A Three-Dimensional Electrical Imaging Method Based on Dynamic Image Fusion

Abstract

This invention relates to a three-dimensional electrical imaging method based on dynamic image fusion. The first step is raw data acquisition: using an electrical measurement system to acquire the boundary capacitance or resistance corresponding to the dynamic process in the imaging area of ​​the three-dimensional electrical sensor, and obtaining the capacitance or resistance time series; the second step is initial image reconstruction: directly reconstructing the initial dielectric constant or conductivity distribution image sequence; the third step is initial image registration: (1) projecting the images in the initial image sequence onto the axis; (2) performing cross-correlation calculation on the axial projections of adjacent images to obtain the displacement between images; the fourth step is image fusion and output: (1) filtering out low-sensitivity regions and dividing the registered images into axial blocks; (2) calculating the spatial frequency of each image block; (3) performing image fusion and correction according to fusion and correction rules, and outputting the final image; this invention has the advantages of reducing initial image distortion and artifacts and improving axial resolution, providing a new technical approach for the realization of three-dimensional electrical imaging.

Description

Technical Field

[0001] This invention relates to the field of sensor technology, and in particular to a three-dimensional electrical imaging method based on dynamic image fusion in electrical tomography (ET). Background Technology

[0002] As a method of process tomography, electrical tomography (ET) is a real-time detection technique that uses two-phase or multiphase flow as the detection object and mainly employs electrical measurements to study the distribution of process parameters. This technique reconstructs the internal dielectric constant / conductivity distribution of the container or pipe by measuring the capacitance / resistivity values ​​between electrodes installed on the surface of the unknown container or pipe, thus rapidly and non-destructively obtaining the medium distribution inside the unknown container. Compared to other imaging methods, ET has advantages such as being radiation-free, non-invasive, having a fast response, strong real-time performance, simple structure, and low cost. Therefore, ET is widely used in process monitoring, especially in industrial process inspection.

[0003] In traditional electrical tomography, a single-layer electrode array is typically deployed outside the measured field to measure the capacitance / resistivity between electrode pairs. The dielectric constant / conductivity distribution within the measured region is then retrieved using image reconstruction algorithms. Due to the thickness of the electrodes, the reconstructed dielectric constant / resistivity distribution is usually the axial average of the dielectric constant / conductivity within the measured region. In recent years, electrical imaging technology has gradually evolved towards three-dimensional imaging. In addition to reconstructing the radial two-dimensional tomographic electrical parameter distribution, it also reconstructs the axial dielectric constant / conductivity distribution of the measured field, thereby obtaining information on the actual material distribution and physical characteristics within the measured field. Multilayer electrode arrays are also increasingly being adopted. By increasing the capacitance / resistivity measurements between layers, axial distribution information is enhanced, allowing the acquisition of dielectric constant / resistivity distribution information of the axial cross-section of the measured region. This enables the reconstruction of the three-dimensional interface shape of dynamic processes such as multiphase flow, facilitating further measurements of parameters such as flow pattern and phase content. However, in the development of electrical imaging from two-dimensional to three-dimensional, three-dimensional image reconstruction has become more challenging due to limitations in the number of independent capacitance measurements and soft-field characteristics. In three-dimensional image reconstruction, the number of independent capacitance measurements is far less than the number of pixels in the reconstructed image. Compared to the radial resolution of two-dimensional imaging, three-dimensional imaging requires further consideration of axial resolution. Furthermore, due to the soft-field characteristics of the electric field, the sensitivity of the imaging region is not uniformly distributed; the sensitivity along the axial center is much higher than that at the top and bottom of the sensor, further increasing the difficulty of axial imaging. Therefore, improving axial spatial resolution is urgently needed.

[0004] Several methods exist for improving the axial spatial resolution of electrical 3D imaging. On the hardware side, in "Enhancing Resolution of Electrical Capacitive Sensors for Multiphase Flowsby Fine-Stepped Electronic Scanning of Synthetic Electrodes," Z. Zeeshan et al. used electrical sensors with combinatorially excitable electrodes to increase the number of inter-electrode capacitance measurements along the axial direction, thus improving the axial resolution of directly reconstructed images. However, this method significantly increases the design difficulty and cost of the 3D electrical sensors, measurement, and data processing modules. On the algorithmic side, in "Graph convolutional networks for enhanced resolution 3D electrical capacity tomography image reconstruction," A. Fabijańska and R. Banasiak used graph convolutional networks to correct axial distortion during image reconstruction for low-resolution 3D dielectric constant distribution images with direct axial deformation. However, the neural networks in this method require a large amount of data for training, and the network structure needs to be retrained for different types of datasets.

[0005] Therefore, there is a need for a low-cost and reliable method for improving axial resolution in three-dimensional electrical imaging, and this method is also expected to be easily portable. To address the above issues, this invention provides a three-dimensional electrical imaging method based on dynamic image fusion, thereby improving the axial spatial resolution of three-dimensional electrical imaging. Summary of the Invention

[0006] The technical problem solved by this invention is that the axial resolution still needs to be improved during the process of three-dimensional electrical imaging.

[0007] The purpose of this invention is to propose a three-dimensional electrical imaging method based on dynamic image fusion. This method is easy to implement and can compensate for initial image defects and improve the axial resolution of three-dimensional electrical images with low hardware costs, providing a new technical approach for three-dimensional electrical imaging.

[0008] To achieve the above objectives, the technical solution of the present invention is as follows:

[0009] A three-dimensional electrical imaging method based on dynamic image fusion includes the following steps:

[0010] Step S10, Raw data acquisition:

[0011] An electrical imaging measurement system acquires a sequence of boundary electrical information corresponding to a dynamic process in the imaging region of a multi-electrode array sensor. This electrical information comprises the capacitance or impedance values ​​between electrode pairs. A schematic diagram of the multi-electrode sensor is shown below. Figure 2 , can be adopted as Figure 2 (a) The sensor structure enhances the sensitivity of the central imaging region.

[0012] Step S20, Initial Image Reconstruction:

[0013] Step S21, construct the Kalman filter. The Kalman filter equation can be expressed as formulas (1)-(5):

[0014]

[0015] P k+1|k =P k (2)

[0016] K k+1 =P k+1|k S T [SP k+1|k S T +R] -1 (3)

[0017]

[0018] P k+1 =[IK k+1 S]P k+1|k (5)

[0019] Where S is the normalized sensitivity matrix, which can be calculated through finite element simulation; R is the system measurement noise covariance matrix, which can be calculated from actual measurements or represented by an identity matrix; K k+1 This is the filter gain, where I is the identity matrix. and P k Let be the estimated value and its mean square error matrix for the k-th iteration;

[0020] Step S22: Initialize filter parameters and initial estimates. The reconstruction results can be estimated using the zero vector or filtered back projection (LBP) algorithm. The estimation error covariance matrix P0 and the noise covariance matrix R can be represented by the identity matrix αI and βI, respectively. α and β are positive constants. α can be arbitrarily chosen, such as 0.1, while β needs to be adjusted according to the reconstruction distribution. Its value range is usually [0.001, 1000].

[0021] Step S23: Construct a Takagi-Sugemo (TS) type fuzzy controller. Use this fuzzy controller to evaluate the output image quality of the Kalman filter and adjust the filter parameter β. This controller has two inputs: capacitance error e and capacitance error change Δe, and one output: the filter parameter adjustment step size u, as shown in formulas (6)-(8):

[0022]

[0023] Δe k =e k -e k-1 (7)

[0024] log 10 β k+1 =log 10 β k +u k (8)

[0025] Where f k The sign of the capacitance error e is +1 or -1, determined by a binary classifier.

[0026] In this controller, Gaussian membership functions or triangular membership functions are used to fuzzify the input. The input e is fuzzified to E, and the fuzzy set is [N]. a N a-1 ,...N1,N0,P0,P1,...,P a-1 ,P a The input Δe is fuzzified to EC, and the fuzzy set is [N]. b N b-1 ,...N1,ZO,P1,...,P b-1 ,P b ];

[0027] In this controller, the fuzzy rules have the following form:

[0028] if E is N a and EC is N b , then u=A(1)*e+B(1)*Δe+C(1)

[0029] Where A, B, and C are coefficient column vectors of length 2(a+1)(2b+1), which can be obtained by fitting the training dataset using the least squares method;

[0030] Step S24: Construct a training dataset. Use different filter parameters and iteration numbers to reconstruct common flow patterns, such as bubbly flow, laminar flow, and annular flow. Manually evaluate and label the acquired reconstructed images. Images with clear contours and large edge artifacts are labeled as +1, and images with blurred edges are labeled as -1. Calculate the capacitance error e and capacitance error change Δe corresponding to the reconstructed images. Adjust the filter parameters step size u to obtain a training dataset consisting of images and image labels.

[0031] Step S25: Based on the training dataset obtained in step S24, construct the binarized classifier in step S23 using classification algorithms such as support vector machine, and estimate the coefficient column vectors A, B, and C in step S23 using the least squares method.

[0032] Step S26: The original capacitance / resistance time series is reconstructed into a three-dimensional initial dielectric constant / conductivity distribution image sequence using a trained fuzzy adaptive Kalman filter (FAKaF).

[0033] Step S30, Initial image registration:

[0034] Step S31: First, project the three-dimensional initial dielectric constant / conductivity distribution image within the initial image sequence axially, and calculate its axial dielectric constant / conductivity projection. For an M*N*L pixel image within the sequence, its axial projection value P(l) is...

[0035]

[0036] Where P(l) is the axial projection value of the l-th layer of the image, and F(m,n,l) is the dielectric constant or conductivity of the image at point (m,n,l);

[0037] Step S32: Calculate the cross-correlation coefficient of projection values ​​between adjacent images. For two adjacent axial projections within the sequence, the coefficient is P. A ,P B The cross-correlation coefficient between two images is calculated as shown in formula (10):

[0038]

[0039] Where H is the cross-correlation vector between images A and B, and W is the number of axial layers within the observation window;

[0040] Step S33: Find the axial displacement between adjacent frame images. This displacement value is the abscissa of the peak of the axial cross-correlation vector H between adjacent frame images. Perform image registration based on the axial displacement between the initial images.

[0041] Step S40, Image fusion and output:

[0042] Step S41, perform registration on the image sequence [IM1 IM2 ... IM...] D The image within the image is processed by removing the portions with lower axial sensitivity, namely the working area of ​​the uppermost electrode and the lower half of the lowermost electrode, and then dividing the image into blocks, such as...

[0043] Step S42: Calculate the spatial frequency of each image patch. For an image block of size M1*N1*L1, its spatial frequency SF can be calculated using formulas (11) and (12):

[0044]

[0045]

[0046] Step S43: Perform axial block fusion on each image block, and the fusion rules are shown in formulas (13) and (14):

[0047]

[0048]

[0049] Where Index(i) is the source image number of the i-th image patch, TH is the adjustable threshold, and F is the fused image;

[0050] Step S44: Correct the fused image and output the final image. The correction rules are as follows:

[0051] If the source image labels of the upper and lower image blocks of a certain image block are both greater or smaller than the source label of this image block, then the source label of this image is replaced with the average of the source labels of the upper and lower images, and the images are re-fused.

[0052] The advantages of this invention compared to the prior art are:

[0053] 1. An axial image layer-by-layer fusion strategy based on spatial frequency is proposed, which utilizes time series information to improve the axial resolution of the reconstructed image. This imaging method does not require an additional increase in the number of hardware measurement electrodes, thus avoiding the increase in hardware design costs for three-dimensional electrical sensors and data measurement and processing modules.

[0054] 2. By adopting a registration strategy based on axial projection and cross-correlation, and an image layer fusion strategy based on spatial frequency, this method can achieve image alignment and extract relatively clear image blocks from the image sequence for fusion without requiring a large amount of network training data and pre-trained network parameters. Attached Figure Description

[0055] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description taken in conjunction with the accompanying drawings:

[0056] Figure 1 This is a structural diagram of the imaging method of the present invention;

[0057] Figure 2 This is a structural diagram of a common electrical imaging system, in which, Figure 2 (a) is a three-dimensional electrical sensor with a multilayer electrode array. Figure 2 (b) is the measurement and data processing module. Figure 2 (c) is the imaging and display module;

[0058] Figure 3 This is a structural diagram of the fuzzy Kalman filter established in S20 of this invention;

[0059] Figure 4 The images are reconstructed from simulation data of the Kalman filter algorithm under different filter parameters mentioned in this invention for four simple manifolds. Figure 4 (a) is a laminar flow. Figure 4 (b) is a circular flow. Figure 4 (c) represents the core flow. Figure 4 (d) and Figure 4 (e) is a bubbly flow;

[0060] Figure 5 This invention presents a comparison of reconstructed images of experimental data under different manifold models using two typical algorithms: the LBP algorithm and the Landweber algorithm, as well as a fuzzy Kalman filter algorithm based on S20. Figure 5 (a) is a wave flow. Figure 5 (b) is a laminar flow. Figure 5 (c) is a circular flow. Figure 5 (d) is the core flow. Figure 5 (e) is bubbly flow;

[0061] Figure 6 This is a comparison of the correlation coefficients between reconstructed images and reference images of experimental data under different manifold models, using two typical algorithms in this invention: the LBP algorithm and the Landweber algorithm, as well as the fuzzy Kalman filter algorithm based on S20. Figure 6 (a) is a wave flow. Figure 6 (b) is a laminar flow. Figure 6 (c) is a circular flow. Figure 6 (d) is the core flow. Figure 6 (e) is bubbly flow;

[0062] Figure 7This is a schematic diagram of the cross-correlation registration image of the S30 axial dielectric constant / conductivity projection in this invention;

[0063] Figure 8 This is a schematic diagram of the S40 spatial frequency-based image block fusion and correction method in this invention;

[0064] Figure 9 This is a schematic diagram illustrating the fusion of initial image sequences of wave flow and bubble flow in this invention. Figure 9 (a) is a wave flow. Figure 9 (b) is bubbly flow;

[0065] Figure 10 This is a comparison chart of the correlation coefficients between the initial image sequences and fused image sequences of wave flow and bubble flow and the reference distribution in this invention.

[0066] Figure 11 This is an example of a fuzzy rule in this invention. Detailed Implementation

[0067] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. It should be noted that the specific embodiments described herein are only for further detailed and in-depth description of the present invention and are not intended to limit the invention. To facilitate understanding and implementation of the present invention by those skilled in the art, only the parts relevant to the present invention are shown in the accompanying drawings.

[0068] Combination Figure 1 A three-dimensional electrical imaging method based on dynamic image fusion includes the following steps:

[0069] Step S10, Raw data acquisition:

[0070] pass Figure 2 The electrical imaging measurement system shown acquires a sequence of boundary capacitance information corresponding to a certain dynamic process. Figure 2 The three-dimensional capacitive sensor used in (a) has 4 layers with 6 electrodes in each layer. The sensor uses non-uniform axial electrodes to enhance the sensitivity of the central imaging region, thereby improving the imaging quality of the central region.

[0071] Step S20, Initial Image Reconstruction:

[0072] like Figure 3 A fuzzy controller is constructed to adjust the parameters of the Kalman filter, and the sequence of capacitance measurements is reconstructed into a dielectric constant distribution.

[0073] Step S21, construct the Kalman filter. The Kalman filter equation can be expressed as formulas (1)-(5):

[0074]

[0075] P k+1|k =P k (2)

[0076] K k+1 =P k+1|k S T [SP k+1|k S T +R] -1 (3)

[0077]

[0078] P k+1 =[IK k+1 S]P k+1|k (5)

[0079] Where S is the normalized sensitivity matrix, which can be calculated through finite element simulation; R is the system measurement noise covariance matrix, which can be calculated from actual measurements or represented by an identity matrix; K k+1 This is the filter gain, where I is the identity matrix. and P k Let be the estimated value and its mean square error matrix for the k-th iteration;

[0080] Step S22: Initialize filter parameters, initial estimates. The reconstruction result can be estimated using the zero vector or filtered back projection (LBP) algorithm. The estimation error covariance matrix P0 and the noise covariance matrix R are represented by the identity matrix αI and βI, respectively. α and β are positive constants, where α can be arbitrarily chosen. In this embodiment, the value is 0.1. β needs to be adjusted according to the reconstruction distribution. In this embodiment, the value range is selected as [0.001, 1000].

[0081] Step S23: Construct a Takagi-Sugemo (TS) type fuzzy controller. This controller has two inputs: capacitance error e and capacitance error change Δe, and one output: filter parameter adjustment step size u, as shown in formulas (6)-(8):

[0082]

[0083] Δe k =e k -e k-1 (7)

[0084] log 10 β k+1 =log 10 β k +u k (8)

[0085] Where fk The sign of the capacitance error e is +1 or -1, determined by a binary classifier.

[0086] In this controller, the universe of discourse for input e is [-1, 1]. After dividing the universe of discourse into eight equal parts, it is fuzzified to E using the Gaussian membership function, with the fuzzy set being [N3, N2, N1, N0, P0, P1, P2, P3]. The universe of discourse for input Δe is [-1.5, 1.5]. After dividing the universe of discourse into seven equal parts, Δe is fuzzified to EC using the Gaussian membership function, with the fuzzy set being [N3, N2, N1, ZO, P1, P2, P3].

[0087] In this controller, the fuzzy rule table is as follows: Figure 11 As shown, a specific fuzzy rule takes the following form:

[0088] if E is N a and EC is N b , then u=A(1)*e+B(1)*Δe+C(1)

[0089] Where A, B, and C are coefficient column vectors of length 56, which can be obtained by fitting the training dataset using the least squares method.

[0090] Step S24: Construct a training dataset and use different filter parameters and iteration numbers to reconstruct and simulate common flow patterns, such as bubbly flow, laminar flow, and annular flow. In this embodiment, α is set to 0.1, β is set to [0.001, 0.01, 0.1, 1, 10, 100, 1000], and the iteration number is selected as 5, 10, 20, 30. Figure 4 The reconstruction results of a partial distribution under certain parameters are shown. In these images, images with clear outlines and large edge artifacts are marked as +1, and images with blurred edges are marked as -1. In addition, the parameters corresponding to these images, namely capacitance error e, capacitance error change Δe, and corresponding filter parameter adjustment step size u, are calculated and stored together with the images, forming a training dataset consisting of images, image annotations, corresponding image errors, and adjustment step sizes.

[0091] Step S25: Based on the training dataset obtained in step S24, construct the binarized classifier in step S23 using the support vector machine algorithm, and estimate the coefficient column vectors A, B, and C in step S23 using the least squares method.

[0092] Step S26: Input the capacitance values ​​measured in experiments under different manifold models into the trained fuzzy Kalman filter to obtain the initial reconstructed image sequence.

[0093] To evaluate the effectiveness of step S20, this algorithm was applied in a multiphase flow visualization measurement simulation experiment. Figure 2 On the ECT system shown, reconstruction experiments were conducted on wave flow, laminar flow, circulation flow, core flow, and bubbly flow models. During the measurement process, the three-dimensional sensor used was a 4-layer, 24-electrode sensor with electrode lengths designed based on common property transformation. The several multiphase flow models imaged were composed of 3D printed molds and sand, where the dielectric constant of the sand was 3.

[0094] The following is combined with Figure 4 , Figure 5 , Figure 6 This paper describes the image reconstruction effects of the present invention under different flow patterns. The correlation coefficient (CC) is used to quantitatively evaluate the quality of the reconstructed images.

[0095]

[0096] Among them, G and These are the reference dielectric constant distribution and the reconstructed dielectric constant distribution, where F is the number of pixels in the image. and They are G and The mean.

[0097] from Figure 4 It can be seen that when directly using an image reconstruction algorithm based on a Kalman filter to reconstruct an image, as the filter parameter β increases, the edges of the reconstructed image gradually become clearer, but edge artifacts increase, eventually leading to divergence and distortion. Therefore, the selection of filter parameters has a significant impact on image quality, and a fuzzy controller is needed to adjust the filter parameters.

[0098] Figure 5 In this study, LBP, Landweber, and fuzzy Kalman filter-based reconstruction algorithms were used to reconstruct five distributions. First, a comparison was made... Figure 4 , Figure 5 The reconstruction results of the same type of flow pattern show that the algorithm based on the fuzzy Kalman filter can adjust the filter parameters to reconstruct images with clear boundaries and fewer artifacts for typical flow patterns such as ring-shaped, layered, and bubbly flows. Next, we will compare... Figure 5 The reconstruction results of the three algorithms show that, in laminar and annular flow, the image generated by this algorithm has fewer artifacts than Landweber. In bubbly flow, the image generated by this algorithm has clearer contours of objects and is closer to the reference distribution than the images reconstructed by LBP and Landweber algorithms.

[0099] from Figure 6 It can be seen that, for the four distributions, the reconstructed images of the proposed algorithm have higher correlation coefficients in all four manifolds, which proves the effectiveness of the algorithm.

[0100] Step S30, Initial image registration:

[0101] like Figure 7 First, the reconstructed initial dielectric constant image sequence is axially projected, and then the displacement values ​​between the images are obtained by cross-correlation of the axial dielectric constants.

[0102] Step S31: First, project the three-dimensional initial dielectric constant distribution image within the initial image sequence axially, and calculate its axial dielectric constant / conductivity projection. For an M*N*L pixel image within the sequence, its axial projection value P(l) is...

[0103]

[0104] Where P(l) is the axial projection value of the l-th layer of the image, and F(m,n,l) is the dielectric constant or conductivity of the image at point (m,n,l);

[0105] Step S32: Calculate the cross-correlation coefficient of projection values ​​between adjacent images. For two adjacent axial projections within the sequence, the coefficient is P. A ,P B The cross-correlation coefficient between two images is calculated as shown in formula (11):

[0106]

[0107] Where H is the cross-correlation vector between images A and B, and W is the number of axial layers within the observation window;

[0108] Step S33: Find the axial displacement between adjacent frame images. This displacement value is the x-coordinate of the peak of the axial cross-correlation vector H between adjacent frame images. Perform image registration based on the axial displacement between the initial images.

[0109] Step S40, Image fusion and output:

[0110] like Figure 8 First, the low-sensitivity regions of the registered image sequence are filtered out, then the sequence is divided into blocks, the spatial frequency of each block is calculated, and finally the fusion and correction are performed based on the fusion rules.

[0111] Step S41, perform registration on the image sequence [IM1 IM2 ... IM...] D The image within the image is processed by removing the portions with lower axial sensitivity, namely the working area of ​​the uppermost electrode and the lower half of the lowermost electrode, and then dividing the image into blocks, such as...

[0112] Step S42: Calculate the spatial frequency of each image patch. For an image block of size M1*N1*L1, its spatial frequency SF can be calculated using formulas (12) and (13):

[0113]

[0114]

[0115] Step S43: Perform axial block fusion on each image block, and the fusion rules are shown in formulas (14) and (15):

[0116]

[0117]

[0118] Where Index(i) is the source image number of the i-th image patch, TH is the adjustable threshold, and F is the fused image;

[0119] Step S44: Correct the fused image and output the final image. The correction rules are as follows:

[0120] If the source image labels of the upper and lower image blocks of a certain image block are both greater or smaller than the source label of this image block, then the source label of this image is replaced with the average of the source labels of the upper and lower images, and the images are re-fused.

[0121] The following is combined with Figure 9 , Figure 10 Steps S30 and S40 are explained as fusing the initial reconstructed image sequences of the two distributions. Figure 9 In (a), a wave flows past the sensor. Figure 9 In (b), two spheres, 9 cm apart at their centers and with radii of 2 cm and 3 cm respectively, pass through the sensor. The fuzzy Kalman algorithm in step S20 is used to reconstruct the initial image from four sets of data collected at different times during the two dynamic processes. Then, the axial gray-level cross-correlation image registration and spatial frequency-based hierarchical fusion algorithm proposed in steps S30 and S40 are used for fusion. The CC (Carbon Difference) method is used to quantitatively evaluate the quality of the fused image. Figure 9 As can be seen in (b), due to the soft field effect of the electric field, the initial reconstructed image has higher image quality in the middle region along the axis, while the reconstructed image at both ends is deformed and distorted. For example, the ball can be reconstructed in the middle region, but the reconstruction result at both ends will be distorted. The fused image extracts the high-quality parts of each image, filters out the low-quality image blocks, and reconstructs the two balls clearly without distortion.

[0122] from Figure 10 It can be seen that for the two image sequences, the fused image produced by the proposed algorithm has a higher similarity coefficient than the initial image, which proves the effectiveness of the fusion algorithm.

[0123] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

Claims

1. A three-dimensional electrical imaging method based on dynamic image fusion, characterized in that, Includes the following steps: Step S10: Raw data acquisition. Use the electrical imaging measurement system to acquire the boundary capacitance or resistance information corresponding to the dynamic process in the imaging area of ​​the three-dimensional electrical sensor, and obtain the capacitance or resistance time series. Step S20: Initial image reconstruction. A Kalman filter is constructed to convert the measured boundary capacitance or resistance information into a three-dimensional electrical image. A Takagi-Sugeno type fuzzy controller is constructed to evaluate the output image quality of the Kalman filter and adjust the filter parameters. An initial image sequence characterizing the dielectric constant distribution or conductivity distribution inside the imaging region is obtained through multiple filter iterations. Step S30, initial image registration: Calculate the displacement between adjacent frames in the initial image sequence and perform registration according to the following method: First, calculate the axial dielectric constant or conductivity distribution projection vector P of the 3D image within the initial image sequence. This is for a 3D image with M*N*L pixels. The projection formula is as shown in formula (1): (1) in, (l) is the axial projection value of the l-th layer of the image. It is the dielectric constant or conductivity of the image at point (m, n, l); Next, calculate the cross-correlation vector of the projection vectors of the axial dielectric constant or conductivity distribution between adjacent frames, as shown in formula (2): (2) in, is the cross-correlation vector between images A and B, and W is the axial layer number within the observation window; Finally, based on the peak position of the cross-correlation vector, the axial displacement between adjacent frames is found. This displacement value is the x-coordinate of the peak of the axial cross-correlation vector H between adjacent frames. Image registration is then performed based on the axial displacement between the images. Step S40, Image Fusion and Output: First, filter out the low-sensitivity parts of the registered image, namely the upper half of the top electrode and the lower half of the bottom electrode, divide the image into axial blocks, calculate the spatial frequency of each image block, and then perform image fusion according to the spatial frequency and fusion rules. After fusion, correct the image according to the correction rules and output the final fused image.

2. The three-dimensional electrical imaging method based on dynamic image fusion according to claim 1, characterized in that, Step S20 includes: (3) (4) (5) (6) (7) Step S21: Construct a Kalman filter and use it to convert the measured capacitance or resistance information into an initial three-dimensional electrical image, as shown in formulas (3)-(7): Where k is the number of iterations. It is the normalized measured change in capacitance or resistance, and S is the normalized sensitivity matrix, which can be obtained through finite element simulation. It is the filter gain. As a unit array, and These are the electrical image estimates and their mean square error matrices, respectively, and R is the measurement noise covariance matrix. Step S22: Initialize filter parameters and initial estimates. The reconstruction result can be estimated using the zero vector or filtered back projection (LBP) algorithm, and the error covariance matrix can be estimated. The noise covariance matrix R can be derived from the identity matrix. , express, , For positive integers, where You can choose any value, such as 0.

1. Then it needs to be adjusted according to the reconstructed distribution, and its value range is usually [0.001, 1000]; Step S23: Construct a Takagi-Sugeno (TS) type fuzzy controller, and use this fuzzy controller to evaluate the output image quality of the Kalman filter and adjust the filter parameters. The controller has two inputs: capacitance error e and capacitance error change. e, an output, filter parameter adjustment step size u, as shown in formulas (8)-(10): (8) (9) (10) in, The sign of the capacitance error is +1 or -1, determined by a binary classifier. In this controller, the input e is fuzzified to E, and the fuzzy set is [ , ,... , , , ,..., , ],enter e is fuzzified to EC, and the fuzzy set is... , ,... ZO ,..., , ]; In this controller, the fuzzy rules have the following form: in , , It is a length of The coefficient column vector can be obtained by fitting the data in the training dataset using the least squares method. Step S24: Construct a training dataset and perform reconstruction simulations on common flow patterns, such as bubbly flow, laminar flow, and annular flow, using different filter parameters and iteration numbers. Manually evaluate and label the acquired reconstructed images: images with clear contours and large edge artifacts are marked as +1, while images with blurred edges are marked as -1. Calculate the capacitance error e and the change in capacitance error corresponding to the reconstructed images. e, the filter parameter adjustment step size u, to obtain a training dataset consisting of images and image annotations; Step S25: Based on the training dataset obtained in step S24, construct the binarized classifier from step S23 using classification algorithms such as support vector machines, and estimate the coefficient column vector from step S23 using the least squares method. , , .

3. The three-dimensional electrical imaging method based on dynamic image fusion according to claim 1, characterized in that, Step S40 includes: Step S41, image preprocessing, processing the registered image sequence [ ... First, remove the low-sensitivity regions along the axial direction of the image, namely the upper half of the top electrode and the lower half of the bottom electrode. Then, divide the image into axial blocks, such as... ; Step S42: Calculate the spatial frequency of each image patch. ; Step S43: Perform axial block fusion on the image, with fusion rules as shown in formulas (11) and (12): (11) (12) in, is the source image number of the i-th image patch, TH is the adjustable threshold, and F is the fused image; Step S44: Correct the fused image and output the final image. The correction rules are as follows: If the source image labels of the upper and lower image blocks of a certain image block are both greater or smaller than the source label of this image block, then the source label of this image is replaced with the average of the source labels of the upper and lower images, and the images are re-fused.

Images