EMT Image Reconstruction Method Based on Manifold Recognition and Variation Sensitivity Matrix

Abstract

An EMT image reconstruction method based on manifold recognition and change sensitivity matrix is ​​proposed. First, random noise is added to measurement voltage data samples of k different manifolds to obtain a manifold sample library V (100 samples for each manifold, totaling 100k samples) and a sensitivity matrix S corresponding to the k original manifolds. Second, the orthogonal matching pursuit (OMP) algorithm from compressed sensing theory is used to calculate the sparse solutions of the test sample and standard samples projected onto the overcomplete training sample set V, and the linear correlation coefficients between the sparse solutions corresponding to the test sample and all standard samples are calculated. The manifold corresponding to the maximum linear correlation coefficient is determined as the manifold to which the test sample belongs. Finally, the corresponding manifold sensitivity matrix is ​​selected based on the identified manifold for image reconstruction. This invention effectively improves the image reconstruction accuracy of the EMT system.

Description

Technical Field

[0001] This invention belongs to the field of image processing technology, specifically relating to an EMT image reconstruction method based on manifold recognition and change sensitivity matrix. Background Technology

[0002] Electromagnetic tomography (EMT) is a novel electrical tomographic imaging technique applied to multiphase flow detection. Based on the principle of electromagnetic induction, it reconstructs the distribution of target objects within a pipe by detecting the electrical properties of materials with both electrical and magnetic conductivity around the pipe. Due to its non-invasive, non-contact, safe, and fast response characteristics, EMT has been widely applied and developed in industrial process control, foreign object detection, and biomedical fields in recent years.

[0003] The overall framework of the EMT system is as follows: Figure 1 As shown, the EMT system consists of three parts: a sensor array, a data packet processing unit, and a computer imaging unit. The sensor array includes an excitation coil and a detection coil. The excitation coil acts as an excitation source, generating an excitation signal. This signal penetrates the object under test, producing a time-varying magnetic field. The eddy current field generated by this time-varying magnetic field then produces a secondary magnetic field, causing changes in the current and voltage in the detection coil. These changes reflect the distribution of conductivity within the target object. The detection coil transmits the detection signal reflecting these field changes to the data processing unit for analysis. The data processing unit, also known as the electronic control unit, primarily receives the voltage signal from the detection coil and converts the raw signal into usable data that can be read by a computer through demodulation and filtering. After obtaining the data signal containing the field distribution information, the computer imaging unit performs image reconstruction using a computer to reproduce the internal distribution of the measured object's field. As the most complex and crucial part of electromagnetic tomography, how to quickly and accurately reconstruct the complex conductivity distribution of the target object is the main research problem.

[0004] In recent years, optimization algorithms for EMT image reconstruction accuracy have been continuously proposed, such as the Linear Back-projection (LBP) algorithm, the Tikhonov regularization algorithm, and the Total Variation (TV) regularization algorithm. Among them, the LBP algorithm is the earliest proposed fast online reconstruction algorithm, and it is the most widely used due to its simplicity and speed. However, its limitation lies in the lower image accuracy for reconstructing complex flow patterns, so it is mainly used for qualitative analysis of the distribution of fluids in pipes. The Tikhonov regularization algorithm is one of the most widely used regularization algorithms for solving ill-conditioned inverse problems, but its image reconstruction effect is highly dependent on the regularization parameter. A smaller regularization parameter can give a good approximate solution to the original problem, but the influence of error may make the solution physically unacceptable. On the other hand, a larger regularization parameter reduces the sensitivity of the solution to error, but the obtained approximate solution deviates more from the true value. In practical applications, a trade-off between the two should be made. Therefore, if the parameters are appropriate, it will achieve better results than the LBP algorithm. However, the selection of regularization parameters currently relies mainly on empirical values, making it difficult to accurately and efficiently determine their values. The Total Variation (TV) regularization algorithm is similar to the Tikhonov regularization algorithm, also solving the ill-posed inverse problem of the EMT system through regularization, and thus also suffers from dependence on regularization parameters. Furthermore, TV is non-differentiable, and approximations are usually used to avoid this, but the smooth approximation of the algorithm affects the quality of the reconstructed image, blurring sharp boundaries. This effect can be reduced to some extent by adjusting the approximation parameters, but this also slows down the algorithm's convergence speed. Therefore, how to select regularization parameters and control TV approximation parameters to achieve overall system balance requires further research and exploration. All the above algorithms aim to optimize the quality of reconstructed images by adjusting the solution to the EMT inverse problem. However, due to the severe nonlinearity, ill-conditioned nature, and soft-field characteristics of the EMT system, the optimization degree of these existing algorithms is very limited, resulting in low reconstructed image accuracy and unstable reconstruction effects for different manifolds. Therefore, how to expand optimization ideas and directions to better solve the image reconstruction problem remains one of the main challenges in current EMT system research.

[0005] The imaging problem in EMT (Electronic Media Theory) is solved by inversely solving for the conductivity distribution vector by measuring the detection voltage and sensitive field distribution function of the sensor array. Generally, the optimization direction for imaging problems is to improve the accuracy of the inversion problem, and the sensitive field distribution function is basically based on the sensitivity matrix under empty field conditions as a priori conditions for image reconstruction. However, because the sensitive field of an EMT system has underdeterministic, ill-conditioned, and soft-field characteristics, its distribution is easily affected by changes in the medium within the measured object's field. Therefore, a fixed sensitivity matrix cannot accurately reflect the sensitive field distribution under different flow patterns. Summary of the Invention

[0006] To overcome the shortcomings of existing technologies, this invention provides an EMT image reconstruction method based on manifold recognition and a variable sensitivity matrix. First, random noise is added to measurement voltage data samples of k different manifolds to obtain a manifold sample library V (100 samples for each manifold, totaling 100k samples) and a sensitivity matrix S corresponding to the k original manifolds. Second, the orthogonal matching pursuit algorithm (OMP) in compressed sensing theory is used to calculate the sparse solutions of the test sample and standard samples projected onto the overcomplete training sample set V, and the linear correlation coefficient between the sparse solutions corresponding to the test sample and all standard samples is calculated. The manifold corresponding to the maximum linear correlation coefficient is determined as the manifold to which the test sample belongs. Finally, the corresponding manifold sensitivity matrix is ​​selected based on the identified manifold for image reconstruction. This method effectively improves the image reconstruction accuracy of the EMT system and outperforms general EMT imaging methods in terms of image error and linear correlation coefficient.

[0007] The technical solution adopted by this invention to solve its technical problem is:

[0008] An EMT image reconstruction method based on manifold recognition and change sensitivity matrix includes the following steps:

[0009] Step 1: Obtaining and normalizing the voltage vectors for standard flow patterns. Using multiphysics simulation software, obtain the corresponding voltage vectors for k standard flow patterns (such as core flow, two-sphere flow, three-sphere flow, four-sphere flow, half-pipe flow, annular flow, full-pipe flow, and empty-pipe flow). Then, use the minimum-maximum normalization method to normalize the voltage vectors, obtaining normalized voltage vector samples for the k standard flow patterns.

[0010]

[0011] Among them, v j ∈R m×1 (j = 1, 2, ..., n) i ) represents the j-th training sample in the i-th flow pattern, i.e., the measured voltage vector obtained by the system from the i-th flow pattern; m = l × (l-1)2 is the number of independent voltages in the l-coil measurement environment;

[0012] Step two, generating the training sample set: First, by adjusting the medium distribution of the standard flow pattern, four different measured voltage vectors are obtained for each standard flow pattern, thus providing five measured voltage vector sample data for each standard flow pattern. Then, based on the obtained standard flow pattern voltage vectors, the voltage vector data samples for each flow pattern are expanded to 100 by adding 20dB, 30dB, and 40dB of Gaussian random noise respectively. The total training sample set V is then expressed as:

[0013] V = [V1, V2, ..., V k ]∈Rm×n (2) Where: n = n1 + n2 + ... + n k ;

[0014] Step 3: Generation of the sensitivity matrix library. The image reconstruction problem of the EMT system is represented as:

[0015] V=Sg (3)

[0016] Where V is a 1×m measured voltage vector, S∈R m×n It is the sensitivity distribution matrix of the measured object field region, g∈R n ×1 is the conductivity distribution vector of the measured object field, and n is the mesh fraction; based on the measured voltage vector, in order to solve for the conductivity distribution vector g in reverse, the sensitivity matrix S needs to be obtained. In the EMT simulation experiment, the corresponding k-type sensitivity matrices of k standard flow patterns are obtained based on the field quantity extraction method, forming a sensitivity matrix library S:

[0017] S = [S1,S2,…,S] k (4)

[0018] This provides prior data for the subsequent reconstruction of the image vector g;

[0019] Step four, manifold identification. For unknown signals to be measured, it is necessary to determine their manifold and then reconstruct the image;

[0020] Step 5: Selection of the flow pattern sensitivity matrix. Since the approximate characteristics of the measured signal cannot be predicted, a fixed sensitivity matrix is ​​used for image reconstruction. However, fixed sensitivity matrices are mostly solved based on empty field conditions and cannot accurately reflect the sensitivity of the object field to changes in medium distribution under different flow patterns. Therefore, after knowing the flow pattern classification of the measured voltage signal, the sensitivity matrix S corresponding to the flow pattern is selected from the sensitivity matrix library based on the flow pattern classification result of the measured voltage signal obtained from flow pattern identification. i Perform image reconstruction;

[0021] Step 6, Image Reconstruction: Based on the measured voltage signal and the selected sensitivity matrix, solve formula (3) to recover the image vector g using the LBP algorithm, Landweber iterative algorithm and Tikhonov regularization algorithm respectively.

[0022] Furthermore, the steps in step four are as follows:

[0023] Step 4.1, linear measurement process, based on compressed sensing signal reconstruction theory, for the i-th manifold, if the training set V i If the model is complete or overcomplete, then any measured voltage vector λ of this type of manifold can be obtained from its training set V. i Linear representation:

[0024]

[0025] Where: coefficient α i (j=1,2…n i () is a real number. As a coefficient vector, in practical applications, since the class to which any measured voltage vector λ belongs cannot be predicted, we consider re-representing it as a linear combination of the training sample set V composed of k manifolds:

[0026] λ=Vx0 (6)

[0027] In the above formula: As a sparse vector, only the coefficients at the corresponding positions of the i-th manifold corresponding to the measured voltage vector λ may be non-zero, while the rest are 0. Thus, the measured voltage vector λ obtained from the EMT system can be sparsely represented by an overcomplete dictionary transformation basis V composed of the training sample set. Let the random Gaussian matrix B∈R d×m For the measurement matrix, the voltage vector to be measured is linearly measured by the following formula:

[0028]

[0029] in, The observed value is a d×1 vector. The voltage vector corresponding to each standard flow pattern and the observed value of the voltage signal to be measured can be calculated by formula (7).

[0030] Step 4.2, Solving for sparse solutions, since the observation vector The dimension d is much smaller than the dimension of the sparse signal x0, and solving formula (7) is an ill-conditioned problem, which can be transformed into the following mathematical model:

[0031]

[0032] Therefore, the optimization problem under this L0 norm is solved by the compressed sensing signal reconstruction algorithm, and the sparse solution x0 of the measured voltage signal λ corresponding to the overcomplete dictionary transformation basis V composed of the training sample set is obtained.

[0033] Step 4.3: Determine the manifold type by calculating the sparse solution x of each standard manifold corresponding to the overcomplete dictionary transformation basis V composed of the training sample set. i After finding the sparse solution x0 corresponding to (i = 1, ..., k) and the voltage signal to be measured, calculate x0 and x i The linear correlation coefficient is calculated using the following formula:

[0034]

[0035] in, and x0 and xi The average value of the linear correlation coefficient is used to determine the flow type corresponding to the maximum value of the linear correlation coefficient as the flow type to which the test voltage vector belongs, thereby enabling image reconstruction.

[0036] The beneficial effects of this invention are mainly reflected in: effectively improving the image reconstruction accuracy of the EMT system, and outperforming general EMT imaging methods in terms of image error and linear correlation coefficient. Attached Figure Description

[0037] Figure 1 This is a schematic diagram of an electromagnetic tomography system.

[0038] Figure 2 This is a block diagram of the overall system structure.

[0039] Figure 3 This is a diagram showing the manifold identification results.

[0040] Figure 4 This is a comparison chart of the reconstruction results. Detailed Implementation

[0041] The present invention will now be further described with reference to the accompanying drawings.

[0042] Reference Figures 2-4 An EMT image reconstruction method based on manifold recognition and change sensitivity matrix includes the following steps:

[0043] Step 1: Obtaining and normalizing the voltage vectors for standard flow patterns. Using multiphysics simulation software, obtain the corresponding voltage vectors for k standard flow patterns (such as core flow, two-sphere flow, three-sphere flow, four-sphere flow, half-pipe flow, annular flow, full-pipe flow, and empty-pipe flow). Then, use the minimum-maximum normalization method to normalize the voltage vectors, obtaining normalized voltage vector samples for the k standard flow patterns.

[0044]

[0045] Among them, v j ∈R m×1 (j = 1, 2, ..., n) i ) represents the j-th training sample in the i-th flow pattern, i.e., the measured voltage vector obtained by the system from the i-th flow pattern; m = l × (l-1)2 is the number of independent voltages in the l-coil measurement environment;

[0046] Step two, generating the training sample set: First, by adjusting the medium distribution of the standard flow pattern, four different measured voltage vectors are obtained for each standard flow pattern, thus providing five measured voltage vector sample data for each standard flow pattern. Then, based on the obtained standard flow pattern voltage vectors, the voltage vector data samples for each flow pattern are expanded to 100 by adding 20dB, 30dB, and 40dB of Gaussian random noise respectively. The total training sample set V is then expressed as:

[0047] V = [V1, V2, ..., V k ]∈R m×n (2)

[0048] Where: n = n1 + n2 + ... + n k ;

[0049] Step 3: Generation of the sensitivity matrix library. The image reconstruction problem of the EMT system is represented as:

[0050] V=Sg (3)

[0051] Where V is a 1×m measured voltage vector, S∈R m×n It is the sensitivity distribution matrix of the measured object field region, g∈R n ×1 is the conductivity distribution vector of the measured object field, and n is the mesh fraction; based on the measured voltage vector, in order to solve for the conductivity distribution vector g in reverse, the sensitivity matrix S needs to be obtained. In the EMT simulation experiment, the corresponding k-type sensitivity matrices of k standard flow patterns are obtained based on the field quantity extraction method, forming a sensitivity matrix library S:

[0052] S = [S1,S2,…,S] k (4)

[0053] This provides prior data for the subsequent reconstruction of the image vector g;

[0054] Step four, manifold identification. For unknown signals to be measured, it is necessary to determine their manifold and then reconstruct the image;

[0055] The steps in step four are as follows:

[0056] Step 4.1, linear measurement process, based on compressed sensing signal reconstruction theory, for the i-th manifold, if the training set V i If the model is complete or overcomplete, then any measured voltage vector λ of this type of manifold can be obtained from its training set V. i Linear representation:

[0057]

[0058] Where: coefficient α i (j=1,2…ni () is a real number. As a coefficient vector, in practical applications, since the class to which any measured voltage vector λ belongs cannot be predicted, we consider re-representing it as a linear combination of the training sample set V composed of k manifolds:

[0059] λ=Vx0 (6)

[0060] In the above formula: As a sparse vector, only the coefficients at the corresponding positions of the i-th manifold corresponding to the measured voltage vector λ may be non-zero, while the rest are 0. Thus, the measured voltage vector λ obtained from the EMT system can be sparsely represented by an overcomplete dictionary transformation basis V composed of the training sample set. Let the random Gaussian matrix B∈R d×m For the measurement matrix, the voltage vector to be measured is linearly measured by the following formula:

[0061]

[0062] in, The observed value is a d×1 vector. The voltage vector corresponding to each standard flow pattern and the observed value of the voltage signal to be measured can be calculated by formula (7).

[0063] Step 4.2, Solving for sparse solutions, since the observation vector The dimension d is much smaller than the dimension of the sparse signal x0, and solving formula (7) is an ill-conditioned problem, which can be transformed into the following mathematical model:

[0064]

[0065] Therefore, the optimization problem under this L0 norm is solved by the compressed sensing signal reconstruction algorithm, and the sparse solution x0 of the measured voltage signal λ corresponding to the overcomplete dictionary transformation basis V composed of the training sample set is obtained.

[0066] Step 4.3: Determine the manifold type by calculating the sparse solution x of each standard manifold corresponding to the overcomplete dictionary transformation basis V composed of the training sample set. i After finding the sparse solution x0 corresponding to (i = 1, ..., k) and the voltage signal to be measured, calculate x0 and x i The linear correlation coefficient is calculated using the following formula:

[0067]

[0068] in, and x0 and x i The average value of the linear correlation coefficient is used to determine the flow type corresponding to the maximum linear correlation coefficient, thereby enabling image reconstruction.

[0069] Step 5: Selection of the flow pattern sensitivity matrix. Since the approximate characteristics of the measured signal cannot be predicted, a fixed sensitivity matrix is ​​used for image reconstruction. However, fixed sensitivity matrices are mostly solved based on empty field conditions and cannot accurately reflect the sensitivity of the object field to changes in medium distribution under different flow patterns. Therefore, after knowing the flow pattern classification of the measured voltage signal, the sensitivity matrix S corresponding to the flow pattern is selected from the sensitivity matrix library based on the flow pattern classification result of the measured voltage signal obtained from flow pattern identification. i Perform image reconstruction;

[0070] Step 6, Image Reconstruction: Based on the measured voltage signal and the selected sensitivity matrix, solve formula (3) to recover the image vector g using the LBP algorithm, Landweber iterative algorithm and Tikhonov regularization algorithm respectively.

[0071] To verify the performance of the method of this invention, a simulation experiment of the EMT image reconstruction system was conducted. First, a three-dimensional simulation model of the EMT system was established using COMSOL Multiphysics software. Eight flow patterns were simulated, including core flow, two-sphere flow, three-sphere flow, four-sphere flow, half-pipe flow, annular flow, full-pipe flow, and empty-pipe flow, to obtain measured voltage data samples and the sensitivity matrix corresponding to each flow pattern. Finally, data processing and image reconstruction were performed using MATLAB R2019a simulation tools. The three-dimensional simulation model established using COMSOL Multiphysics is as follows: the pipe is a circular pipe with an 8-coil sensor array, i.e. The internal cross-section of the pipe is divided into 40×40 pixels, i.e., N=1600; the pipe radius is 0.05m; the shielding layer radius is 0.07m; the detection coil radius is 0.01m; the filling material inside the pipe has a conductivity of σ=3.774×10 7 Aluminum with a conductivity of S / m and air with a conductivity of σ = 0. The obtained voltage data were amplified to a training sample set of 800 samples (100 samples for each flow pattern) by adjusting the dielectric distribution and adding random Gaussian white noise with a signal-to-noise ratio of 40 dB. The flow pattern identification process is as follows: Figure 3 As shown.

[0072] During the experiment, image reconstruction was performed on eight flow patterns under both varying and fixed sensitivity matrices. Since a fixed sensitivity field typically uses an empty field sensitivity matrix, no comparative experiment was conducted on the empty tube flow pattern. The reconstruction results are as follows: Figure 4 As shown.

[0073] The imaging results clearly show that the reconstructed image obtained by the method of this invention is clearer, has higher contour edge fidelity, and is closer to the original image than that obtained by general imaging algorithms. To further verify the image reconstruction performance of the method of this invention, the correlation and error between the reconstructed image and the original image were linearly calculated.

[0074] The formula for calculating the error between images is:

[0075]

[0076] Among them, g and These are the original image vector and the reconstructed image vector, respectively, and the correlation coefficient represents the degree of linear correlation.

[0077] The degree of correlation between the two is measured by the linear correlation coefficient, which is calculated as follows:

[0078]

[0079] in, It is the average value of vector g. It is a vector The average value.

[0080] The performance parameters of different methods are shown in Tables 1 and 2:

[0081]

[0082]

[0083] Table 1

[0084]

[0085] Table 2

[0086] The data in the table shows that the method of this invention outperforms existing methods in terms of performance indicators such as image error and correlation coefficient, and the reconstructed image quality is higher when using the same reconstruction algorithm. Thanks to the flexibility of the varying sensitivity field, the EMT images reconstructed by the method of this invention have clear contour edges and intuitive imaging visual effects.

[0087] The embodiments described in this specification are merely examples of implementations of the inventive concept and are for illustrative purposes only. The scope of protection of this invention should not be considered limited to the specific forms described in these embodiments; rather, it extends to equivalent technical means conceived by those skilled in the art based on the inventive concept.

Claims

1. An EMT image reconstruction method based on manifold recognition and change sensitivity matrix, characterized in that, The method includes the following steps: Step 1: Obtaining and normalizing the standard flow pattern voltage vectors. Using multiphysics simulation software, obtain the corresponding voltage vectors for k standard flow pattern states. Then, normalize the voltage vectors using the max-min normalization method to obtain normalized voltage vector samples for the k standard flow patterns. Among them, v j ∈R m×1 Let j represent the j-th training sample in the i-th flow pattern, where j = 1, 2, ..., n. i , that is, the measurement voltage vector obtained by the system from the i-th flow type; m = l × (l-1) / 2 is the number of independent voltages under the measurement environment of coil l; Step two, generating the training sample set: First, by adjusting the medium distribution of the standard flow pattern, four different measured voltage vectors are obtained for each standard flow pattern, thus providing five measured voltage vector sample data for each standard flow pattern. Then, based on the obtained standard flow pattern voltage vectors, the voltage vector data samples for each flow pattern are expanded to 100 by adding 20dB, 30dB, and 40dB of Gaussian random noise respectively. The total training sample set V is then expressed as: V=[V1,V2,…,V k ]∈R m×n (2); Where: n = n1 + n2 + ... + n k ; Step 3, generation of the sensitivity matrix library. The image reconstruction problem of the EMT system is represented as: V m =Sq (3); Among them, V m It is an m×1 measured voltage vector, S∈R m×n It is the sensitivity distribution matrix of the measured object field region, g∈R n×1 Here, n is the conductivity distribution vector of the measured object field, and n is the mesh fraction. Based on the measured voltage vector, to solve for the conductivity distribution vector g in reverse, the sensitivity matrix S needs to be obtained. In the EMT simulation experiment, the corresponding k-type sensitivity matrices of k standard flow patterns are obtained based on the field quantity extraction method, forming a sensitivity matrix library S: S=[S1,S2,…,S k ] (4); This provides prior data for the subsequent reconstruction of the image vector g; Step 4, manifold identification: For unknown signals to be measured, it is necessary to determine their manifold and then reconstruct the image. Step 5: Selection of the flow pattern sensitivity matrix. Since the approximate characteristics of the measured signal cannot be predicted, a fixed sensitivity matrix is ​​used for image reconstruction. However, fixed sensitivity matrices are mostly solved based on empty field conditions and cannot accurately reflect the sensitivity of the object field to changes in medium distribution under different flow patterns. Therefore, after knowing the flow pattern classification of the measured voltage signal, the sensitivity matrix S corresponding to the flow pattern is selected from the sensitivity matrix library based on the flow pattern classification result of the measured voltage signal obtained from flow pattern identification. i Perform image reconstruction; Step 6, Image Reconstruction: Based on the measured voltage signal and the selected sensitivity matrix, solve formula (3) to recover the image vector g using the LBP algorithm, Landweber iterative algorithm and Tikhonov regularization algorithm respectively.

2. The EMT image reconstruction method based on manifold recognition and change sensitivity matrix as described in claim 1, characterized in that, The steps in step four are as follows: Step 4.1, linear measurement process, based on compressed sensing signal reconstruction theory, for the i-th manifold, if the training set V i If the model is complete or overcomplete, then any measured voltage vector λ of this type of manifold can be obtained from its training set V. i Linear representation: Where: coefficient α j For real numbers, As a coefficient vector, in practical applications, since the class to which any measured voltage vector λ belongs cannot be predicted, we consider re-representing it as a linear combination of the training sample set V composed of k manifolds: λ=Vx0 (6); In the above formula: As a sparse vector, only the coefficients at the corresponding positions of the i-th manifold corresponding to the measured voltage vector λ may be non-zero, while the rest are 0. Thus, the measured voltage vector λ obtained from the EMT system can be sparsely represented by an overcomplete dictionary transformation basis V composed of the training sample set. Let the random Gaussian matrix B∈R d×m For the measurement matrix, the voltage vector to be measured is linearly measured by the following formula: in, The observed value is a d×1 vector. The voltage vector corresponding to each standard flow pattern and the observed value of the voltage signal to be measured can be calculated by formula (7). Step 4.2, Solving for sparse solutions, since the observation vector The dimension d is much smaller than the dimension of the sparse signal x0, and solving formula (7) is an ill-conditioned problem, which can be transformed into the following mathematical model: Therefore, the optimization problem under this L0 norm is solved by the compressed sensing signal reconstruction algorithm, and the sparse solution x0 of the measured voltage signal λ corresponding to the overcomplete dictionary transformation basis V composed of the training sample set is obtained. Step 4.3: Determine the manifold type by calculating the sparse solution x of each standard manifold corresponding to the overcomplete dictionary transformation basis V composed of the training sample set. i After obtaining the sparse solution x0 corresponding to the voltage signal to be measured, i = 1,...,k, calculate x0 and x i The linear correlation coefficient is calculated using the following formula: in, and x0 and x i The average value of the linear correlation coefficient is used to determine the flow type corresponding to the maximum value of the linear correlation coefficient as the flow type to which the test voltage vector belongs, thereby enabling image reconstruction.

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