An image reconstruction method and system based on electrical capacitance tomography and a storage medium

Abstract

The application relates to an image reconstruction method based on electrical capacitance tomography, comprising the following steps: calculating and normalizing a sensitivity matrix based on an electrode arrangement of an electrical capacitance tomography sensor and electromagnetic field simulation data; obtaining original capacitance measurement values of the electrical capacitance tomography sensor and performing normalization processing to obtain preprocessed capacitance data; performing back projection operation on the preprocessed capacitance data and the sensitivity matrix to reconstruct a rough estimation image; inputting the rough estimation image into a pre-trained deep learning image artifact removal model, and outputting a high-precision reconstruction image with artifacts suppressed by the deep learning image artifact removal model. Through the above design, the application effectively overcomes the contradiction between speed and accuracy in the traditional method, and significantly improves the quantitative accuracy, visual clarity and anti-interference robustness of the reconstructed image in three dimensions.

Description

Technical Field

[0001] This invention relates to the field of multiphase flow detection, and in particular to an image reconstruction method, system and storage medium based on capacitance tomography. Background Technology

[0002] Capacitance tomography (CMT) is a non-invasive or invasive detection technique that uses an array of capacitance sensors to visualize the dielectric constant distribution within a measured area. Its basic principle is to measure capacitance using electrode pairs within the sensor array, and then use the obtained capacitance data, combined with specific image reconstruction algorithms, to reconstruct the dielectric distribution within the measured area.

[0003] Linear Back Projection (LBP) is one of the most commonly used real-time reconstruction algorithms in capacitance tomography. Based on the sensitivity matrix, this algorithm projects capacitance measurements backward onto the imaging region, thus quickly obtaining a rough image of the dielectric constant distribution. However, as a method for solving a severely underdetermined problem, LBP has inherent technical flaws, resulting in poor image quality, specifically in the following aspects: First, the reconstructed images contain significant artifacts related to the sensor's physical structure, such as obvious vertical stripe artifacts and cross-shaped artifacts. These artifacts stem from the high inhomogeneity of the sensitivity matrix, severely obscuring the true phase interface information and making it difficult to determine the flow pattern.

[0004] Secondly, the algorithm lacks sufficient spatial resolution for low-contrast media. Under conditions such as laminar flow, the gas-liquid interface often appears blurry, making it difficult to accurately identify the position and shape of the phase interface.

[0005] Furthermore, the LBP algorithm is quite sensitive to drift and noise in the measurement system. In particular, changes in the mineralization of the medium can cause drift in the electrical characteristics of the measurement system. If fixed calibration parameters are used directly for LBP reconstruction, the error will increase significantly under different mineralization conditions, affecting the stability and reliability of the measurement.

[0006] To improve the quality of LBP-reconstructed images, post-processing methods are commonly used in existing technologies. Existing image reconstruction improvement schemes can be roughly divided into three categories: First, iterative algorithms (such as Landweber iteration) approximate the true value by successively correcting it, but they have slow convergence, poor real-time performance, and are also affected by the ill-conditioned nature of the sensitivity matrix; Second, post-processing filtering methods (such as HDTV anisotropic diffusion), whose processing power is limited by filtering priors and it is difficult to balance artifact suppression and detail preservation; Third, end-to-end deep learning schemes directly reconstruct images from capacitance data. Although they have strong nonlinear fitting capabilities, their training depends on a large amount of labeled real data, which is difficult to obtain in actual working conditions. Furthermore, when trained with pure simulation data, there is a significant distribution gap between the data and real measurements. At the same time, the lack of physical prior anchoring makes it difficult to guarantee the physical consistency of the reconstruction results.

[0007] Therefore, there is an urgent need in this field for an image reconstruction method that can effectively overcome the above-mentioned defects, and can significantly suppress artifacts while maintaining or even enhancing the ability to resolve phase interfaces and improve robustness to different working conditions.

[0008] It should be noted that the information disclosed in the background section above is only for understanding the background of the present invention, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0009] The technical problem solved by this invention is "how to overcome the inherent technical defects of traditional linear back projection (LBP) reconstruction methods for capacitance tomography, such as severe artifacts, low spatial resolution, and sensitivity to measurement condition drift, and achieve efficient synergistic optimization of speed and accuracy in capacitance tomography image reconstruction".

[0010] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows.

[0011] This invention provides an image reconstruction method based on capacitance tomography, comprising the following steps: Sensitivity matrix construction steps: Based on the electrode arrangement and electromagnetic field simulation data of the capacitance tomography sensor, calculate and normalize the sensitivity matrix; Capacitance data preprocessing steps: Obtain the raw capacitance measurement values ​​of the capacitance tomography sensor and perform normalization processing to obtain preprocessed capacitance data; Back projection reconstruction steps: Perform back projection operation on the preprocessed capacitance data and sensitivity matrix to reconstruct a coarsely estimated image; Deep learning artifact removal steps: Input the coarsely estimated image into a pre-trained deep learning image artifact removal model, and the deep learning image artifact removal model outputs a high-precision reconstructed image with artifacts suppressed.

[0012] In some embodiments, during the capacitance data preprocessing step, the raw capacitance measurements acquired from multiple electrode pairs of the capacitance tomography sensor are calibrated and normalized using a matching self-calibration method to obtain the preprocessed capacitance data for each electrode pair. , represented as:

[0013] in, The original capacitance value that was actually measured at the moment. The capacitance calibration value under the same experimental conditions is the full-load state. This refers to the capacitance calibration value under the same experimental conditions in the empty tube state.

[0014] In some embodiments, the capacitance data preprocessing step further includes a failed electrode pair repair step: For each electrode pair, determine whether it meets one of the following conditions; if it does, it is determined to be a failed electrode pair: The absolute value of the difference between the capacitance calibration value of the electrode in the full tube state and the capacitance calibration value in the empty tube state is less than a preset threshold, or the difference is negative; The calculated preprocessed capacitance data of this electrode exceeds the preset physical reasonable range; For an electrode pair that is determined to be a failed electrode pair, its corresponding preprocessed capacitance data value is replaced with the average of the preprocessed capacitance data values ​​of its adjacent non-failed electrode pairs. The adjacent non-failed electrode pairs are the closest non-failed electrode pairs determined from the left and right sides of the failed electrode pair according to the index order of each electrode pair.

[0015] In some embodiments, the process of reconstructing a coarsely estimated image in the back-projection reconstruction step includes: reshaping the result of the back-projection operation into a two-dimensional cross-sectional image, and setting the pixel values ​​of the region outside the pipe in the two-dimensional cross-sectional image to zero to obtain a coarsely estimated image.

[0016] In some embodiments, the deep learning image artifact removal model is built on the U-Net network structure, wherein the U-Net network structure adopts an encoder-decoder structure and uses reflection padding in the convolution operation.

[0017] In some embodiments, the training set of a deep learning image artifact removal model is constructed through the following steps: Simulation steps: Generate a true image of phase distribution based on the preset flow pattern; Forward projection step: The true phase distribution image is forward projected through the initial sensitivity matrix calculated based on the electrode arrangement of the capacitance tomography sensor to obtain simulated ideal capacitance data; Data synthesis steps: Superimpose real experimental noise onto ideal capacitance data to obtain synthesized capacitance data; Back projection step: The synthesized capacitance data is processed by back projection operation in the back projection reconstruction step to obtain a coarse estimated image with artifacts. Pairing step: Pair the coarsely estimated image with artifacts with the ground truth image of the phase distribution to form training samples.

[0018] In some embodiments, the deep learning image artifact removal model is trained using a composite loss function, which includes mean squared error loss, total variation regularization term and outside region constraint term.

[0019] In some embodiments, the training of the deep learning image artifact removal model employs a data augmentation method that only flips left and right, and uses an early stopping strategy based on an independent validation set.

[0020] In some embodiments, an image reconstruction system based on capacitance tomography is also provided, comprising: The sensitivity matrix construction module is used to calculate and normalize the sensitivity matrix based on the electrode arrangement and electromagnetic field simulation data of the capacitance tomography sensor. The capacitance data preprocessing module is used to acquire the raw capacitance measurement values ​​of the capacitance tomography sensor and perform normalization processing to obtain preprocessed capacitance data. The linear back-projection reconstruction module is used to perform back-projection operations on the preprocessed capacitance data and the sensitivity matrix to reconstruct a coarsely estimated image. The deep learning artifact removal module is used to input a coarsely estimated image into a pre-trained deep learning image artifact removal model, which outputs a high-precision reconstructed image with artifacts suppressed.

[0021] In some embodiments, a computer-readable storage medium is also provided, on which a computer program is stored, which, when executed by a processor, implements the image reconstruction method based on capacitance tomography of the present invention.

[0022] The present invention has the following beneficial effects: This invention achieves significant benefits through the synergistic combination of its various technical features. First, the "sensitivity matrix construction step" calculates and normalizes the sensitivity matrix based on the electrode arrangement and electromagnetic field simulation data of the capacitance tomography sensor. This feature, by utilizing the sensor's physical layout and the fundamental principles of electromagnetic fields, provides an accurate mathematical basis for subsequent reconstruction, ensuring the physical rationality of the reconstruction process. Second, the "capacitance data preprocessing step" obtains and normalizes the raw capacitance measurements from the capacitance tomography sensor to obtain preprocessed capacitance data. This feature, through the standardization of the raw measurement data, effectively reduces the direct impact of measurement system drift and noise, providing stable and reliable data input for subsequent calculations. Next, the "backprojection reconstruction step" performs backprojection operations on the preprocessed capacitance data and the sensitivity matrix to reconstruct a coarsely estimated image. This feature fully utilizes the advantages of the LBP algorithm—fast computation speed and simple implementation—to quickly generate an initial image reflecting the approximate outline of the medium distribution. Finally, the "deep learning artifact removal step" inputs the coarsely estimated image into a pre-trained deep learning image artifact removal model, which outputs a high-precision reconstructed image with artifacts suppressed. This feature utilizes the powerful nonlinear mapping and feature learning capabilities of the deep learning model to intelligently identify and suppress artifacts related to the physical sensor structure in the coarsely estimated image, while restoring and enhancing the real phase interface details.

[0023] Clearly, the aforementioned technical features are not simply superimposed, but rather form an organic whole. The "sensitivity matrix construction step" and the "capacitance data preprocessing step" provide optimized inputs for the "backprojection reconstruction step," while the output of the "backprojection reconstruction step" serves as input for the "deep learning artifact removal step." Ultimately, through the complementary advantages of the computational efficiency of the "backprojection reconstruction step" and the strong nonlinear fitting capability of the "deep learning artifact removal step," a deep fusion of physical priors and data-driven optimization is achieved. Specifically, the "backprojection reconstruction step" ensures the real-time performance of the method, providing preliminary reconstruction results for deep learning processing; while the "deep learning artifact removal step" focuses on suppressing artifacts and enhancing details, significantly improving image quality. This invention effectively overcomes the contradiction between speed and accuracy in traditional methods through the synergy of the aforementioned technical features, resulting in significant improvements in quantitative accuracy, visual clarity, and robustness against interference in reconstructed images.

[0024] Other beneficial effects of the present invention will be further described below. Attached Figure Description

[0025] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein: Figure 1 This is a schematic diagram of the deep learning image artifact removal model network used in the embodiments of the present invention and its positional relationship in the image reconstruction process; Figure 2 This is a comparison diagram of the reconstruction effect of Embodiment 1 of the present invention under various working conditions of gas-water two-phase flow, which shows a visual comparison between the reconstruction results of different methods and the true value of phase distribution. Figure 3 This is a comparison of the reconstruction results of Embodiment 2 of the present invention in a gas-oil two-phase flow scenario, which shows a visual comparison between the reconstruction results of different methods and the true values ​​of phase distribution. Figure 4 This is a schematic diagram of the electrode arrangement structure of a capacitance tomography sensor (Wiremesh). Detailed Implementation

[0026] The embodiments of the present invention will be described in detail below. It should be emphasized that the following description is merely exemplary and not intended to limit the scope and application of the present invention.

[0027] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of embodiments of the present invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0028] This invention recognizes that existing capacitance tomography (LBP) reconstruction methods suffer from severe image artifacts, low spatial resolution, and sensitivity to measurement condition drift. These artifacts, such as vertical stripes and cross-shaped patterns, are not random noise but rather a highly spatially structured and predictable systematic error caused by the inhomogeneity of the sensitivity field determined by the sensor electrode arrangement. This structural artifact (systematic error) is separable from the true phase distribution in the feature space. Therefore, this invention proposes a technical solution based on the following mechanism: Linear backprojection can be viewed as a fast but coarse forward transformer, whose output contains both true medium distribution information and systematic errors with fixed patterns. A specially trained deep learning model can learn the inverse transform of this forward transformer process, effectively separating the true signal mixed in the coarsely estimated image from the systematic error. Accordingly, this invention proposes a scheme of "firstly, rapidly reconstructing the coarsely estimated image through linear backprojection, and then using a pre-trained deep learning image artifact removal model to perform nonlinear artifact removal enhancement on the coarse image," to solve the specific technical problems of improving image quality, eliminating artifacts, and enhancing robustness.

[0029] It should be noted that the reason why this invention adopts a step-by-step architecture of "first back-projection coarse reconstruction, then deep learning to remove artifacts" instead of end-to-end direct regression is that back-projection provides physical prior anchors, so that the network only needs to learn local artifact inverse mappings instead of global nonlinear mappings, which significantly reduces the demand for training data and ensures the physical consistency between the reconstruction results and the sensitivity matrix.

[0030] In some embodiments, the present invention provides an image reconstruction method based on capacitance tomography, the steps of which include: Step 1: Sensitivity Matrix Construction. Extract the x and y components of the electric field from the 16 electrode electric field data (E1~E16.txt) exported from the COMSOL simulation, and calculate the initial sensitivity matrix according to the electrode pair relationship:

[0031] in , These represent the electric field components in the x and y directions at various points in space for the i-th excitation electrode. The sensitivity matrix is ​​normalized column-wise to ensure uniform sensitivity vector amplitudes for each electrode pair. This prevents nearby high-amplitude electrode pairs from dominating imaging during backprojection and drowning out weak signals at distant points, while also improving the numerical conditions of the backprojection matrix. Column-wise normalization is a classic preprocessing technique in capacitance tomography sensitivity backprojection. The imaging region is divided into a 50×50 grid, containing 2500 spatial sampling points. Each electric field data file contains the electric field components at each sampling point when the corresponding electrode is excited. Based on this, the constructed sensitivity matrix has a dimension of 64×2500 (64 electrode pairs × 2500 sampling points).

[0032] Step 2: Capacitor Data Preprocessing. Extract 64 pairs of capacitance values ​​from the raw capacitance data by column index, and normalize them using a matching self-calibration method.

[0033] Each mineralization level is represented by the full-volume segment extracted from the same data collection. Empty pipe section as To ensure that the calibration data and the test data are from the same batch and there is no cross-time drift; for failed electrode pairs with excessively small capacitance differences between full and empty tubes, adjacent value interpolation is used for repair; the determination of failed electrode pairs includes two categories: first, those with an absolute value of the capacitance difference between full and empty tubes less than 5 or a negative difference are judged as hard failed pairs. This threshold is an engineering experience value, which is much smaller than the capacitance difference of hundreds of orders of magnitude for normal electrode pairs; second, after normalization... Pairs exceeding the physically reasonable range of [-2, 5] are considered numerically abnormal. For each of the above-mentioned failed pairs, the nearest valid electrode pair on its left and right sides is used. Mean replacement, because outliers themselves contain no useful information and their outliers can actually contaminate the entire image in back projection, introduces far less error than retaining outliers, effectively suppressing the propagation of outliers. It should be noted that liquid mineralization is frequently involved in practical experiments. Mineralization refers to the total amount of dissolved salt ions in water, characterized in this paper by solution conductivity, in μS / cm.

[0034] Step 3: LBP linear back projection coarse reconstruction. Inversion formula:

[0035] Reshape g to a 50×50 cross-sectional image, setting the region outside the pipe to zero. Normalize to the dielectric constant range [1, 80.1] (gas-water) / [1, 2.5] (gas-oil).

[0036] Step 4: Deep Learning for Artifact Removal and Reconstruction. This step constructs a deep learning image artifact removal model based on a U-Net convolutional neural network to enhance the LBP coarse-estimated image by removing artifacts. The overall process and network structure are shown in the attached figure. Figure 1 As shown, the network takes a single-channel 50×50 LBP coarse estimation image as input and adopts a symmetrical encoder-bottleneck-decoder structure. The encoder downsamples layer by layer to extract multi-scale features, and the decoder upsamples layer by layer and fuses shallow and deep features with skip connections. The final output is a 50×50 phase content distribution map constrained to [0,1] by Sigmoid. The input and output sizes are consistent, the area outside the pipe is zeroed with a mask, and the convolution boundary is filled with reflection to avoid edge artifacts. The training set of the network is constructed by physical simulation and real noise synthesis: the true value GT of phase distribution is generated according to the preset flow pattern (mainly horizontal laminar flow, covering empty pipe to full pipe and including low liquid level conditions). The ideal normalized capacitance is obtained by forward projection of the sensitivity matrix. Then, the cn domain noise extracted from real dynamic experiments is superimposed, and the coarse reconstruction map with artifacts is obtained by backprojection with the same LBP aperture as the inference stage. It is then paired with the GT as training samples.

[0037] In the training set, each sample is synthesized sample-by-sample from the true phase distribution generated by simulation software MATLAB and COMSOL, along with real experimental noise. Non-simulated samples are mixed with real samples in a fixed ratio. Training is supervised by a composite loss (mean squared error, total variational regularization, and weighted by external constraints), employing early stopping on an independent validation set and only left / right flipping enhancement to preserve prior gravity direction. During inference, a coarsely reconstructed image from actual measurements is input into the trained network, outputting a high-quality reconstructed image with artifacts removed. The principle is that LBP artifacts possess a learnable spatial structure related to the inhomogeneity of the sensitivity matrix, and the network learns a nonlinear mapping from artifact-contaminated images to the true phase distribution through end-to-end supervision.

[0038] It should be noted that the appendix Figure 1 The channel size shown is based on the gas-oil example (base=48); the gas-water example uses base=32 (bottleneck 256). The two have the same network structure, only the number of feature channels is different.

[0039] The following will further describe specific embodiments of the present invention. These embodiments are merely illustrative and do not mean that the present invention is limited to the following examples.

[0040] Specifically, compared to the traditional two-stage approach of "reconstruction first, followed by fine-tuning," this invention has the following outstanding technical advantages in practical implementation: Firstly, a matching self-calibration method is adopted, which automatically identifies the full tube state and empty tube state from the data collected in the same batch as the calibration benchmark. There is no need to preset the calibration conditions, which effectively avoids the impact of calibration drift and changes in medium mineralization on reconstruction accuracy. Secondly, an automatic criterion for failing electrode pairs is established. Electrode pairs with excessively small or negative capacitance differences in the full-void tube, or those with normalized capacitance exceeding the physically reasonable range, are automatically identified as failing. Adjacent value interpolation is used for repair, effectively avoiding the contamination of the reconstructed image by abnormal channels. Third, the training set is synthesized sample by sample by superimposed with the true values ​​of the simulated phase distribution and real experimental noise, and is generated with the same back projection caliber as the inference stage. This makes the artifacts seen in the network training stage and the real inference the same source, and can effectively avoid the distribution gap between the simulated data and the real data without the need to introduce explicit domain adaptation.

[0041] Example 1: Static section reconstruction of gas-water two-phase flow Experimental conditions: 5cm inner diameter pipe, 8×8 wiremesh electrode grid. The medium consisted of water with three mineralization levels (0, 19.6, 39.2 μS / cm) and air. Four liquid level heights were set for each mineralization level: full water, 67mm (between conductors 6 and 7), 45mm (between conductors 4 and 5), and 23mm (between conductors 2 and 3). The average of stable data (>1000 frames) for each operating condition was used as the reconstruction input.

[0042] Calibration method: A self-calibration method is adopted, that is, the full-water section with this salinity is extracted from the same data collection (as the full-pipe calibration). ) and empty pipe section (as empty pipe calibration) The data is from the same batch and under the same experimental conditions as the data to be tested, avoiding calibration drift across time periods. The true value is generated in the pipe cross-sectional geometry model according to the liquid level: water accumulates in the lower part in the direction of gravity, and gas is in the upper part.

[0043] See attached reconstruction comparison. Figure 2 The reconstruction error of each method is measured using the root mean square error (RMSE) of pixels within the tube, defined as follows:

[0044] in Let i be the normalized value of the i-th pixel within the tube reconstructed by a certain method. is the true value, and N is the total number of pixels in the tube. Table 1 shows the RMSE quantization comparison for each operating condition.

[0045] Table 1: RMSE data of gas-liquid two-phase flow from four directions (each mineralization is self-calibrated).

[0046] As shown in Table 1, among the three processing methods (LBP, HDTV, and CNN), CNN achieved the best RMSE in 8 out of 9 liquid level conditions. The improvement is represented by the RMSE reduction of CNN relative to LBP. The last row is the arithmetic mean of the 9 liquid level conditions. Even after excluding the full-water condition used as the calibration benchmark, the average RMSE of CNN in the 9 blind liquid level conditions is still 0.410, a 34% reduction compared to LBP (0.623), demonstrating a robust advantage.

[0047] Further analysis of the generalization ability and robustness of this method reveals that the aforementioned CNN model, trained only on data with a mineralization of 0 μS / cm, can be directly used for reconstruction of higher mineralization values ​​such as 19.6 and 39.2 μS / cm. Its ability to operate across mineralization levels and its transferability across different media are not accidental. Regarding cross-mineralization, the capacitance obtained from the forward projection is normalized... Later becoming a dimensionless quantity, the measurement differences caused by mineralization are mainly reflected in the calibration values ​​and are eliminated in this normalization. Therefore, a model trained with a single mineralization can be directly used for other mineralizations. Regarding cross-media, although the dielectric constants of water and oil differ significantly, the reconstructed images are all normalized to the [0,1] phase content space, and LBP artifacts under different media have similar spatial structures (all stemming from the inhomogeneity of the sensitivity matrix). Therefore, this method can be generalized across media—it is equally effective after retraining with gas and oil data in the same way in gas and oil scenarios. Both of these indicate that the network learns a general mapping rather than a memory of specific operating conditions, which is the source of its generalization ability.

[0048] Regarding training robustness, the training set uses simulated ground truth combined with real noise synthesis, covering conditions from empty to full pipes including low liquid levels. Combined with total variational regularization, external pipe constraints, enhancements based solely on left and right flips, and an early stopping strategy based on an independent validation set (validation loss approximately 0.012 and converges consistently with the training loss), overfitting is effectively suppressed. In Table 1, the CNN (RMSE 0.509) for the 0 μS / cm-23mm condition is slightly higher than the LBP (0.461). This is because at this extremely low liquid level, the water volume inside the pipe is small, the phase interface is in a less sensitive region, and the measurement information itself is insufficient. This is an interpretable boundary condition and does not affect the other conditions or the overall generalization conclusions.

[0049] This method also incorporates specific designs to ensure the reliability of the self-calibration and the consistency between simulation and reality. The selection of full-pipe and empty-pipe sections is based on the preset operating conditions of the calibration experiment—the experiment is conducted in the order of full pipe, gradually decreasing the liquid level until the pipe is empty, and the start and end times of each stable section are given by the experimental records. In cases requiring automation, the stability can also be automatically identified based on the signal characteristics of the capacitance time series, i.e., the full-pipe section corresponds to the stable section with the highest overall mean and smallest inter-frame variance for all capacitances, and the empty-pipe section corresponds to the stable section with the lowest overall mean and smallest variance. If a measurement does not involve a full-pipe or empty-pipe state, calibration data collected by the same sensor under the same medium conditions can be used as an alternative. More importantly, since the noise used for training is directly taken from real dynamic experiments, and the training set generation and actual inference use the same LBP reconstruction aperture, the artifact patterns seen by the network during the training phase are of the same origin as those during real inference. Therefore, there is no need to introduce explicit domain adaptation to avoid the distribution gap between simulation and reality. The fact that the model trained with only 0 μS / cm data can successfully infer unseen high mineralization conditions is direct evidence of the effectiveness of this domain consistency design.

[0050] Example 2: Static cross-section reconstruction of gas-oil two-phase flow Experimental conditions: The medium was ordinary mineral oil (dielectric constant approximately 2.5) and air. For the static oil experiment, one frame was sampled every 29 frames, for a total of N=200 frames. On-site sky full-tube calibration was used, employing the same U-Net architecture as in Example 1. Comparison methods: A. Original LBP (baseline), B. LBP + cubic interpolation post-processing, C. Physically constrained CNN (the method of this invention).

[0051] Table 2: Three-dimensional comparison of RMSE data for gas-oil two-phase flow (N=200, GT ε=2.5)

[0052] As shown in Table 2, the overall error RMSE of CNN is 0.791, which is 22.2% lower than that of LBP and 17.6% lower than that of cubic interpolation. In terms of mean bias, CNN (-0.474) is 41% better than LBP (-0.808). This CNN model is trained using dynamic gas and oil experimental data, but can be directly used for static oil reconstruction.

[0053] Appendix Figure 3 In the diagram, each row corresponds to a static liquid level condition, and each column shows the true GT value, the original LBP reconstruction, the LBP+cubic interpolation post-processing, and the reconstruction result using a physical constraint CNN (the method of this invention). The color scale represents the relative permittivity. (1.0~2.5, red for oil, blue for gas). As shown in the figure: the original LBP reconstructed image has severe striped and cross-shaped artifacts, and the oil-gas phase interface is submerged and unrecognizable by the artifacts; cubic interpolation can only smooth the image, and the striped structure still exists; the physically constrained CNN significantly suppresses various artifacts, and the reconstructed oil-gas phase distribution and phase interface position are basically consistent with the true GT value. Moreover, as the liquid level decreases, the decreasing trend of the oil phase proportion and interface movement reconstructed by CNN are consistent with the true value, with only a small amount of residual error near the pipe wall. This shows that the method of the present invention is also stable and effective in gas and oil media.

[0054] It is understood that this invention provides an implementation method for image reconstruction based on capacitance tomography. This implementation method solves the problems of severe artifacts in traditional LBP reconstruction and limited artifact removal capabilities of traditional post-processing methods (HDTV anisotropic diffusion, cubic interpolation) by constructing a sensitivity matrix, performing matching self-calibration preprocessing, using LBP linear back projection coarse reconstruction and U-Net convolutional neural network for artifact removal enhancement.

[0055] Experiments show that: (1) In 12 static working conditions of gas-water two-phase flow, the average RMSE of this method is 0.309, which is 52% lower than LBP (0.648) and 51% lower than HDTV (0.630), and it is stable for three mineralization levels from 0 to 39.2 μS / cm; however, image reconstruction also shows that the increase in mineralization will have a certain impact on image reconstruction. The higher the mineralization, the less accurate the measured capacitance data. (2) In the static scenario of gas-oil two-phase flow, the RMSE of this method is 0.791, which is 22.2% lower than LBP (1.018) and 17.6% lower than traditional cubic interpolation post-processing (0.960). This method achieves stable performance across media (water / oil), across mineralization levels (0~40 μS / cm), and across scenarios (dynamic training / static inference).

[0056] It should be clarified that the above discussion of the structural characteristics of the wiremesh sensor is an in-depth disclosure of the causes of the technical effects in conjunction with the preferred embodiments of the present invention, and does not constitute a limitation on the type of "capacitance tomography sensor" in the present invention. Those skilled in the art will understand that the method defined in this invention is also applicable to capacitance tomography systems employing other electrode configurations (such as conventional ring electrode arrays), as long as it follows the core process of sensitivity matrix construction, capacitance data preprocessing, back-projection coarse reconstruction, and deep learning artifact removal, and falls within the protection scope of this invention.

[0057] Furthermore, the technical effects of this invention are synergistic with the structural characteristics of the wiremesh sensor used. For example... Figure 4 As shown, the wiremesh sensor consists of two sets of orthogonally arranged electrode wires. The sensitive areas of each measurement channel are concentrated near the intersection stripes of the corresponding row and column wires. During linear back-projection reconstruction, this strip-shaped sensitive distribution is obscured as vertical stripe artifacts along the direction of the electrode wires and cross-shaped artifacts at the wire intersections. Since the spatial position and shape of these artifacts are uniquely determined by the sensor's geometry and are independent of the medium type, mineralization, and flow conditions, they constitute a deterministic and predictable systematic error, rather than random noise. This invention utilizes this structural characteristic: the wiremesh sensor generates highly structured artifact patterns, while the deep learning artifact removal model specifically learns its inverse mapping for this type of structured systematic error. The organic combination of the two enables the deep learning model to effectively suppress this structural systematic error determined by the sensor's geometry. Experiments show that this method reduces the reconstruction error by 52% and 22% compared to traditional methods in gas-water and gas-oil media, respectively, verifying the aforementioned synergistic enhancement effect.

[0058] In summary, the present invention has the following beneficial effects: (1) Significantly reduced reconstruction error: The average RMSE of CNN under the gas-water 12 working condition was 0.309, which was 52% lower than LBP (0.648) and 51% lower than HDTV (0.630).

[0059] (2) Effectively suppress strip artifacts: CNN can automatically learn and suppress the vertical stripes and cross-shaped artifacts of LBP.

[0060] (3) Generalization ability across mineralization: CNN significantly outperforms LBP and HDTV in all three mineralization levels (0~39.2 μS / cm).

[0061] (4) Method transferability across media: This method is equally effective after retraining in the gas and oil scenario (CNN vs LBP RMSE improvement of 22.2%).

[0062] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0063] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0064] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0065] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0066] The background section of this invention may include background information about the problems or environment in which the invention is being developed, and is not necessarily a description of prior art. Therefore, the content included in the background section does not constitute an admission of prior art by the applicant.

[0067] The above description provides a further detailed explanation of the present invention in conjunction with specific / preferred embodiments, and it should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various substitutions or modifications can be made to these described embodiments without departing from the concept of the present invention, and all such substitutions or modifications should be considered within the scope of protection of the present invention. In the description of this specification, the reference to terms such as "an embodiment," "some embodiments," "preferred embodiment," "example," "specific example," or "some examples," etc., indicates that the specific features, structures, materials, or characteristics described in connection with that embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in any suitable manner in one or more embodiments or examples. Without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification and the features of different embodiments or examples. Although the embodiments of the present invention and their advantages have been described in detail, it should be understood that various changes, substitutions, and modifications can be made herein without departing from the scope of protection of the patent application.

Claims

1. An image reconstruction method based on capacitance tomography, characterized in that, Includes the following steps: Sensitivity matrix construction steps: Based on the electrode arrangement and electromagnetic field simulation data of the capacitance tomography sensor, calculate and normalize the sensitivity matrix; Capacitance data preprocessing steps: Obtain the raw capacitance measurement values ​​of the capacitance tomography sensor and perform normalization processing to obtain preprocessed capacitance data; Back projection reconstruction step: Perform back projection operation on the preprocessed capacitance data and the sensitivity matrix to reconstruct a coarsely estimated image; Deep learning artifact removal steps: The coarsely estimated image is input into a pre-trained deep learning image artifact removal model, which outputs a high-precision reconstructed image with artifacts suppressed.

2. The image reconstruction method based on capacitance tomography according to claim 1, characterized in that, In the capacitance data preprocessing step, the raw capacitance measurements collected from multiple electrode pairs of the capacitance tomography sensor are calibrated and normalized using a matching self-calibration method to obtain the preprocessed capacitance data for each electrode pair. , represented as: in, The original capacitance value that was actually measured at the moment. The capacitance calibration value under the same experimental conditions is the full-load state. This refers to the capacitance calibration value under the same experimental conditions in the empty tube state.

3. The image reconstruction method based on capacitance tomography according to claim 2, characterized in that, The capacitance data preprocessing step also includes a failed electrode pair repair step: For each electrode pair, determine whether it meets one of the following conditions; if it does, it is determined to be a failed electrode pair: The absolute value of the difference between the capacitance calibration value of the electrode in the full tube state and the capacitance calibration value in the empty tube state is less than a preset threshold, or the difference is negative; The calculated preprocessed capacitance data of this electrode exceeds the preset physical reasonable range; For an electrode pair that is determined to be a failed electrode pair, its corresponding preprocessed capacitance data value is replaced with the average of the preprocessed capacitance data values ​​of its adjacent non-failed electrode pairs; wherein, the adjacent non-failed electrode pairs are the closest non-failed electrode pairs determined from the left and right sides of the failed electrode pair according to the index order of each electrode pair.

4. The image reconstruction method based on capacitance tomography according to claim 1, characterized in that, The process of reconstructing a coarsely estimated image in the back-projection reconstruction step includes: reshaping the result of the back-projection operation into a two-dimensional cross-sectional image, and setting the pixel values ​​of the area outside the pipe in the two-dimensional cross-sectional image to zero, so as to obtain the coarsely estimated image.

5. The image reconstruction method based on capacitance tomography according to claim 1, characterized in that, The deep learning image artifact removal model is built on the U-Net network structure, which adopts an encoder-decoder structure and uses reflection padding in the convolution operation.

6. The image reconstruction method based on capacitance tomography according to claim 1, characterized in that, The training set for the deep learning image artifact removal model is constructed through the following steps: Simulation steps: Generate a true image of phase distribution based on the preset flow pattern; Forward projection step: The true phase distribution image is forward projected through the initial sensitivity matrix calculated based on the electrode arrangement of the capacitance tomography sensor to obtain simulated ideal capacitance data; Data synthesis step: Superimpose real experimental noise onto the ideal capacitance data to obtain synthesized capacitance data; Back projection step: The synthesized capacitance data is subjected to back projection operation in the back projection reconstruction step to obtain a coarse estimated image with artifacts; Pairing step: Pair the coarsely estimated image with artifacts with the ground truth image of phase distribution to form training samples.

7. The image reconstruction method based on capacitance tomography according to claim 1, characterized in that, The deep learning image artifact removal model is trained using a composite loss function, which includes mean squared error loss, total variation regularization term, and outside region constraint term.

8. The image reconstruction method based on capacitance tomography according to claim 1, characterized in that, The deep learning image artifact removal model is trained using a data augmentation method that only flips left and right, and employs an early stopping strategy based on an independent validation set.

9. An image reconstruction system based on capacitance tomography, characterized in that, include: The sensitivity matrix construction module is used to calculate and normalize the sensitivity matrix based on the electrode arrangement and electromagnetic field simulation data of the capacitance tomography sensor. The capacitance data preprocessing module is used to acquire the raw capacitance measurement values ​​of the capacitance tomography sensor and perform normalization processing to obtain preprocessed capacitance data. The linear back-projection reconstruction module is used to perform back-projection operations on the preprocessed capacitance data and the sensitivity matrix to reconstruct a coarsely estimated image. The deep learning artifact removal module is used to input the coarsely estimated image into a pre-trained deep learning image artifact removal model, which outputs a high-precision reconstructed image with artifacts suppressed.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the image reconstruction method based on capacitance tomography as described in any one of claims 1 to 8.

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