Method for reconstructing distribution of electrical characteristics of material using electrical impedance tomography

Abstract

To provide a method for processing EIT measurements to improve the spatial resolution of an image.SOLUTION: A method reconstructs the distribution of electrical characteristics of at least one material of a body including a cylindrical portion containing a fluid using data related to electrical values of the body measured in advance by electrical impedance tomography using electrodes arranged around the cylindrical portion of the body. Each electrode is excited by a predefined potential pattern. The neural network includes an auto-encoder including a plurality of levels (L1,...,J), each comprising at least one convolutional layer and at least one dropout layer, and an attention module including attention gates (AG1,...,AGJ-1), each having a corresponding attention signal (gj).SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present invention relates to the field of electrical impedance tomography.

[0002] More particularly, the present invention relates to a method for reconstructing the distribution of electrical properties of the material of a body comprising a cylindrical portion containing a fluid, using data on the electrical properties of the body previously measured by electrical impedance tomography and a neural network.

[0003] The invention also relates to a computer program product configured to carry out this method.

[0004] A primary application of the present invention is in monitoring fluid flow that can change rapidly, such as can occur with fluids flowing under high temperature and pressure.

[0005] One application of particular interest is the monitoring of pipes in nuclear facilities, although other applications may be envisaged within the scope of the present invention. [Background technology]

[0006] Electrical impedance tomography (EIT) is a non-invasive, non-destructive technique that allows real-time, continuous visualization of the interior of an object by measuring its electrical properties (potential and current) at its surface. The method is robust and particularly suitable for performing non-invasive measurements in high-pressure and / or high-temperature environments.

[0007] Compared to MRI and CT, EIT has a high frame rate of several kHz, but the spatial resolution is low due to the nonlinearity of the inverse problem.

[0008] More precisely, EIT involves injecting a current or potential through a set of non-invasive electrodes placed on the surface of the object being monitored, and then measuring the potential or current at the surface of the object.

[0009] The electrodes may only be in contact with the outer surface of the object, however, if the surface of the object is metallic, the electrodes must penetrate the wall and contact the fluid.

[0010] A mapping between current and voltage is obtained by modeling the excitation applied by the electrode pairs and measuring the voltage. The impedance map inside the object is reconstructed by solving the corresponding inverse problem to determine the internal distribution of conductivity and permittivity according to Ohm's law.

[0011] Initially, the algorithms used to solve the nonlinear inverse problem of EIT were mainly iterative mathematical theories, such as Tikhonov regularization (TR), linear backprojection (LBP), Gauss-Newton method (GNM), and Newton one-step error reconstruction (NOSER). These methods use first-order linear approximations to conjugate the nonlinear mapping, which results in poor resolution and high sensitivity to noise during measurement, not to mention the exponential growth of computation time with the amount of data.

[0012] Over the past 30 years, methods using artificial neural networks have enabled significant advances in the field of EIT due to their ability to map complex nonlinear relationships with good convergence and low levels of error, thereby improving spatial resolution and reducing execution time when solving inverse problems, as well as when denoising, achieving super-resolution, and segmenting images.

[0013] Patent application FR 3 121 234 describes an image reconstruction method that uses the NOSER algorithm and implements frequency multiplexing, in which an excitation signal is applied to all electrodes simultaneously. To distinguish between signals, each electrode is excited by a triangular signal. By simultaneously exciting all electrodes, the redundancy seen in data acquired when paired electrodes are excited sequentially can be avoided. However, the acquired spatial resolution may be insufficient to detect specific objects.

[0014] In paper [1], the ADALINE network based on adaptive linear elements is described. In the work described in paper [2], a backpropagation network is applied, and in the work described in paper [3], a Bayesian multilayer perceptron is investigated. These studies are carried out on a linearly formed reconstruction operator that measures the difference between voltage measurements, thereby avoiding the nonlinearity between voltage and conductivity.

[0015] To overcome the nonlinearity of EIT, a method in [4] uses a radial basis function neural network, and a method in [5] explores a dense neural network using simulated EIDORS data. Recent research has focused more on complex architectures, as in [6] where a finely tuned autoencoder method is applied to EIT lung monitoring, or in [7] where a multilayer autoencoder is proposed. Researchers in [8] explore the use of energy-based priors along with physics-informed neural networks to improve model training, and researchers in [9] use hybrid fusion learning for high-resolution reconstruction.

[0016] Patent application WO2022 / 77866 describes an electrical impedance imaging method that uses an original voltage data set measured in a test area. An initial conductivity distribution sequence from this area forms a corresponding training data set, to which noise is added. A variational autoencoder is trained using this training data. In response to the input voltage data set, an encoder of the variational autoencoder is trained to capture features of the input voltage data, and a decoder of the trained variational autoencoder is used to establish a mapping relationship between the input voltage data set and the corresponding conductivity distribution sequence.

[0017] Continued advances in deep learning in EIT are beginning to obtain results that are superior to those obtained with traditional algorithms.

[0018] Traditionally, inverse problems have been solved without considering the benefits of providing artificial intelligence (AI) with instructions on what to prioritize in order to improve the spatial resolution of the results.

[0019] However, improving image reconstruction is essential: identifying the optimal correspondence between injected current or potential and conductivity distribution can lead to poor spatial resolution due to an inadequate representation of the nature of the problem. [Prior art documents] [Patent documents]

[0020] [Patent Document 1] French Patent Application Publication No. 3121234 [Patent Document 2] International Publication No. 2022 / 077866 Summary of the Invention [Problem to be solved by the invention]

[0021] Therefore, there is a need to provide a method for processing EIT measurements that overcomes the shortcomings of the prior art and, in particular, improves the spatial resolution of the images.

[0022] It is an object of the present invention to at least partially fulfill this need. [Means for solving the problem]

[0023] To this end, the present invention relates, according to one of its aspects, to a method for reconstructing the distribution of electrical properties of a body comprising a cylindrical part through which a fluid flows, using a neural network and data on the electrical values ​​of the body previously measured by electrical impedance tomography using electrodes arranged around the cylindrical part of the body, each electrode being excited by an electrical potential of a predefined form, The neural network A plurality of levels L1,...,L each including at least one convolutional layer and at least one dropout layer J an autoencoder including Each corresponds to an attention signal g j Attention gates AG1,…,AG with J-1 and an attention module containing and wherein the method comprises the following steps: i) Data on electrical values ​​are encoded to each layer level L1,...,L J For the encoded data x1,…,x J At each level L1,…,L of the convolutional and dropout layers of the neural network autoencoder, we obtain J and ii) Attention Gate AG j Coefficient α of j To calculate the latter, we must at least consider the top-ranked attention gate AG. j+1 Output data

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[0024] The invention allows the electrical properties of a material, in particular the distribution of its conductivity and permittivity, to be reconstructed with higher spatial resolution.

[0025] The method according to the present invention uses an end-to-end neural network that can be called Autoencoder Improved Attention-Net (AIA-Net). The first segment is an autoencoder used as an architecture to extract remodeling features for voltage input, and the second segment is an improved attention module that can solve the inverse problem and delivers an image of the distribution of the electrical properties of the material under test.

[0026] Since the excitation potentials of the electrodes are in a known, predefined form, it is possible to reconstruct the electrical conductivity and / or permittivity. Due to the attention gate of the present invention, which knows the correspondence between the measured electrical values ​​and the electrical properties of the material, the spatial resolution of the output image is very good.

[0027] Autoencoder Dropout layers are used in a known manner to activate or deactivate neurons. This technique reduces overfitting during model training. Within the network, some neurons and all their corresponding input and output connections may be temporarily deactivated. The selection of the deactivated neurons is advantageously random.

[0028] In a preferred embodiment, to compress the data relating to the electrical values, certain layer levels L1,...,L J Maximum pooling is used from one layer level to another. This process is called max pooling. The max pooling process is performed by passing a window or filter of a given size over the entire input. The window moves over the image and selects the maximum value in each part of the image (called the pooling window or region). The window slides over the input and at each window position the maximum value is selected and placed in the output matrix.

[0029] Advantageously, the encoded data x1,...,x J to the input of the attention gate,J In a known manner, this technique allows a convolutional neural network to bypass a particular layer and connect directly to a deeper or shallower layer.

[0030] Preferably, in step ii) the encoded data (x1,...,x J ), depending on its spatial dimension, is convolved or transposed to match the spatial dimension of the attention signal in question.

[0031] Attention Module The attention gate of the attention module in the decoder is advantageously used as a filter of the information crossing between the coding and decoding parts by transferring features through skip connections, which can be enhanced by adding features extracted from each layer of the decoder to the higher layers.

[0032] Known EIT methods that use artificial intelligence focus on the nonlinear correspondence between voltage and conductivity without giving the neural network instructions on where to look.

[0033] The attention mechanism was introduced in the paper

[10] , where the so-called soft attention was formulated as follows:

[0034]

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[0035] Preferably, the corresponding attention gate AG j Coefficient α of j is calculated by the following formula:

[0036]

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[0037] During the ceremony,

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[0038] The attention module allows highlighting regions that are important for feature extraction and removing irrelevant regions from the image during the execution of the convolutional layer.

[0039] Preferably, each attention signal g is weighted primarily to increase the matching weights and decrease the non-matching weights. j An addition operation of the coded data is performed on all input data using , which reduces the spatial information and highlights important features.

[0040] Advantageously, the features extracted from the input are used to generate an attention signal g j The selection is based on the information contained in

[0041] Input features x1,…,x J is a trilinear interpolation

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[0042] In a preferred embodiment, the transformation ψ is calculated by the attention coefficient (α i,1 ,α i,2 ,α i,3 ,α i,4 )∈[0,1].

[0043] A resampler can be used to expand the dimension of the weight matrix.

[0044] At the output of each attention gate, an attention signal g j and output data

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[0045] The element-wise multiplication between the input features and the attention coefficients advantageously yields the output data

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[0046] Preliminary Measurement In a preferred embodiment, EIT measurements of a body comprising a cylindrical portion containing a fluid include the steps of: i. Around the cylindrical part of the main body e placing electrodes; ii.n e simultaneously exciting each of the electrodes, each electrode being energized with a potential V having the form n exc is excited by

[0047]

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[0048] where A is the signal amplitude, θ n is electrode E n Angular position of, fm = m × f0 is the oscillation frequency, f0 is the frequency of f for any m m is a fundamental frequency selected to be lower than the Nyquist frequency of the system; iii.n e measuring an electrical characteristic of the body using the electrodes; iv. Processing the data generated in the measurement step iii, which comprises the following sub-steps: a) Each electrode E n Regarding

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[0049] Use of the method The invention also relates to the use of the method described above for reconstructing the distribution of electrical properties of pipes, in particular of two-phase flows passing through the pipes of a nuclear facility.

[0050] computer program products According to another aspect, the present invention also relates to a computer program product comprising a medium and processor-readable instructions recorded on the medium that, when executed, enable a reconstruction method according to the present invention to be carried out.

[0051] device The invention finally relates to a device for carrying out the method according to the invention, comprising: an acquisition system including at least one programmable logic array, a module for generating an analog signal, and a module for measuring the analog signal, in particular a plurality of electrodes connected to the acquisition system; a computer configured to control the acquisition system; A neural network integrated into or connected to a computer, comprising: A plurality of levels L1,...,L each including at least one convolutional layer and at least one dropout layer J an autoencoder including Each corresponds to an attention signal g j Attention gates AG1,…,AG with J-1 and an attention module containing and a neural network containing Equipped with.

[0052] Features described above with respect to the method are applicable to the use, computer program product and device, and vice versa. [Brief explanation of the drawings]

[0053] [Figure 1] 2 is a flow chart showing an example of the steps performed in the method according to the present invention. [Figure 2] FIG. 1 shows an example of an architecture for implementing the method according to the invention. [Figure 3a] FIG. 2 is a detailed diagram of an example of an attention gate used in the present invention. [Figure 3b] FIG. 2 is a detailed diagram of an example of an attention gate used in the present invention. [Figure 4] FIG. 10 is a diagram showing the results of a comparison between the method according to the present invention and the prior art. [Figure 5] 4 is a graph showing the mean squared error obtained when using the method according to the invention; DETAILED DESCRIPTION OF THE INVENTION

[0054] FIG. 1 shows a flow chart illustrating the steps of an example of the implementation of the method according to the invention.

[0055] In a first step, experimental measurements are performed on an object with a cylindrical portion through which a fluid flows, using electrodes arranged around the cylindrical portion of the body, each excited by a predefined electrical potential. As shown in Figure 2, the electrodes are non-invasively arranged around the circumference of the body. In this example, the electrodes are regularly distributed in angular directions around the circumference of the body.

[0056] The electrodes are connected to a printed circuit board, which is connected to a data acquisition system. A screen can display the data and images generated from these data. The data acquisition system includes a Linux operating system (HOST) that controls the FPGA, which is also included in the data acquisition system.

[0057] The acquisition system makes it possible to generate analog excitation signals and to measure analog measurement signals emitted by the electrodes.

[0058] In this way, the electrical value M n Data regarding (k) is obtained.

[0059] In the second step, these data are fed to each layer level L1,...,L of the autoencoder, as shown in Figure 2. J For the encoded data x1,…,x J The data is processed by an autoencoder of the neural network according to the present invention to remodel it to obtain a . Each level includes at least one convolutional layer and at least one dropout layer. The data is processed and concatenated by these layers.

[0060] As can be seen from FIG. 2, in order to compress the data relating to the electrical values, certain layer levels L1,...,L JMax pooling from to another layer level is used.

[0061] In the third step, to solve the inverse problem, an attention module according to the present invention is used, which calculates the attention signals g j Attention gates AG1,…,AG with J-1 Includes:

[0062] As shown in Figure 3a and Figure 3b, the attention gate AG j Coefficient α of j To calculate the latter, we must at least consider the top-ranked attention gate AG. j+1 Output data

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[0063] Preferably, in the example in question, the corresponding attention gate AG j Coefficient α of j is calculated by the following formula:

[0064]

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[0065] During the ceremony,

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[0066] The transformation ψ generates a weight matrix that is fed into a sigmoid activation function to constrain the values ​​of the attention coefficients, and the resampler is used to expand the dimension of the weight matrix.

[0067] In the example shown, as can be seen from FIG. 2, the encoded data x1,...,x J to the input of the attention gate, J A skip connection is formed between them.

[0068] In the step of calculating the attention coefficient, as shown in Figure 3a and Figure 3b, the coded data x1,...,x J Depending on its spatial dimension, it is convolved or transposed to match the spatial dimension of the attention signal in question.

[0069] For example, in attention gate AG1, the spatial dimension of x1 is twice that of attention signal g1. Therefore, to be able to add them together, the dimension of x1 needs to be divided by 2 (Conv2D with stride=2). Other signals x received as inputs jFor x, the spatial dimension is smaller than that of the attention signal g, except for x, which is at the same dimensional level. Therefore, to sum the signal with g, we need to perform deconvolution with different strides (stride = 1 for x, stride = 2 for x, and stride = 4 for x).

[0070] The same principle applies to AG2, AG3 and AG4.

[0071] In this diagram, F, H, W, D, and F int are the feature, height, width, input channel, or depth in case of 3D data, and intermediate features, respectively.

[0072] As shown in Figure 3a and Figure 3b, the jth attention gate AG j Output data

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[0073] As shown in FIG. 2, in the last step of FIG. 1, the output data of the first attention gate (AG1) is used to obtain a data matrix representing an image of the distribution of the electrical properties of at least one material of the body.

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[0074] Figure 4 shows some of the results obtained by implementing the method according to the invention in comparison with other known architectures: 2D-CNN, Variational-Auto-Encoder (VAE), GenerativeDNN with U-Net, Dense ResNet, Conv ResNet, U-Net3++, and Attention-Net.

[0075] The images from left to right in Figure 4 correspond to tests performed on a body having a cylindrical portion, Two rods of circular cross section (1 cm and 2 cm diameter), Two rods with circular cross section (1 cm diameter), 1 rod with a circular cross section (2 cm diameter), 1 rod with rectangular cross section (area 2.5 x 1 cm), Two rods with circular cross-sections (1 cm and 2 cm diameter) may include:

[0076] For brevity, the results of only a few studies are shown, but it should be noted that the conclusions are the same for all studies performed.

[0077] It can be seen that known architectures prior to U-Net3++ were not fully optimized for reconstructing electrical conductivity, primarily due to the vanishing gradient problem, due to the absence of skipped connections. The exception is the DNN+U-Net architecture, where U-Net includes skipped connections, but feature extraction begins with a deep neural network that is not optimized for image data compared to convolutional neural networks. Looking at the second image from left to right, U-Net3++ shows that the network is unable to identify the spatial features necessary for accurate reconstruction. This is improved by a conventional attention-net network, but this neural network has difficulty with the conductivity of the background water, as seen in image No. 5 in Figure 4. The network used in this invention shows significantly better reconstruction results, with improved spatial edge identification.

[0078] Table 1 shows that the present invention provides better measurement results. 2 Despite the high values ​​of , this can be misleading. The RMSE and SER values ​​are very low, which is a sign of good regression and is within the range of the MSE loss function, as shown in Figure 5.

[0079] [Table 1]

[0080] Figure 5 shows that the mean squared error loss function is very low, indicating good agreement between the voltage input data and the conductivity output data. The validation loss shows small fluctuations, indicating that the implemented neural network model is stable. Additionally, the closeness of the two loss values ​​indicates that there is no over- or under-fitting.

[0081] The invention is not limited to the examples described above, and in particular it is possible to combine the features of the examples shown with one another in variants not shown.

[0082] Other variations and modifications can be envisaged without departing from the scope of the invention, in particular the method according to the invention can be implemented by neural networks different from the one described, in particular neural networks including additional layers.

[0083] The invention can be used in the nuclear field, in particular as a method for preventing the generation of bubbles in the primary circuit and cavitation in pumps of various circuits. The invention is applicable in the medical field, in particular in lung monitoring and abnormality detection when simultaneous excitation is used.

[0084] The method according to the invention can be used in the food processing sector, in particular for counting fruits and vegetables, in the petroleum sector, in particular for detecting fouling of production wells, and also in the pharmaceutical sector, for example for detecting foreign bodies during the production of medicines.

[0085] (References) [1] R. Guardo & al., "A Neural Network Approach To Image Reconstruction In Electrical Impedance Tomography", IEEE, 1991 [2] A. Nejatali & al., "An iterative algorithm for electrical impedance imaging using neural networks", IEEE, 1998 [3] J. Lampinen & al., "Application of Bayesian neural network in electrical impedance tomography", IEEE, 1999 [4] Chao Wang & al., "RBF neural network image reconstruction for electrical impedance tomography", IEEE, 2004 [5] Xiuyan Li & al., "An image reconstruction framework based on deep neural network for electrical impedance tomography", IEEE, 2017 [6] Jin KS & al., "A Learning-Based Method for Solving Ill-Posed Nonlinear Inverse Problems: A Simulation Study of Lung EIT", SIAM J. Imaging sciences, 2019 [7] Xiaoyan C. & al., "Deep Autoencoder Imaging Method for Electrical Impedance Tomography", IEEE, 2021 [8] Akarsh P. & al., "Improved Training of Physics-Informed Neural Networks Using Energy-Based Priors: a Study on Electrical Impedance Tomography", ICLR, 2023 [9] Hao Y. & al., "High-resolution conductivity reconstruction by electrical impedance tomography using structure-aware hybrid-fusion learning", Sciencedirect, 2024

[10] Ozan Oktay & al., "Attention U-Net: Learning Where to look for the Pancreas", 1 st Conference on MIDL, 2018

Claims

1. 1. A method for reconstructing the distribution of electrical properties of a body comprising a cylindrical portion through which a fluid flows, using a neural network and data relating to electrical values ​​of the body previously measured by electrical impedance tomography using electrodes arranged around the cylindrical portion of the body, wherein each electrode is excited by an electrical potential of a predefined form, The neural network A plurality of levels (L) each including at least one convolutional layer and at least one dropout layer 1 ,…,L J ), and an autoencoder containing Each corresponds to an attention signal (g j ) with Attention Gate (AG) 1 ,…,AG J-1 ) and the attention module said method comprising the steps of: i) the data relating to electrical values ​​is encoded to form a layer level (L 1 ,…,L J ) for the coded data (x 1 ,…,x J ) at each level (L 1 ,…,L J ) ii) Attention Gate (AG) j ) coefficient (α j ), the attention module calculates the number of attention gates (AG j+1 ) output data [Equation 1] The connection of the top-ranked attention gate (AG j+1 ) higher rank level (L j+2 ) and the decoded data resulting from the corresponding attention gate (AG j ) attention signal (g j ) to the encoded data (x 1 ,…,x J ), and the coefficient (α j a step in which the result of said addition is transformed by at least one mathematical function to obtain iii) jth attention gate (AG j ) output data [Equation 2] To obtain the layer level (L j ) output data (x J ) to the corresponding attention gate (AG j ) the coefficient (α j ) multiplying iv) First Attention Gate (AG) 1 ) output data [Equation 3] In order to obtain the first attention gate (AG 1 ), and v) said first attention gate (AG) for obtaining a data matrix representing an image of the distribution of the electrical properties of at least one material of said body; 1 ) the output data [Equation 4] But the second level (L 2 ) and the decoded data sent by A method comprising:

2. To compress the data on electrical values, a certain layer level (L 1 ,…,L J ) to another layer level is used.

3. The encoded data (x 1 ,…,x J ) to the input of the attention gate, 1 ,…,L J 3. The method of claim 1, wherein a skip connection is formed between the first and second inputs.

4. In step ii), the encoded data (x 1 ,…,x J 4. The method of claim 1, wherein, depending on its spatial dimension, σ is convolved or transposed to match the spatial dimension of the attention signal in question.

5. The corresponding attention gate (AG j ) the coefficient (α j ) is expressed as follows: [Equation 5] where: [Equation 6] is the attention coefficient α j is the attention quotient used to determine σ 1 and σ 2 are the rectified linear unit, also known as ReLU, and sigmoid activation functions, respectively. [Equation 7] aims to reduce the consumption of parameters and computational resources, and att To form the bias term [Equation 8] 5. The method of claim 1, wherein the transformation is a linear transformation combined with

6. 6. The method of claim 5, wherein the transformation (ψ) generates a weight matrix that is applied to the sigmoid activation function to constrain the values ​​of the attention coefficients, and a resampler is used to expand the dimension of the weight matrix.

7. Use of the method according to any one of claims 1 to 6 for reconstructing the distribution of electrical properties of a pipe, in particular of a two-phase flow passing through said pipe of a nuclear facility.

8. A computer program product comprising a medium and processor readable instructions recorded on said medium that, when executed, enable the computer to carry out the method of any one of claims 1 to 6.

9. A device for carrying out the method according to any one of claims 1 to 6, comprising: an acquisition system including at least one programmable logic array, a module for generating an analog signal, and a module for measuring the analog signal, in particular a plurality of electrodes connected to said acquisition system; a computer configured to control the acquisition system; a neural network integrated into or connected to said computer, A plurality of levels (L) each including at least one convolutional layer and at least one dropout layer 1 ,…,L J ), and an autoencoder containing Each corresponds to an attention signal (g j ) with Attention Gate (AG) 1 ,…,AG J-1 ) and the attention module and a neural network containing 1. A device comprising:

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