinear and ill-posed problem. Currently, many methods have been proposed to solve this inverse problem: traditional numerical analysis method, deep learning method, etc. Traditional electrical impedance reconstruction methods include Newton-Raphson method, linear back projection (LBP) and Tikhonov regularization. Newton-Raphson method solves the conductivity value in the measured field by minimizing the square of the difference between the actual measured value and the calculated value of the forward problem. This algorithm has good convergence, but it is sensitive to noise because it uses the difference between the initial value and the measured value in the calculation. LBP method assumes a linear relationship between boundary voltage and conductivity, which is computationally efficient, but has insufficient description ability for complex distribution. Tikhonov regularization enhances noise suppression by introducing a regularization term, but it can easily lead to a decrease in resolution. In addition, the finite element method model driven method directly solves the physical model, but the computational complexity is high and it is sensitive to initial values and parameters.

[0003] In recent years, deep learning algorithms have been introduced into EIT image reconstruction: EIT reconstruction algorithm based on deep dictionary, which uses deep learning to train the dictionary, and then performs image reconstruction through sparse reconstruction algorithm; based on artificial neural networks (ANN), a supervised automatic encoder neural network reconstruction algorithm is proposed for EIT image reconstruction, and different deep learning algorithms are used to train and test the data set. In addition, the EIT reconstruction based on convolutional neural network (CNN) also achieves good reconstruction effect; the deep learning model based on generative adversarial network (GANs) generates realistic data through the adversarial training of generator and discriminator, and in EIT reconstruction, GANs are often used to map voltage data to conductivity distribution while maintaining the smoothness of the solution and physical constraints; the unsupervised learning model based on automatic encoder learns the latent representation of the data by compressing and decompressing the input data, and the automatic encoder is used for data dimensionality reduction and feature extraction, and then used for reconstruction of the conductivity distribution; the graph neural network (GNNs) is a deep learning model based on graph structure, and EIT imaging itself involves the propagation of electric field from sensors to the interior of the object, and GNNs can be used to handle the inverse problem of EIT. After the deep learning model is trained on a large amount of data, it can directly map the boundary voltage to the conductivity distribution of the target area, and this method does not strictly rely on the physical model and can effectively handle noise and complex data distribution. However, the pure data-driven method is highly dependent on data quality and quantity, and lacks of interpretability in specific physical scenarios, which restricts its application range. SUMMARY

[0004] The present application aims to at least partially solve one of the technical problems existing in the prior art.

[0005] To this end, the present application proposes a resistance impedance imaging method, device and storage medium based on data-driven and physical model fusion, by adding the constraint of Jacobian matrix in the loss function, the gradient of network prediction is consistent with the actual physical law, the ambiguity of the reconstruction result is reduced, the reconstruction error and physical consistency are jointly optimized through the multi-task learning framework, the generalization ability of the model is effectively improved, and the accuracy and reliability of the reconstruction are improved.

[0006] In order to achieve the above purpose, the technical scheme adopted by the present application is as follows:

[0007] The first aspect of the present application provides a resistance impedance imaging method, comprising the following steps:

[0008] The boundary measurement voltage of a simulation target object is acquired, an initial distribution of the electrical conductivity of the simulation target object is calculated by using a finite element method, and after normalization processing, a training data set is formed;

[0009] An encoder and a decoder embedded with a Jacobian matrix are respectively constructed, the Jacobian matrix is used to reflect the sensitivity between the electrical conductivity distribution and the boundary voltage, a physically guided neural network is constructed by using the encoder and the decoder, a total loss function is constructed based on a data error loss and a physical consistency loss, the neural network is trained by using the training data set and the total loss function, and a trained neural network is obtained;

[0010] The boundary voltage of a target object to be measured is acquired, and is input into the trained neural network to obtain the electrical conductivity distribution of the target object to be measured.

[0011] In some embodiments, the simulation target object has different numbers, geometric shapes and / or electrical conductivity values.

[0012] In some embodiments, the electrical conductivity value of the simulation target object is set in the range of 0.1 s / m to 2 s / m.

[0013] In some embodiments, the training data set contains a plurality of training samples, and each training sample records the current injection mode used when the simulation target object is simulated by EIT simulation, the corresponding boundary measurement voltage and the electrical conductivity distribution inside the simulation target object.

[0014] In some embodiments, the encoder comprises an input layer, a first convolutional layer, a second convolutional layer, a flattening layer and a first fully connected layer connected in sequence, the input layer is used to transmit the boundary measurement voltage input into the encoder to the first convolutional layer, 32 3*3 convolutional kernels are arranged in the first convolutional layer to extract low-level features of the boundary measurement voltage, 64 3*3 convolutional kernels are arranged in the second convolutional layer to extract higher-level features of the boundary measurement voltage to obtain a feature map, the flattening layer is used to convert the feature map obtained by the second convolutional layer into a one-dimensional vector, and the first fully connected layer is used to map the one-dimensional vector obtained by the flattening layer to a 256-dimensional voltage space.

[0015] The decoder comprises a second full connection layer, a third full connection layer, a reshaping layer, a first deconvolution layer, a second deconvolution layer and an output layer connected in sequence; the second full connection layer and the third full connection layer are used for gradually expanding the feature dimension output by the first full connection layer, the reshaping layer is used for reconstructing a one-dimensional vector output by the third full connection layer into a three-dimensional tensor of 32*32*2, the first deconvolution layer and the second deconvolution layer are used for gradually restoring the three-dimensional tensor of 32*32*2 output by the reshaping layer to the spatial resolution of the conductivity, and finally the conductivity distribution is reconstructed by the output layer.

[0016] In some embodiments, the difference between the conductivity distribution reconstructed by the neural network and the real conductivity distribution is taken as the data error loss; and the difference between the Jacobian matrix calculated by the electrical impedance model and the Jacobian matrix predicted by the neural network is taken as the physical consistency loss.

[0017] In some embodiments, the root mean square error between the boundary measurement voltage and the boundary predicted voltage obtained by the neural network is taken as the data error loss; and the difference between the Jacobian matrix calculated by the electrical impedance model and the Jacobian matrix predicted by the neural network is taken as the physical consistency loss.

[0018] In some embodiments, the total loss function is denoted as L, and the expression is as follows:

[0019] L=α·L V +β·L J

[0020]

[0021] wherein L V is the data error loss; is the boundary measurement voltage of the i-th training sample input into the neural network, is the boundary predicted voltage of the i-th training sample obtained by the neural network; m is the number of training samples used when training the neural network; is the physical Jacobian matrix of the i-th training sample, which is calculated according to the boundary measurement voltage and the conductivity distribution σ i of the i-th training sample by using the electrical impedance model, is the predicted Jacobian matrix of the i-th training sample, which is calculated according to the boundary predicted voltage and the conductivity distribution σ i of the i-th training sample by the neural network; and α and β are two hyperparameters.

[0022] The second aspect of the present application provides an electrical impedance imaging device, comprising:

[0023] The first module is configured to obtain a boundary measurement voltage of a simulation target object, calculate an initial distribution of the electrical conductivity of the simulation target object by using a finite element method, and form a training data set after normalization processing;

[0024] The second module is configured to construct an encoder and a decoder embedded with a Jacobian matrix respectively, the Jacobian matrix is used to reflect the sensitivity between the electrical conductivity distribution and the boundary voltage, construct a physically guided neural network by using the encoder and the decoder, construct a total loss function based on a data error loss and a physical consistency loss, train the neural network by using the training data set and the total loss function, and obtain a trained neural network.

[0025] The third module is configured to obtain a boundary voltage of a target object to be measured, input the boundary voltage into the trained neural network, and obtain the electrical conductivity distribution of the target object to be measured.

[0026] The third aspect of the present application provides a computer readable storage medium, the computer readable storage medium stores computer instructions, the computer instructions are used to make the computer execute the electrical impedance imaging method according to any one of the embodiments of the first aspect of the present application.

[0027] Compared with the prior art, the present application has the following characteristics and beneficial effects:

[0028] The present application combines a physical model and a deep learning method, and constructs a deep learning framework with physical constraints to improve the physical consistency and reconstruction accuracy. The model adopts an encoder-decoder structure, and uses the measured boundary voltage as the input to predict the electrical conductivity distribution of the target region. In order to improve the performance of the model, a physical information Jacobian matrix is introduced to describe the sensitivity of the boundary voltage to the electrical conductivity. A physical regularization loss function is constructed to compare the Jacobian matrix calculated by the physical calculation with the Jacobian matrix predicted by the neural network. The final loss function combines the reconstruction error loss and the physical consistency loss. The framework uses physical constraints to guide the training of the data-driven model, realizes the combination of physical information and deep learning, significantly improves the accuracy of electrical impedance reconstruction and the generalization ability of the model, and provides a new solution for the fields of medicine, flexible electronics and environmental monitoring. BRIEF DESCRIPTION OF DRAWINGS

[0029] Figure 1 A whole flowchart of an electrical impedance imaging method provided for the first aspect of the present application is provided;

[0030] Figure 2 A comparison chart of ablation experiment results designed for the embodiment of the present application is provided;

[0031] Figure 3 A comparison chart of anti-noise experiment results designed for the embodiment of the present application is provided;

[0032] Figure 4 A structural schematic diagram of an electronic device is provided for a third aspect embodiment of the present application. DETAILED DESCRIPTION

[0033] In order to make the purpose, technical scheme and advantages of the present application more clear, the present application is further described in detail below in combination with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application. On the contrary, the present application covers any alternative, modification, equivalent method and scheme made within the spirit and scope of the present application defined by the claims. Further, in order to make the public have a better understanding of the present application, some specific details are described in the following detailed description of the present application. The present application can also be completely understood without the description of these details by those skilled in the art.

[0034] Referring to Figure 1 The first aspect embodiment of the present application provides a method for electrical impedance imaging, comprising the following steps:

[0035] Step S1, obtaining the boundary measurement voltage of the simulation target object, calculating the initial distribution of the electrical conductivity of the simulation target object by using the finite element method, and forming a training data set after normalization processing;

[0036] Step S2, respectively constructing an encoder and a decoder embedded with a Jacobian matrix, the Jacobian matrix is used to reflect the sensitivity between the electrical conductivity distribution and the boundary voltage, and a physically guided neural network is constructed by using the encoder and the decoder; a total loss is constructed based on a data error loss and a physical consistency loss, wherein the data error loss is used to measure the difference between the reconstructed electrical conductivity distribution and the real electrical conductivity distribution, so as to reflect the fitting accuracy of the neural network to the target electrical conductivity distribution, and the physical consistency loss is used to measure the difference between the Jacobian matrix calculated by the electrical impedance model and the Jacobian matrix predicted by the neural network, so as to ensure that the neural network can reasonably capture the physical constraints and the spatial characteristics of the electrical conductivity distribution in the prediction process; the training data set obtained in step S1 and the constructed total loss are used to train the neural network, and a trained neural network is obtained;

[0037] Step S3, obtaining the boundary voltage of the target object to be measured, inputting it into the trained neural network, and obtaining the electrical conductivity distribution of the target object to be measured.

[0038] In some embodiments, step S1 specifically comprises the following steps:

[0039] Step S11, first, a simulation model of the EIT system is constructed, the simulation model including a plurality of simulation target objects arranged in a target region, and a plurality of electrodes uniformly distributed on the periphery of the target region; then, an adjacent current injection excitation mode is used for the simulation model, and boundary measurement voltage data is obtained; in the adjacent current injection excitation mode, the current is injected into the target region through a pair of adjacent electrodes and returned to the other adjacent electrode, while another pair or multiple pairs of electrodes are used for measuring the boundary voltage, all the electrodes are sequentially used as current injection electrodes to form a cyclically covered excitation mode; then, the conductivity distribution inside the simulation target objects in the target region is calculated by using the finite element method, and normalized processing is performed thereon; a training sample is constructed by using the obtained boundary measurement voltage, the normalized conductivity distribution and the corresponding current injection mode;

[0040] In one specific embodiment of the application, a 2D circular simulation model with 16 electrodes is used, in which the current is injected through the first pair of electrodes, and the voltage is measured through the remaining electrode pairs, the next excitation mode moves to the second pair of electrodes to inject the current, and the above steps are repeated until all the electrode pairs complete the excitation. The simulation model is carried out in the EIDORS tool kit of Matlab, the measurement tool simulates the measurement of the boundary voltage, and provides voltage data matched with the excitation mode.

[0041] Step S12, different training samples are obtained by changing the number, geometry and / or conductivity of the simulation target objects in the simulation model constructed in step S11 and the current injection mode, and a training data set is constructed by using all the training samples.

[0042] Optionally, the geometry of the simulation target object can be circular, rectangular, triangular and the like; the conductivity of the simulation target object is set in the range of 0.1 s / m to 2 s / m, covering the impedance characteristics of typical biological tissues and industrial materials.

[0043] In some embodiments, step S2 aims to obtain a neural network with physical guidance, by introducing the Jacobian matrix in the EIT model into the data-driven neural network, to ensure that the gradient learned by the neural network is consistent with the gradient of the EIT model, so as to more accurately fit the physical law of EIT, and at the same time improve the accuracy and generalization ability of the reconstruction. Step S2 specifically includes:

[0044] Step S21, neural network construction

[0045] The input of the neural network is the boundary measurement voltage, and the output is the predicted conductivity distribution. The inverse operation of the electrical impedance reconstruction is integrated into the EIT training of the neural network as an auxiliary task to improve the generalization performance of the neural network by constraining the complexity of the neural network and increasing the data richness. The model is divided into two parts of encoder and decoder, and the regression models of the encoder and the decoder are used to fit the explicit mapping functions of the forward and inverse EIT models respectively. The Jacobian matrix is embedded in the encoder and the decoder. Specifically, the Jacobian matrix in the encoder is used to reflect the sensitivity of the input real conductivity distribution to the predicted boundary voltage of the neural network, and the Jacobian matrix in the decoder is used to reflect the sensitivity of the predicted boundary voltage of the neural network to the predicted conductivity distribution. In the neural network, each layer of neurons is connected through an activation function, a weight and a bias. Based on the EIT regression model of the neural network, the weight and the bias are continuously optimized to make the output training value as close to the real value as possible. The boundary voltage is taken as the input of the encoder, and the intermediate implicit variable is output; the conductivity distribution is decoded from the implicit variable by the decoder. Both the encoder and the decoder use a multi-layer fully connected network, and the activation function is ReLU to improve the nonlinear fitting capability. The nonlinear mapping function of the neural network is constructed to map the input conductivity distribution to the boundary voltage, and the goal is to make the predicted boundary voltage close to the measured voltage, while outputting an accurate conductivity distribution. At the same time, in order to enhance the generalization ability of the model, the reconstructed conductivity and the boundary voltage are combined, and the network not only optimizes the output conductivity, but also optimizes the predicted boundary voltage through physical consistency constraint.

[0046] In a specific embodiment of the present application, the encoder includes an input layer, a first convolutional layer, a second convolutional layer, a flattening layer and a first fully connected layer connected in sequence; wherein the input layer is used to pass the boundary measurement voltage input into the encoder to the first convolutional layer; 32 3x3 convolutional kernels are arranged in the first convolutional layer to extract low-level features of the boundary measurement voltage; 64 3x3 convolutional kernels are arranged in the second convolutional layer to extract higher-level features of the boundary measurement voltage to obtain a feature map; the flattening layer is used to convert the feature map obtained by the second convolutional layer into a one-dimensional vector; and the first fully connected layer is used to map the one-dimensional vector obtained by the flattening layer to a 256-dimensional voltage space. The decoder includes a second fully connected layer, a third fully connected layer, a reshaping layer, a first deconvolutional layer, a second deconvolutional layer and an output layer connected in sequence; wherein the second fully connected layer and the third fully connected layer are used to gradually expand the feature dimension output by the first fully connected layer, the reshaping layer is used to reconstruct the one-dimensional vector output by the third fully connected layer into a 32x32x2 three-dimensional tensor, and the two deconvolutional layers are used to gradually restore the 32x32x2 three-dimensional tensor output by the reshaping layer to the spatial resolution of the conductivity, and finally output the reconstructed conductivity distribution.

[0047] The differential calculation process of the neural network is described as follows:

[0048] In order to make the Jacobian matrix predicted by the neural network directly correspond to the physical Jacobian matrix, the neural network differential calculation is introduced so that the neural network has stronger explainability in the process of reconstructing the conductivity distribution. The differential calculation of the neural network realizes the fusion of the data-driven model and the physical priori knowledge, so that the deep learning not only depends on the data but also can embed the physical law, and more accurately fit the complex nonlinear relationship. The differential calculation refers to the calculation of the gradient of the output of the neural network with respect to the input or the weight parameter, and the derivative of the output of the neural network with respect to the input is calculated based on the chain rule, aiming at making the data-driven neural network regression model better represent the physical EIT forward model.

[0049] Through the decomposition of the derivative calculation by the chain rule, the weight parameters of the neural network are used for layer-by-layer transmission calculation. In EIT, the input and output in the neural network and the objective function are redefined, wherein the hidden layer variable z represents the conductivity distribution inside the object to be reconstructed. The inverse problem is to update the conductivity distribution by using the measured voltage V:

[0050]

[0051] In the formula, the learning rate is η, and the loss is the loss function.

[0052] The gradient propagation of the Jacobian matrix uses the Jacobian matrix to update the gradient of the encoder and the decoder part combined by the chain rule, which is represented as:

[0053]

[0054] In the formula, the encoder part The influence of the conductivity distribution σ based on the forward model on the boundary measured voltage V is described; the decoder part is used for back propagation to update the conductivity distribution, which corresponds to the solution of the EIT inverse problem.

[0055] Step S22, constructing a total loss function

[0056] The main goal of electrical impedance reconstruction is to reconstruct the conductivity distribution inside the object according to the voltage or current measurement data on the boundary. For this purpose, the Jacobian matrix is used to describe how the change of the conductivity distribution affects the voltage. Based on the conductivity distribution, the forward problem is solved, and the Jacobian matrix is constructed by calculating the derivative of the forward model with respect to the conductivity. The inverse Jacobian matrix is used to update the conductivity distribution based on the measured voltage or current data. In the data-driven deep learning model, the Jacobian matrix information of the EIT physical principle is embedded in the deep learning network, and the network introduces physical constraints by calculating and comparing the Jacobian matrix. In the forward problem of electrical impedance reconstruction, the Jacobian matrix describes the sensitivity of the boundary voltage to the conductivity distribution, which is specifically: ​

[0057]

[0058] In the formula, J phys is the physical Jacobian matrix calculated based on the EIT physical model; V measured is the boundary voltage of the object, and σ is the conductivity distribution of the object.

[0059] In order to ensure that the neural network can truly represent the EIT forward model, the Jacobian matrix J net of the object calculated by the neural network should be consistent with the physical Jacobian matrix J phys as much as possible. By adding a Jacobian matrix-based constraint in the training process, the neural network is forced to learn the gradient information consistent with the physical model. The gradient of the conductivity distribution with respect to the boundary predicted voltage is calculated using the automatic differentiation mechanism of the neural network:

[0060]

[0061] In the formula, V predicted is the boundary voltage of the object predicted by the neural network.

[0062] The physical Jacobian matrix J phys is compared with the Jacobian matrix J net calculated by the neural network to ensure consistency in gradient information. By introducing Jacobian information, the interpretability of the neural network is enhanced, and the dependence of the neural network on physical laws is more explicit. The neural network obtains the predicted Jacobian matrix through training, and compares it with the physically calculated Jacobian matrix to enhance the physical consistency of the neural network. The error term ΔJ of the Jacobian matrix is expressed as:

[0063] ΔJ=J net -J phys

[0064] In the subsequent process of optimizing the neural network, ΔJ is introduced as a regularization term, so that the Jacobian matrix predicted by the neural network is closer to the true EIT physical law. In the neural network training, the error term ΔJ of the Jacobian matrix is included in the loss function to ensure that the network prediction result is consistent with the true physical model. The conductivity distribution reconstruction result is further optimized by sparse regularization technology to enhance the spatial resolution.

[0065] In the neural network training process, the Jacobian matrix predicted by the neural network is calculated using the automatic differentiation mechanism, and by comparing it with the physical Jacobian matrix, a physical consistency constraint term is introduced in the loss function. The error between the physical Jacobian matrix and the Jacobian matrix of the neural network is added to the loss function as a regularization term, which is explicitly expressed as:

[0066] ΔJencoder = J NN，encoder - J physical，encoder

[0067] ΔJ decoder = J NN，decoder - J physical，decoder

[0068] where ΔJ encoder represents the Jacobian difference between the encoder of the neural network and the physical model; J NN，encoder represents the Jacobian matrix of the boundary voltage output by the encoder; J physical，encoder represents the true Jacobian matrix derived based on the physical model; ΔJ decoder represents the inverse Jacobian difference between the decoder of the neural network and the physical model; J NN，decoder represents the Jacobian matrix when the decoder inverts the conductivity distribution from the voltage space; J physical，decoder represents the approximate Jacobian obtained from the physical model.

[0069] Based on the above principle, in EIT reconstruction, the Jacobian error is included in the loss function, and the Jacobian matrix information in the physical model is embedded into the data-driven neural network to ensure that the gradient learned by the neural network is consistent with the gradient of the physical model. During the training of the neural network, the difference between the Jacobian matrix of the network and the Jacobian matrix of the physical EIT forward model is defined as part of the loss function, aiming to more accurately fit the physical law of EIT and improve the accuracy and generalization ability of its reconstruction.

[0070] Data error loss L σ is used to measure the gap between the reconstructed conductivity distribution and the true conductivity distribution, reflecting the fitting accuracy of the model to the target conductivity distribution, thereby guiding the neural network optimization process and improving the accuracy of the reconstruction result. Data error loss L σ is represented as:

[0071]

[0072] where m represents the number of training samples used when training the neural network, represents the true conductivity distribution of the i-th training sample, represents the conductivity distribution of the i-th training sample predicted by the neural network.

[0073] Since EIT is a highly nonlinear and ill-posed inverse problem, training only with conductivity data error can cause the neural network to be difficult to converge in some cases. The constrained neural network not only correctly predicts the conductivity distribution, but also ensures that the predicted value can produce the correct voltage response after calculation by the physical equation. Therefore, the embodiment of the present application calculates the data prediction error in the voltage measurement space, that is, the root mean square error (MSE) of the boundary measurement voltage and the boundary voltage predicted by the neural network is used to replace the L σ as the data error loss, denoted as L V :

[0074]

[0075] In the formula, represents the boundary measurement voltage of the i-th training sample input into the neural network, represents the boundary predicted voltage of the i-th training sample obtained by the neural network.

[0076] The physical consistency loss is used to measure the deviation between the Jacobian matrix calculated by the physical equation and the Jacobian matrix predicted by the neural network, so as to ensure that the neural network can reasonably capture the physical constraints and the spatial characteristics of the conductivity distribution in the prediction process, that is, to ensure that the prediction of the neural network conforms to the physical law, denoted as:

[0077]

[0078] In the formula, represents the physical Jacobian matrix of the i-th training sample, represents the predicted Jacobian matrix of the i-th sample.

[0079] The loss function is added with the physical constraint, the data error and the physical regularization term are combined, the physical information is integrated into the core of the data-driven model, and the final total loss function L of the EIT reconstruction is represented as:

[0080] L = a L V + b L J

[0081] In the formula, a is a hyperparameter, which controls the weight of the data error loss; b is a hyperparameter, which controls the weight of the physical consistency loss, L V is the data prediction error, that is, the root mean square error between the measured voltage and the predicted voltage, L J is the physical consistency error, that is, the root mean square error between the Jacobian matrix calculated by the physical model and the Jacobian predicted by the neural network.

[0082] In some embodiments, step S3 specifically comprises the following:

[0083] In the forward propagation phase, the boundary voltage data is used as input and processed by the encoder and decoder to obtain the predicted conductivity distribution. Next, the data error (which can be the conductivity distribution or the boundary voltage) between the predicted result and the true value is calculated, as well as the error associated with the Jacobian matrix. In the backward propagation phase, the chain rule is applied to calculate the gradient of the total loss function, thereby updating the weights and biases of the neural network. The iterative optimization process continuously repeats the forward propagation and backward propagation steps above. The neural network training uses the gradient descent method to minimize the total loss function L, updates the weights and biases of the neural network, and iteratively optimizes and repeats the above steps until the total loss function reaches the convergence condition, ensuring that the performance of the neural network is fully optimized.

[0084] The effectiveness of the method of the embodiment of the present invention is verified below with reference to the accompanying drawings:

[0085] (1) Design ablation experiments to verify the contribution of physical constraints

[0086] Design Experiment Example 1: For a square with two identical sides and different impedances, four groups of samples with different impedance values ​​are randomly generated, labeled CASE1, CASE2, CASE3, and CASE4. An ablation experiment is designed to verify the contribution of physical constraints and evaluate the impact of the Jacobian matrix on the accuracy and consistency of the neural network. In this experiment, the Jacobian matrix regularization term is completely removed from the neural network, and the neural network is trained solely in a data-driven manner, relying solely on the data error loss function to optimize the network parameters. This allows the impact of the lack of physical constraints on the accuracy and consistency of the neural network reconstruction to be evaluated.

[0087] Design Experiment 2: For Cases 1, 2, 3, and 4 above, retain the neural network's Jacobian matrix learning process, but do not introduce the physical Jacobian matrix as a constraint. This leaves the neural network without physical guidance and optimizes solely through gradient information learned within the network. This explores the specific role of the physical Jacobian matrix in improving neural network performance. Using the physically calculated Jacobian matrix as a guide, completely remove the neural network's Jacobian matrix learning process, evaluate the contribution of the physical Jacobian matrix alone to the neural network, and compare its effectiveness in combination with the Jacobian matrix predicted by the neural network.

[0088] The experimental results are as follows Figure 2 As shown, Figure 2 is the true distribution of conductivity (see Figure 2 The first row in the figure shows a comparison of the conductivity reconstruction distribution obtained by completely removing the Jacobian matrix regularization term in the neural network and using the method of the embodiment of the present invention.

[0089] Figure 2In the figure, the first line is the true conductivity distribution of CASE1 to CASE4, the second line is the conductivity reconstructed distribution obtained by completely removing the Jacobian matrix regularization term in the neural network, and the third line is the conductivity reconstructed distribution obtained by using the method of the embodiment of the present invention. Figure 2 It can be seen that using the physically calculated Jacobian matrix as a guide can produce better reconstruction results in the same case.

[0090] (2) Design of noise resistance experiment

[0091] Design a noise resistance experiment. To make the results more generalizable, the samples are squares with three identical sides and different impedances. Four groups of samples with different impedance values ​​are randomly generated and recorded as CASE1, CASE2, CASE3, and CASE4. Gaussian noise with uniform distribution is added to each sample. Different signal-to-noise ratios (SNRs) or noise standard deviations are set to generate multiple sets of data. Set from low noise to high noise: SNR = 50, 40, 30, and 20 dB, respectively. The electrical impedance tomography method of the embodiment of the present invention is used to reconstruct multi-impedance objects, test the attenuation trend of the model performance when the noise level increases, and compare the generalization ability of the model under high noise conditions. The experimental results are as follows: Figure 3 As shown by Figure 3 It can be seen that using the physically calculated Jacobian matrix as a guide in the same case can still achieve good reconstruction results.

[0092] A second embodiment of the present invention provides an electrical impedance imaging device, comprising:

[0093] The first module is configured to obtain a boundary measurement voltage of a simulated target object, calculate an initial distribution of the conductivity of the simulated target object using a finite element method, and form a training data set after normalization;

[0094] A second module is configured to respectively construct an encoder and a decoder embedded with a Jacobian matrix, wherein the Jacobian matrix is ​​used to reflect the sensitivity between the conductivity distribution and the boundary voltage, construct a physics-guided neural network using the encoder and the decoder, construct a total loss function based on data error loss and physical consistency loss, and train the neural network using the training data set and the total loss function to obtain a trained neural network;

[0095] The third module is configured to obtain the boundary voltage of the target object to be measured, input the boundary voltage into the trained neural network, and obtain the conductivity distribution of the target object to be measured.

[0096] It should be noted that the above explanations of the electrical impedance tomography method are also applicable to the electrical impedance tomography device of this embodiment, and will not be repeated here.

[0097] In order to implement the above embodiment, the embodiment of the present invention further provides a computer-readable storage medium on which a computer program is stored. The program is executed by a processor to perform the electrical impedance imaging method of the above embodiment.

[0098] Reference below Figure 4 , which shows a schematic diagram of the structure of an electronic device suitable for implementing an embodiment of the present invention. It should be noted that the electronic devices in the embodiments of the present invention may include, but are not limited to, mobile terminals such as mobile phones, laptop computers, digital broadcast receivers, PDAs (personal digital assistants), PADs (tablet computers), PMPs (portable multimedia players), and in-vehicle terminals (e.g., in-vehicle navigation terminals), as well as fixed terminals such as digital TVs, desktop computers, and servers. Figure 4 The electronic device shown is only an example and should not limit the functions and scope of use of the embodiments of the present invention.

[0099] like Figure 4 As shown, the electronic device may include a processing device (e.g., a central processing unit, a graphics processing unit, etc.) 101, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 102 or a program loaded from a storage device 108 into a random access memory (RAM) 103. Various programs and data required for the operation of the electronic device are also stored in the RAM 103. The processing device 101, the ROM 102, and the RAM 103 are connected to each other via a bus 104. An input / output (I / O) interface 105 is also connected to the bus 104.

[0100] Typically, the following devices may be connected to the I / O interface 105: an input device 106 including, for example, a touch screen, a touchpad, a keyboard, a mouse, a camera, a microphone, etc.; an output device 107 including, for example, a liquid crystal display (LCD), a speaker, a vibrator, etc.; a storage device 108 including, for example, a magnetic tape, a hard disk, etc.; and a communication device 109. The communication device 109 may allow the electronic device to communicate with other devices wirelessly or by wire to exchange data. Figure 4 The electronic device is shown with various devices, but it should be understood that it is not required to implement or possess all of the devices shown. More or fewer devices may be implemented or possessed instead.

[0101] In particular, the processes described above with reference to the flowcharts can be implemented as a computer software program in accordance with embodiments of the present application. For example, embodiments include a computer program product comprising a computer program carried on a computer readable medium, the computer program comprising program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via the communication device 109, or installed from the storage device 108, or installed from the ROM 102. When the computer program is executed by the processing device 101, the above-described functions defined in the methods of the embodiments of the present application are performed.

[0102] Note that the computer readable medium described above in the present application can be a computer readable signal medium or a computer readable storage medium or any combination thereof. The computer readable storage medium may, for example, be, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, device, or apparatus, or any suitable combination of the above. More specific examples of the computer readable storage medium can include, but are not limited to, an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present application, the computer readable storage medium can be any tangible medium that contains or stores a program used or used in conjunction with an instruction execution system, device, or apparatus. In the present application, the computer readable signal medium can include a data signal carried in a baseband or as a part of a carrier wave, which carries computer readable program code. Such a propagated data signal can take on many forms, including but not limited to an electromagnetic signal, an optical signal, or any suitable combination of the above. The computer readable signal medium can also be any computer readable medium that can send, propagate, or transfer a program for use by or in connection with an instruction execution system, device, or apparatus. The program code contained on the computer readable medium can be transmitted using any suitable medium, including but not limited to wire, cable, fiber optic, RF (radio frequency), or any suitable combination of the above.

[0103] The computer readable medium described above can be included in the electronic device described above; or can exist separately from the electronic device and be not assembled into the electronic device.

[0104] The computer readable medium described above carries one or more programs, which, when executed by the electronic device, cause the electronic device to perform the electrical impedance imaging method described above.

[0105] Computer program code for performing the operations of the present invention may be written in one or more programming languages, or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, C++, Python, and conventional procedural programming languages ​​such as "C-" or similar programming languages. The program code may be executed entirely on the user's computer, partially on the user's computer, as a stand-alone software package, partially on the user's computer and partially on a remote computer, or entirely on the remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., through the Internet using an Internet service provider).

[0106] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification and features of different embodiments or examples without contradiction.

[0107] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of the technical features being referred to. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of such features. Throughout the description of this application, "plurality" means at least two, for example, two, three, etc., unless otherwise specifically defined.

[0108] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, segment or portion of code comprising one or more executable instructions for implementing the steps of a specific logical function or process, and the scope of the preferred embodiments of the present application includes alternative implementations in which functions may be performed out of the order shown or discussed, including performing functions in a substantially simultaneous manner or in the reverse order depending on the functions involved, which should be understood by those skilled in the art to which the embodiments of the present application belong.

[0109] The logic and / or steps represented in the flowcharts and / or described herein, for example, can be considered as a sequence of instructions to implement logical functions, and can be embodied in any computer-readable medium for use by an instruction execution system, apparatus, or device, such as a computer-based system, processor- based system, or other system that can fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions. For purposes of this specification, a "computer-readable medium" can be any apparatus that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device. The computer-readable medium can be a computer- readable storage medium or a computer-readable signal medium. The computer- readable storage medium can be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer-readable storage medium include the following: an electrical connection having one or more wires (electrical connections), a portable computer diskette (a magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, and a portable compact disc read-only memory (CDROM). In addition, the computer-readable medium can even be paper or another suitable medium upon which the program is printed, as the program can be electronically captured, for example, via optical scanning of the paper or other medium, then compiled, interpreted, or otherwise processed in a suitable manner, if necessary, and stored in a computer memory.

[0110] It should be understood that aspects of the application can be implemented in hardware, software, firmware or combinations thereof. In the above embodiments, the various steps or methods can be implemented in software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented in hardware, and in another embodiment, any of the following technologies, known in the art, or their combinations can be used: discrete logic circuitry having logic gates for implementing logic functions on data signals, application specific integrated circuits having appropriate combinational logic gates, programmable gate arrays (PGA), field programmable gate arrays (FPGA), and the like.

[0111] Those skilled in the art can understand that all or part of the steps carried out by the above-mentioned embodiments can be completed by programs instructing related hardware, and the developed programs can be stored in a computer-readable storage medium. When the program is executed, it includes one or a combination of the steps of the method embodiments.

[0112] In addition, each function unit in each embodiment of the present application can be integrated in one processing module, or each unit can be physically present separately, or two or more units can be integrated in one module. The integrated module can be realized in the form of hardware or in the form of a software function module. The integrated module, if realized in the form of a software function module and sold or used as an independent product, can also be stored in a computer readable storage medium.

[0113] The storage medium mentioned above can be a read-only memory, a magnetic disk or an optical disk, etc. Although the embodiments of the present application have been shown and described above, it should be understood that the above embodiments are exemplary and should not be construed as limiting the present application, and those skilled in the art can make changes, modifications, replacements and variations to the above embodiments within the scope of the present application.

[0114] The above specific embodiments further illustrate the purpose, technical solutions and beneficial effects of the present application. It should be understood that the above description is only for specific embodiments of the present application and is not intended to limit the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application should be included in the protection scope of the present application.

Claims

1. An electrical impedance tomography method, characterized in that: The following steps are involved: Obtaining a boundary measurement voltage of a simulated target object, calculating an initial distribution of the conductivity of the simulated target object using a finite element method, and forming a training data set after normalization; An encoder and a decoder are respectively constructed, each embedded with a Jacobian matrix, wherein the Jacobian matrix is ​​used to reflect the sensitivity between the conductivity distribution and the boundary voltage; a physics-guided neural network is constructed using the encoder and the decoder; a total loss function is constructed based on data error loss and physical consistency loss; and the neural network is trained using the training data set and the total loss function to obtain a trained neural network. The boundary voltage of the target object to be measured is obtained and input into the trained neural network to obtain the conductivity distribution of the target object to be measured.

2. The electrical impedance tomography method according to claim 1, wherein: The simulated target objects have different numbers, geometric shapes and / or conductivity values.

3. The electrical impedance tomography method according to claim 2, wherein: The conductivity value of the simulated target object is set in the range of 0.1s / m to 2s / m.

4. The electrical impedance tomography method according to claim 1, wherein: The training data set contains a plurality of training samples, each of which records a current injection mode used when performing EIT simulation on the simulation target object, its corresponding boundary measurement voltage, and the conductivity distribution inside the simulation target object.

5. The electrical impedance tomography method according to claim 1, wherein: The encoder includes an input layer, a first convolutional layer, a second convolutional layer, a flattening layer, and a first fully connected layer connected in sequence. The input layer is used to transmit the boundary measurement voltage input to the encoder to the first convolutional layer; the first convolutional layer is provided with 32 3×3 convolution kernels for extracting low-level features of the boundary measurement voltage; the second convolutional layer is provided with 64 3×3 convolution kernels for extracting higher-level features of the boundary measurement voltage to obtain a feature map; the flattening layer is used to convert the feature map obtained by the second convolutional layer into a one-dimensional vector; the first fully connected layer is used to map the one-dimensional vector obtained by the flattening layer to a 256-dimensional voltage space; The decoder includes a second fully connected layer, a third fully connected layer, a reshaping layer, a first deconvolution layer, a second deconvolution layer and an output layer connected in sequence; the second fully connected layer and the third fully connected layer are used to gradually expand the feature dimensions output by the first fully connected layer, and the reshaping layer is used to reconstruct the one-dimensional vector output by the third fully connected layer into a three-dimensional tensor of 32×32×2; the first deconvolution layer and the second deconvolution layer are used to gradually restore the 32×32×2 three-dimensional tensor output by the reshaping layer to the spatial resolution of conductivity, and finally the conductivity distribution is reconstructed by the output layer.

6. The electrical impedance tomography method according to claim 1, wherein: The difference between the conductivity distribution reconstructed by the neural network and the true conductivity distribution is taken as the data error loss; the difference between the Jacobian matrix calculated by the electrical impedance model and the Jacobian matrix predicted by the neural network is taken as the physical consistency loss.

7. The electrical impedance tomography method according to claim 1, wherein: Taking the root mean square error between the boundary measurement voltage and the boundary prediction voltage obtained by the neural network as the data error loss; The physical consistency loss is taken as the difference between the Jacobian matrix calculated by the electrical impedance model and the Jacobian matrix predicted by the neural network.

8. The electrical impedance tomography method according to claim 1, wherein: Assume that the total loss function is L, and the expression is as follows: L=α·L V +β·L J Among them, L V is the data error loss; is the boundary measurement voltage of the i-th training sample input to the neural network, is the boundary prediction voltage of the i-th training sample obtained by the neural network; m is the number of training samples used in training the neural network; is the physical Jacobian matrix of the i-th training sample, and the voltage measured according to the boundary of the i-th training sample and conductivity distribution σ i And calculated using the electrical impedance model, is the predicted Jacobian matrix of the i-th training sample, and the neural network predicts the voltage based on the boundary of the i-th training sample and conductivity distribution σ i Calculated; α and β are two hyperparameters.

9. An electrical impedance imaging device, characterized in that: include: The first module is configured to obtain a boundary measurement voltage of a simulated target object, calculate an initial distribution of the conductivity of the simulated target object using a finite element method, and form a training data set after normalization; A second module is configured to respectively construct an encoder and a decoder embedded with a Jacobian matrix, wherein the Jacobian matrix is ​​used to reflect the sensitivity between the conductivity distribution and the boundary voltage, construct a physics-guided neural network using the encoder and the decoder, construct a total loss function based on data error loss and physical consistency loss, and train the neural network using the training data set and the total loss function to obtain a trained neural network; The third module is configured to obtain the boundary voltage of the target object to be measured, input the boundary voltage into the trained neural network, and obtain the conductivity distribution of the target object to be measured.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores computer instructions, and the computer instructions are used to enable the computer to execute the electrical impedance imaging method according to any one of claims 1 to 8.

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