A noise-reducing autoencoder-based electrical impedance depth imaging method

Abstract

This invention discloses a impedance depth imaging method based on a denoising autoencoder, combining traditional methods with a denoising autoencoder. First, the finite element method is used to numerically simulate the two-dimensional circular domain impedance imaging problem, obtaining the impedance distribution image and boundary voltage of the two-dimensional circular domain. Then, the split Bregman (SBM) algorithm is used to obtain a coarse image. Finally, the coarse image is used as input, and the true impedance distribution image is used as output to train a denoising autoencoder network. This denoising autoencoder network can be used for impedance imaging. Simulation and experimental results show that, for circular targets, the proposed method can achieve high-precision artifact removal and accurate shape reconstruction.

Description

Technical Field

[0001] This invention belongs to the field of electrical impedance imaging technology, specifically relating to an electrical impedance depth imaging method based on a denoising autoencoder. Background Technology

[0002] Electrical Impedance Tomography (EIT) is a new generation of non-invasive medical imaging technology that has emerged in the last two decades. EIT involves injecting an alternating current signal into the object through electrodes placed on its surface while simultaneously measuring the voltage across the remaining electrodes. The obtained voltage information is then used in a reconstruction algorithm to determine the electrical impedance distribution within the object, thus obtaining an impedance image. However, finding the inverse is a highly ill-posed and nonlinear problem, and the resulting reconstructed image suffers from significant artifacts.

[0003] Several EIT image reconstruction algorithms have been developed, including the Back-Projection Algorithm (BP), the Gauss-Newton Algorithm (GN), and the Iterative Tikhonov Algorithm. Traditional methods have low computational cost and low computer configuration requirements, but their image quality is relatively poor. Modern methods, represented by deep learning, such as Simulated Annealing (SA), Convolutional Neural Networks (CNN), and U2Net, are characterized by high computational cost and high computer configuration requirements, but they produce better image quality.

[0004] A denoising autoencoder (DAE) is an autoencoder that takes corrupted data as input and uncorrupted data as output. Essentially, it is a process of abstracting features layer by layer. The training data no longer needs to be labeled with features, which can save a lot of time and effort. Summary of the Invention

[0005] The purpose of this invention is to provide a resistive impedance depth imaging method based on a denoising autoencoder, to address the problems of poor imaging quality, high computational load, and high computer configuration requirements in existing technologies. To obtain clearer reconstructed images, a depth imaging method combining traditional methods and a denoising autoencoder is proposed.

[0006] To solve the aforementioned technical problems, this invention adopts the following technical solution: a impedance depth imaging method based on a denoising autoencoder. First, the finite element method is used to numerically simulate the two-dimensional circular domain impedance imaging problem, obtaining the impedance distribution image and boundary voltage of the two-dimensional circular domain. Then, the split Bregman (SBM) algorithm is used to obtain a coarse image. Finally, the coarse image is used as input, and the true impedance distribution image is used as output to train a denoising autoencoder network. Specifically, the method includes the following steps:

[0007] S1. Using triangles as the partitioning unit, the background area is partitioned using finite element method. Simulated circular target objects with different radii are generated in the background area, and the impedance distribution data of the target objects are set.

[0008] S2. Based on the impedance distribution data obtained in S1, the impedance distribution image of the two-dimensional circular domain and the boundary voltage of the circular domain are obtained using the finite element method; coarse imaging is obtained using the SBM algorithm based on the boundary voltage value.

[0009] S3. Using the coarse image obtained in S2 as input and the real impedance distribution image as output, train the denoising encoder and continuously adjust the various parameters of the denoising encoder until the optimal trained denoising encoder is obtained.

[0010] S4. Using the boundary voltage value of the object to be measured as the input data, the SBM algorithm is used to obtain a coarse image. The coarse image is then input into the denoising encoder trained in S3 to obtain the impedance imaging map of the object to be measured.

[0011] Furthermore, in step S2, the coefficient matrix of each triangulated element is obtained based on the impedance distribution data of the target object and the model data of the finite element method, thereby obtaining the overall coefficient matrix.

[0012] Boundary conditions are applied to obtain the finite element equation, and the boundary voltage value is finally obtained by solving the finite element equation; the model data of the finite element refers to the grid on the image, and the boundary condition is the excitation current.

[0013] Furthermore, in step S3, the training process of the denoising autoencoder includes encoding and decoding;

[0014] The pixel values ​​of the image after adding noise to the simulated object using the SBM algorithm are defined as noisy data. Noisy data Through the encoding process f of the autoencoder θ Mapping to a low-dimensional hidden feature space y, the decoding process g θ′ Decode y to obtain noise-free image pixel data z;

[0015] The encoding process is represented as follows: The decoding process is represented as: z = g θ′ (y) = s(w²y + b²); where, f θ and g θ′ s(*) is a non-linear activation function; w1 and w2 are weight matrices; b1 and b2 are bias vectors; θ is the parameterization of {w1, b1}; and θ′ is the parameterization of {w2, b2}.

[0016] During training, the backpropagation algorithm is used to minimize the reconstruction error, and the error function is expressed as:

[0017]

[0018] Where x represents the pixel value of the original image of the simulated object; the parameters to be adjusted during training include the learning rate and activation function, and when the error function L... H When (x,z) is minimized, the optimal parameters are obtained, training stops, and the denoising autoencoder network model with the minimum objective function error is obtained.

[0019] Compared with the prior art, the present invention, employing the above technical solution, has the following technical effects:

[0020] The proposed electrical impedance tomography (EI) method based on a denoising autoencoder is trained using simulated data and also exhibits good adaptability to real-world data. Combining traditional methods with a denoising autoencoder offers advantages such as low computational cost, low computer configuration requirements, and good imaging results.

[0021] Denoising encoders belong to unsupervised feature learning, meaning that feature annotation is no longer required for training data, saving significant time and effort. Furthermore, the input data passed through the encoder can create a compressed representation—this compression is essentially an intermediate layer—which can then be used by the decoder to reconstruct the original input, simplifying computation.

[0022] The trained denoising encoder can effectively remove artifacts from the background, making the background area of ​​the image more uniform and the target object clearer. Compared with traditional algorithms, this method has stronger generalization ability and faster computation speed. Attached Figure Description

[0023] Figure 1 This is a flowchart illustrating an embodiment of the present invention;

[0024] Figure 2 This is the denoising autoencoder training process in this embodiment of the invention;

[0025] Figure 3 This is a true image of the agar used to test the object in this invention example;

[0026] Figure 4 This is an agar image generated by the method of the present invention. Detailed Implementation

[0027] To make the objectives, technical effects, and technical solutions of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0028] This invention provides a method for impedance depth imaging based on a denoising autoencoder. First, a large amount of simulated impedance distribution data is randomly generated, and the boundary voltage information of this impedance distribution data is calculated using the finite element method. Then, using the boundary voltage values, a coarse image is obtained using the SBM algorithm. The coarse image and the real impedance distribution image are used as the input and output of the denoising encoder (DAE), respectively, to obtain the training dataset for the denoising encoder. Next, the denoising encoder is trained using the training dataset, and its parameters are continuously adjusted until an optimal denoising encoder is obtained. Finally, the boundary voltage values ​​of the object to be measured are used as input data, and the SBM algorithm is used to obtain a coarse image. This coarse image is then input into the trained denoising encoder to obtain the impedance imaging map of the object under test. Figure 1 As shown, the specific steps include:

[0029] S1. Using triangles as the partitioning unit, the background area is partitioned using the finite element method. Simulated circular target objects with different radii are generated within the background area, and the impedance distribution data of the target objects are set.

[0030] Specifically, the number of objects to be generated is randomly selected as i, where i is between 1 and 3. That is, i points are randomly selected within the background area divided by the finite element method, and then the circular target objects to be generated are selected sequentially. The diameter of the circular target objects is set between 4 and 8.

[0031] S2. Based on the impedance distribution data obtained in S1, the impedance distribution image of the two-dimensional circular domain and the boundary voltage of the circular domain are obtained using the finite element method; coarse imaging is obtained using the SBM algorithm based on the boundary voltage value.

[0032] Specifically, impedance values ​​are assigned to both the element containing the object and the background element to obtain the impedance distribution of the target object. Then, the finite element method is used to calculate and solve the EIT problem. The mathematical model of the EIT field is a partial differential equation.

[0033] The finite element method first discretizes the problem to be solved, performs element analysis, and then combines the results of each element analysis to perform a comprehensive analysis of the whole. Specifically, a finite number of points are selected in the field, and the partial differential equations in the EIT problem are approximated by finite difference equations to obtain the values ​​of the field function at each discrete point.

[0034] The variational principle is the foundation of the finite element method. It transforms the partial differential equation to be solved into a corresponding variational problem. Then, by introducing interpolation polynomials, the variational problem is discretized into a problem of finding the extrema of ordinary multivariable functions. Finally, it is simplified into a problem of solving a system of multivariable function equations. From this, the boundary voltage value of the target object can be obtained.

[0035] Specifically, 16 electrode plates were attached at equal intervals to the boundary of a two-dimensional circular domain. The conductivity of the background region was set to 0.1 S / m, and the conductivity of the target region was set to 0.01 S / m. The EIDORS software package based on MATLAB was used to calculate the voltage values ​​of the circular domain boundary in the adjacent excitation-adjacent measurement mode.

[0036] Specifically, the SBM algorithm is used to obtain a coarse image based on the boundary voltage value, and the image is then converted to grayscale. To improve the resolution after imaging, the pixel values ​​of each image are then extracted, resulting in each sample consisting of 10,000 pixels.

[0037] S3. Using the coarse image obtained in S2 as input and the true impedance distribution image as output, train the denoising encoder. The training process is as follows: Figure 2 As shown, the parameters of the denoising encoder are continuously adjusted until the optimal denoising encoder after training is obtained.

[0038] Specifically, the training process of a denoising autoencoder includes encoding and decoding; the pixel values ​​of the image after noise is added using the SBM algorithm to the simulated object are defined as noisy data. Noisy data Through the encoding process f of the autoencoder θ Mapping to a low-dimensional hidden feature space y, the decoding process g θ′ Decode y to obtain noise-free image pixel data z.

[0039] The encoding process is represented as follows: The decoding process is represented as: z = g θ′ (y) = s(w²y + b²); where, f θ and g θ′ s(*) is a non-linear activation function, and s(*) is an encoding / decoding function; w1 and w2 are weight matrices, b1 and b2 are bias vectors, θ is a parameterization of {w1,b1}, and θ′ is a parameterization of {w2,b2}.

[0040] During training, the backpropagation algorithm is used to minimize the reconstruction error, and the error function is expressed as:

[0041]

[0042] Where x represents the pixel value of the original image of the simulated object. Various parameters, such as the learning rate and activation function, are adjusted using training data, and the error function L is considered. H When (x,z) is minimized, the optimal parameters are obtained, training stops, and the denoising autoencoder network model with the minimum objective function error is obtained.

[0043] Specifically, the DAE model learning rate is set to 0.001; the input and output values ​​are the same, both being the image pixel value of 10000; the encoding activation function is ReLU, and the decoding activation function is sigmoid; the Adam (Adaptive Moment Estimation) optimizer is a combination of SGDM and RMSProp. It runs for 100 epochs with a batch size of 128.

[0044] S4. The boundary voltage value of the object to be tested (such as the lungs of a person simulated by agar) is used as input data. The SBM algorithm is used to obtain a coarse image. The coarse image is then input into the denoising encoder trained in S3 to obtain the impedance imaging map of the object to be tested. Figure 3 This is a real image of agar. Figure 4 It is an agar image generated according to the method of the present invention.

[0045] It should be noted that the above description of the embodiments is only for the purpose of helping to understand the method and core idea of ​​this application. For those skilled in the art, several improvements and modifications can be made to this application without departing from the principle of this application, and these improvements and modifications are also within the protection scope of the claims of this application.

Claims

1. A denoising autoencoder-based electrical impedance depth imaging method, characterized in that, The method comprises the following steps: S1, using finite element subdivision, simulating a simulation circular target object with different radii in the background area, and setting impedance distribution data of the target object, taking a triangle as a subdivision unit for the background area; S2, obtaining an impedance distribution image of a two-dimensional circular domain and a boundary voltage of the circular domain using a finite element method according to the impedance distribution data obtained in S1, and obtaining a coarse image using an SBM algorithm through the boundary voltage value; S3, training a denoising encoder by taking the coarse image obtained in S2 as input and a real impedance distribution image as output, and constantly adjusting various parameters of the denoising encoder until an optimal trained denoising encoder is obtained; S4, taking a boundary voltage value of a measured object to be solved as input data, obtaining a coarse image using an SBM algorithm, and inputting the coarse image into the trained denoising encoder in S3 to obtain an impedance imaging image of the measured object; In step S2, a coefficient matrix of each triangular subdivision unit is obtained according to the impedance distribution data of the target object and model data of the finite element, and then a total system coefficient matrix is obtained; A boundary condition is applied to obtain a finite element equation, and the boundary voltage value is finally obtained by solving the finite element equation; The model data of the finite element refers to a grid on the image, and the boundary condition is an excitation current; In step S3, the training process of the denoising autoencoder includes encoding and decoding; The pixel value of the picture after adding noise to the simulation object using the SBM algorithm is noisy data The noisy data Map to the low-dimensional hidden feature space y through the encoding process f of the autoencoder θ Decoding process g θ′ Decode y to obtain noise-free picture pixel data z The encoding process is represented as: The decoding process is represented as: z = g θ′ (y) = s(w2y + b2); where f θ and g θ′ are non-linear activation functions, s(*) is an encoding-decoding function; w1 and w2 are weight matrices, b1 and b2 are bias vectors, θ is a parameterization of {w1, b1}, θ' is a parameterization of {w2, b2}; In the training process, a back propagation algorithm is used to minimize the reconstruction error, and an error function is represented as: Wherein x represents a pixel value of a simulation object original picture; The debugging parameters in the training process include a learning rate, an excitation function, and when an error function L H The optimal parameters are obtained when the error function L(x,z) is minimized, the training is stopped, and a denoising autoencoder network model with the minimum error of the target function is obtained.

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