Dual background image reconstruction and fusion method for electrical capacitance tomography

Abstract

This invention relates to a method for dual background image reconstruction and fusion in capacitance tomography, the method being as follows: (1) Constructing a capacitance tomography system model and obtaining the sensitivity fields of two capacitance tomography systems that form a dual background relationship. (2) Obtaining capacitance measurement data of a pipe filled with a first medium A and a second medium B; simultaneously obtaining capacitance measurement data with the first medium A as the background and the second medium B as the object under test. (3) Using the Landweber iterative algorithm, reconstructing images with the first medium A and the first medium B as the background respectively, and obtaining their reconstructed image results. (4) Fusing the reconstructed image results based on physical consistency constraints, and outputting the final fused image reconstruction result. This invention improves the quality of the reconstructed image, making the reconstructed medium distribution closer to the real distribution; it also improves the robustness and consistency of the image reconstruction results.

Description

Technical Field

[0001] This invention relates to a method for dual background image reconstruction and fusion in capacitance tomography, belonging to the field of process tomography technology. Background Technology

[0002] Capacitive tomography (CMT) is a process imaging technique for detecting multiphase flow parameters, developed in the mid-to-late 1980s. Due to its advantages such as non-invasiveness, fast response, good safety, and low cost, CMT has a very broad application prospect. Currently, it has been applied in many fields, such as monitoring oil / gas two-phase flow in crude oil pipelines, gas-solid two-phase flow in wind power transmission systems, gas-solid material distribution in fluidized beds, flame imaging in porous media, and grain moisture distribution in grain silos. The basic idea of ​​CMT is to measure the capacitance between all electrode combinations surrounding the measured area and then use an image reconstruction algorithm to infer the internal medium distribution of the pipeline. However, CMT still suffers from underdeterminism, ill-conditioned nature, nonlinearity, and "soft field" characteristics. These problems result in current image reconstruction algorithms having relatively low image accuracy and unsatisfactory edge reconstruction effects. Therefore, research on image reconstruction algorithms based on CMT has significant theoretical and engineering value. Summary of the Invention

[0003] The technical problem this invention addresses is a method for dual background image reconstruction and fusion in capacitance tomography. This invention first obtains the sensitivity fields of two capacitance tomography systems forming a dual background relationship. With the capacitance projection data unchanged, a conventional image reconstruction algorithm (e.g., using the Landweber iterative algorithm) is used to reconstruct the image using a first medium A as the background, yielding a reconstructed image. Simultaneously, another image reconstruction algorithm (e.g., using the Landweber iterative algorithm) is used to reconstruct the image using a first medium B as the background, yielding a reconstructed image. Then, based on physical consistency constraints, the two image reconstruction results forming a dual background relationship are obtained. Finally, the fused image reconstruction result is output. This invention significantly improves the quality of the reconstructed image, making the reconstructed medium distribution closer to the true distribution; it also improves the robustness and consistency of the image reconstruction results.

[0004] To solve the above problems, the specific technical solution of the present invention is as follows:

[0005] A method for dual background image reconstruction and fusion in capacitance tomography includes the following steps:

[0006] Step 1: Construct a capacitance tomography system model and obtain the dielectric constant using Comsol finite element simulation software. Sensitivity field of the capacitance tomography system of the first medium A ; and then obtain a dielectric constant of Sensitivity field of the capacitance tomography system of the second medium B ;

[0007] Sensitivity field of the capacitance tomography system of the first medium A for:

[0008] ;

[0009] in The electric field strength vector inside the pipe when the pipe space is filled with a first medium A, and an excitation voltage V is applied to the i-th plate while the other plates are grounded; The electric field strength vector inside the pipe when the pipe space is filled with a first medium A, and an excitation voltage V is applied to the j-th plate while the other plates are grounded; These are the pixels in the image.

[0010] For the sensitivity field of the capacitance tomography system of the second medium B for:

[0011]

[0012] Among them are The electric field strength vector inside the pipe when the pipe space is filled with the second medium B, and the excitation voltage V is applied to the i-th plate while the other plates are grounded; The electric field strength vector inside the pipe when the pipe space is filled with the second medium B, and the excitation voltage V is applied to the j-th plate while the other plates are grounded; It can be viewed as the pixels of an image.

[0013] Step 2: Obtain the dielectric constant as Using the first dielectric A as the background, and with a dielectric constant of Capacitance measurement data of the object being measured ; Obtain capacitance measurement data when the inside of the pipe is filled with the first medium A ; Obtain capacitance measurement data when the inside of the pipe is filled with the second medium B. .

[0014] Step 3: Based on the sensitivity field of the first medium A and capacitance data Image reconstruction is performed using the first medium A as the background to obtain the reconstructed image result. ;

[0015] Normalized capacitance data is Then, the Landweber image reconstruction algorithm is used for image reconstruction. The iterative formula of the Landweber image reconstruction algorithm is: ;

[0016] in, and These are the image reconstruction results for the k-th and k+1-th reconstructions, respectively, using the first medium A as the background. for , It is a sensitivity field The transpose of the matrix, It is a relaxation factor with the first medium A as the background, and it must satisfy... To ensure algorithm convergence, where yes The largest eigenvalue.

[0017] Step 4: Based on the sensitivity field of the second medium B and capacitance data Image reconstruction is performed using the second medium B as the background to obtain the reconstructed image result. ;

[0018] Normalized capacitance data is Then, the Landweber image reconstruction algorithm is used for image reconstruction. The iterative formula of the Landweber image reconstruction algorithm is: ;

[0019] Among them, here and These are the image reconstruction results for the k-th and k+1-th reconstructions, respectively, using the second medium B as the background. for , It is a sensitivity field The transpose of the matrix, The relaxation factor with the second medium B as the background must satisfy the following conditions. To ensure algorithm convergence, where yes The largest eigenvalue.

[0020] Step 5: Obtain the image reconstruction results of two images that form a dual background relationship based on physical consistency constraints. and The Landweber iterative algorithm and the consistency constraint of the dual background are combined to obtain reconstructed images with a first medium A and a second medium B as backgrounds. The distribution of the first medium A... Distribution of the second medium B and dual variables The updated formula is shown below:

[0021] (a) Update the first distribution :

[0022] ;

[0023] (b) Update the second distribution :

[0024] ;

[0025] (c) Update the dual variable :

[0026] .

[0027] in This represents the distribution of the first medium A after the (k+1)th iteration. This represents the distribution of the second medium B after the (k+1)th iteration. This is the result of the (k+1)th iteration of the dual variable; Based on the first dielectric constant and the first dielectric constant The sum of; The normalized value of the background capacitance is based on the first dielectric A. Normalized value of background capacitance with the first dielectric B as the background capacitance; The relaxation factor is based on the first medium A. The relaxation factor is based on the second medium B. It is a penalty factor that controls the strength of the constraint.

[0028] Step 6: Output the final fused image reconstruction result :

[0029]

[0030] The fusion method here is to reconstruct the results of two images that form a dual background relationship. and Subtract corresponding pixels and then Elements with a pixel value less than 0 are set to 0.

[0031] Beneficial effects of this invention:

[0032] This invention constructs capacitance tomography system models using a first medium A and a second medium B as backgrounds. Specifically, it adds a second medium B with a certain distribution to the first medium A background, and removes a second medium B of the same size and distribution to the second medium B background. This invention fully utilizes the complementary nature of the two capacitance tomography systems forming a dual background relationship. While keeping the capacitance projection data unchanged, it also leverages the two perspectives formed by the dual backgrounds. Using the sensitivity fields of the two capacitance tomography systems forming a dual background relationship, it employs a specific image reconstruction algorithm to obtain image reconstruction results with a dual relationship. Then, based on physical consistency constraints, it obtains the image reconstruction results of the two dual background relationships, and finally outputs the fused image reconstruction result. This invention, to some extent, overcomes the intentional underdeterminacy, nonlinearity, and "soft field" characteristics of capacitance tomography systems, improving the quality of the reconstructed image and making the reconstructed medium distribution closer to the real distribution; it also improves the robustness and consistency of the image reconstruction results. This invention also provides new approaches and methods for the research and application of capacitance tomography, and has significant practical application value. Attached Figure Description

[0033] Figure 1 This is a flowchart illustrating the workflow of a dual background image reconstruction and fusion method for capacitance tomography.

[0034] Figure 2 This is a flowchart of an image reconstruction algorithm based on physical consistency constraints.

[0035] Figure 3 This is a comparison of experimental results for various capacitance tomography image reconstruction methods. Detailed Implementation

[0036] The workflow of the dual background image reconstruction and fusion method for capacitance tomography is as follows: Figure 1 As shown, the method mainly includes the data preparation stage; the dual image reconstruction stage; the dual image fusion stage; and the reconstructed image evaluation stage. The dual background image reconstruction and fusion method for capacitance tomography includes the following steps:

[0037] (1) Data preparation stage

[0038] 1.1) Here, the first medium A is air, and its dielectric constant is... The second dielectric, B, is quartz glass, and its dielectric constant is... The sensitivity field of a capacitance tomography system using air as the first medium A was obtained through Comsol finite element simulation software. Then, the sensitivity field of the capacitance tomography system using quartz glass as the second medium B is obtained. ;

[0039] 1.2) Using air A as the background and quartz glass as the object under test, the object field distribution is as follows: Figure 3 The original flow patterns of two-block and three-block flows are shown, and their capacitance measurement data are obtained respectively. Simultaneously, capacitance measurement data is obtained when the pipe is filled with air. ; Obtain capacitance measurement data when the inside of the pipe is filled with quartz glass. .

[0040] (2) Dual image reconstruction stage

[0041] The flowchart of the dual image reconstruction stage is as follows: Figure 2 As shown. The internal mesh of the pipe is divided into 41*41 sections; the maximum number of iterations is 1000.

[0042] 2.1) Image reconstruction is performed using the first medium A (air) as the background to obtain the distribution of the second medium B (quartz glass). Its capacitance normalized data is as follows: Image reconstruction was performed using the second medium, B (quartz glass), as the background to obtain the distribution of the first medium, A (air). Its capacitance-normalized data is as follows: .

[0043] 2.2) The image reconstruction results obtained by using the linear back projection algorithm as the background of the first medium air A and the second medium quartz glass B are used as the initial values.

[0044] 2.3) The Landweber iterative algorithm and the consistency constraint of the dual background are combined to obtain the reconstructed image results with the first medium A as the background and the second medium B as the background. The distribution of the first medium A... Distribution of the second medium B and dual variables The updated formula is shown below:

[0045] (a) Update the first distribution :

[0046] ;

[0047] (b) Update the second distribution :

[0048] ;

[0049] (c) Update the dual variable :

[0050] ,here It is 4.75.

[0051] (3) Image fusion stage

[0052] The fusion method here is to reconstruct the results of two images that form a dual background relationship. and Subtract corresponding pixels and then Set the values ​​of pixels less than 0 to 0. This will give you the final image reconstruction result.

[0053] (4) Image Reconstruction Evaluation Stage

[0054] The evaluation metric for reconstructed images is image error. and correlation coefficient Their specific formulas are:

[0055]

[0056]

[0057] In the formula The original dielectric constant distribution grayscale vector, The grayscale image vector of the image reconstruction result. and They are respectively and The average value. Image error. The smaller the better; correlation coefficient The larger the better. Table 1 is a comparison table of image reconstruction results indicators between the Tikhonov image reconstruction algorithm and the algorithm of this invention. It can be seen from Table 1 that the method of this invention is completely superior to the reconstruction results of the Tikhonov image reconstruction algorithm.

[0058] Table 1: Comparison of Image Reconstruction Result Indicators between Tikhonov Image Reconstruction Algorithm and the Method of this Invention

[0059]

[0060] The above description is merely a preferred embodiment of the present invention, and the method of the present invention can also be applied to other tomographic imaging systems such as electromagnetic tomography and electrical impedance tomography. It should be noted that those skilled in the art can make various modifications and improvements without departing from the principles of the present invention, and these modifications and improvements should also be considered within the scope of protection of the present invention.

Claims

1. A method for dual background image reconstruction and fusion in capacitance tomography, characterized in that, Includes the following steps: Step 1) Construct a capacitance tomography system model, with the first medium A and the second medium B as backgrounds, and obtain the sensitivity field of the capacitance tomography system with the first medium A and the second medium B as backgrounds respectively using Comsol finite element simulation software. Step 2) Obtain capacitance measurement data with the first medium A as the background and the second medium B as the object field distribution; obtain full-pipe capacitance measurement data when the pipe is filled with the first medium A and when the pipe is filled with the second medium B respectively; Step 3) Based on the sensitivity field and capacitance measurement data of the capacitance tomography system with the first medium A as the background obtained in Step 1) and Step 2), perform image reconstruction to obtain the reconstructed image result with the first medium A as the background. Step 4) Based on the sensitivity field and capacitance measurement data of the capacitance tomography system with the second medium B as the background obtained in Step 1) and Step 2), perform image reconstruction to obtain the reconstructed image result with the second medium B as the background. Step 5) Obtain the reconstruction results of two images that form a dual background relationship based on physical consistency constraints; Step 6) Fuse the reconstruction results of the two images that form a dual background relationship and output the final image reconstruction result.

2. The method for dual background image reconstruction and fusion in capacitance tomography according to claim 1, characterized in that, In step 1), the specific method is as follows: Sensitivity field of capacitance tomography system for: ； in The electric field strength vector inside the pipe when an excitation voltage V is applied to the i-th plate and the other plates are grounded; The electric field strength vector inside the pipe when an excitation voltage V is applied to the j-th plate and the other plates are grounded; These are the pixels in the image.

3. The method for dual background image reconstruction and fusion in capacitance tomography according to claim 1, characterized in that, In step 3), the capacitance measurement data needs to be normalized first, and then the image reconstruction is performed using the Landweber iterative algorithm.

4. The method for dual background image reconstruction and fusion in capacitance tomography according to claim 1, characterized in that, In step 4), the full-pipe capacitance measurement data when the pipe is filled with the second medium B needs to be subtracted from the capacitance measurement data before normalization, and then the image reconstruction is performed using the Landweber iterative algorithm.

5. The method for dual background image reconstruction and fusion in capacitance tomography according to claim 1, characterized in that, In step 5), the Landweber iterative algorithm and the consistency constraint of the dual background are combined to obtain the reconstructed image results with the first medium A as the background and the second medium B as the background. The distribution of the first medium A... Distribution of the second medium B and dual variables The updated formula is shown below: (a) Update the first distribution : ； (b) Update the second distribution : ； (c) Update the dual variable : 。 in This represents the distribution of the first medium A after the (k+1)th iteration. This represents the distribution of the second medium B after the (k+1)th iteration. This is the result of the (k+1)th iteration of the dual variable; Based on the first dielectric constant and the first dielectric constant The sum of; The normalized value of the background capacitance is based on the first dielectric A. Normalized value of background capacitance with the first dielectric B as the background capacitance; The relaxation factor is based on the first medium A. The relaxation factor is based on the second medium B. It is a penalty factor that controls the strength of the constraint.

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