A method for modifying a sensitivity matrix

Abstract

The application provides a correction method of a sensitivity matrix, which is applied to an ECT image reconstruction process, and the method comprises the following steps: obtaining an approximate medium distribution image by using a linear back projection algorithm; determining a target position based on the gray value of each pixel in the approximate medium distribution image; using positive and negative sensitivity repair coefficients to respectively correct the positive and negative sensitivities of the column where the target is located in the empty field sensitivity matrix, so as to obtain a corrected sensitivity matrix; wherein the positive sensitivity repair coefficient is smaller than the negative sensitivity repair coefficient. Based on the method, a better visual effect of a reconstructed image can be obtained, the reconstructed image has fewer artifacts, and the reconstructed gray value is closer to the actual distribution.

Description

Technical Field

[0001] This application belongs to the field of capacitance tomography technology, and particularly relates to a method for correcting a sensitivity matrix. Background Technology

[0002] Electrical capacitance tomography (ECT) is a process tomographic imaging technique that uses the capacitance between electrodes to image the distribution of media inside pipes or equipment. ECT technology has promising prospects due to its non-invasive and non-destructive measurement characteristics. In addition, its low cost, fast response, and measurement safety are also significant advantages. Therefore, ECT has a wide range of potential applications, such as visualization of two-phase flow in pipelines (oil and gas), flame detection in swirl burners, estimation of bubble size and rise velocity in gas-solid fluidized beds, and defect detection in materials.

[0003] The successful application of ECT technology largely depends on the accuracy and speed of image reconstruction algorithms. The ill-conditioned nature and soft-field characteristics of the ECT inverse problem (the non-uniform distribution of sensor sensitivity that varies with the distribution of the measured medium) make it difficult for ECT to obtain high-quality reconstructed images. Currently, image reconstruction algorithms in ECT systems typically use a fixed sensitivity matrix (e.g., the sensitivity matrix for an empty pipe, referred to as empty-field sensitivity) for image reconstruction when the medium is uniformly distributed. However, a fixed sensitivity matrix assumes that the sensitivity matrix is ​​independent of changes in the medium distribution throughout the pipe, which is clearly an unrealistic assumption. Therefore, it is necessary to correct the sensitivity matrix according to changes in the medium distribution.

[0004] Existing methods for modifying the sensitivity matrix include the following: 1) The nonlinear Landweber iterative algorithm that updates the ECT sensitivity matrix during iteration. The basic idea is that the Landweber iterative algorithm reconstructs the image based on the spatial sensitivity matrix to obtain an approximate distribution of the medium, and then resolves the ECT forward problem based on this distribution to update the sensitivity matrix. This method requires resolving the forward problem and updating the sensitivity in each iteration, thus consuming a lot of time and resulting in slow reconstruction speed. 2) The ECT nonlinear iterative reconstruction algorithm based on regularization methods. Its sensitivity matrix is ​​updated only a few times, and a specialized numerical method is used to accelerate the related calculations of the sensitivity matrix. The core idea of ​​the above algorithms is to calculate the forward problem based on the approximate medium distribution. Although using the updated sensitivity matrix improves the quality of the reconstructed image, the process of recalculating the forward problem is time-consuming, resulting in slow reconstruction speed. Summary of the Invention

[0005] In view of this, the purpose of this application is to provide a method for correcting the sensitivity matrix, which uses different repair coefficients for the positive and negative sensitivities of the target column in the spatial sensitivity matrix, and makes the repair coefficient for negative sensitivity greater than that for positive sensitivity. Based on this method, better visual effects of the reconstructed image can be obtained, with fewer artifacts and reconstructed grayscale values ​​that are closer to the actual distribution.

[0006] This application provides a method for correcting a sensitivity matrix, which is applied to the ECT image reconstruction process. The method includes:

[0007] An approximate medium distribution image is obtained using a linear back projection algorithm;

[0008] The location of the target is determined based on the gray values ​​of each pixel in the approximate medium distribution image.

[0009] Using positive and negative sensitivity correction coefficients, the positive and negative sensitivities of the target column in the air field sensitivity matrix are corrected respectively to obtain the corrected sensitivity matrix; wherein, the positive sensitivity correction coefficient is smaller than the negative sensitivity correction coefficient.

[0010] Furthermore, obtaining an approximate medium distribution image using a linear back-projection algorithm includes:

[0011] Based on the normalized capacitance vector and the normalized space-field sensitivity transpose matrix, an approximate medium distribution image is obtained using a linear back-projection algorithm.

[0012] Furthermore, before obtaining an approximate medium distribution image using a linear back-projection algorithm based on the normalized capacitance vector and the normalized space-field sensitivity transpose matrix, the method further includes:

[0013] The capacitance vector and field strength distribution were measured, and the space field sensitivity matrix and the space field sensitivity transpose matrix were calculated.

[0014] The capacitance vector and the transpose matrix of the space field sensitivity are normalized respectively to obtain the normalized capacitance vector and the normalized transpose matrix of the space field sensitivity.

[0015] Furthermore, determining the target location based on the grayscale values ​​of each pixel in the approximate medium distribution image includes:

[0016] For each pixel in an image with an approximate medium distribution, determine whether the pixel's location is the target or the background based on its grayscale value;

[0017] When the grayscale value of a pixel is 0, the location of that pixel is determined to be the background.

[0018] When the grayscale value of a pixel is not 0, the location of that pixel is determined to be the target.

[0019] Furthermore, the positive and negative sensitivity correction coefficients are used to correct the positive and negative sensitivities of the target column in the air-field sensitivity matrix, respectively, to obtain the corrected sensitivity matrix, including:

[0020] Based on the target index value vector, positive and negative sensitivity correction coefficients are used to correct the positive and negative sensitivities of the target corresponding column in the air field sensitivity matrix, respectively, to obtain the corrected sensitivity matrix.

[0021] Furthermore, after obtaining the corrected sensitivity matrix, the method further includes:

[0022] Transpose the modified sensitivity matrix to obtain the modified sensitivity transpose matrix;

[0023] The modified sensitivity matrix and the modified sensitivity transpose matrix are normalized to obtain the normalized sensitivity matrix and the normalized sensitivity transpose matrix, respectively.

[0024] Based on the normalized capacitance vector and the normalized sensitivity transpose matrix, the initial reconstructed image is obtained using a linear back projection algorithm;

[0025] Using the initial reconstructed image as the initial value for iteration, the Landweber iterative algorithm is used to obtain the reconstructed image based on the normalized sensitivity matrix and the normalized sensitivity transpose matrix.

[0026] The sensitivity matrix correction method provided in this application applies different restoration coefficients to the positive and negative sensitivities of the target column in the spatial sensitivity matrix, and makes the restoration coefficient for negative sensitivity greater than that for positive sensitivity. Based on this method, better visual effects of the reconstructed image can be obtained, with fewer artifacts and reconstructed grayscale values ​​that are closer to the actual distribution. Attached Figure Description

[0027] Figure 1 The following diagrams illustrate the air field sensitivity of different electrode pairs provided in embodiments of this application.

[0028] Figure 2 The embodiments of this application illustrate R, R based on different media distributions. 正 R 负 Spatial distribution map;

[0029] Figure 3 A flowchart of a sensitivity matrix correction method provided in an embodiment of this application is shown;

[0030] Figure 4 The embodiments of this application show reconstructed images obtained using different processing methods;

[0031] Figure 5 This application provides a comparison chart of the quality indicators of reconstructed images obtained using different processing methods, as shown in the embodiments of this application.

[0032] Figure 6 The illustrations show photographs of test models for different media provided in the embodiments of this application, approximate prototype distribution images, and reconstructed images corresponding to the three sensitivity processing methods. Detailed Implementation

[0033] To make the objectives, technical solutions, and advantages of this technical solution clearer, the following detailed description, in conjunction with specific embodiments, further illustrates this technical solution. It should be understood that these descriptions are merely exemplary and not intended to limit the scope of this technical solution.

[0034] Example 1: Introduction to electrical capacitance tomography (ECT):

[0035] A typical ECT system consists of three parts: a capacitive sensor array, a data acquisition unit, and an imaging computer. The capacitive sensor array comprises electrodes surrounding the pipe, with any two electrodes forming a capacitor. Changes in the two-phase flow distribution within the pipe cause changes in the capacitor's capacitance. The data acquisition unit measures the capacitor's capacitance and transmits it to the imaging computer. The imaging computer then reconstructs an image of the dielectric constant distribution (i.e., the dielectric distribution) of the pipe's cross-sectional area using reconstruction algorithms.

[0036] ECT image reconstruction is an inverse problem, typically solved using the ECT forward problem model. The ECT forward problem involves determining the capacitance value based on a known dielectric distribution. The discretized and linearized forward problem model can be expressed as formula (1):

[0037] C = Sg; (1)

[0038] In the formula, C is an M×1 dimensional normalized capacitance vector; g is an N×1 dimensional normalized dielectric constant vector (i.e., grayscale vector); and S is an M×N dimensional normalized sensitivity matrix.

[0039] The Landweber iterative algorithm is a typical iterative reconstruction algorithm in ECT, and its iterative formula is expressed as formula (2):

[0040]

[0041] In the formula, Let be the grayscale vector of the k-th iteration. Let be the grayscale vector of the (k+1)th iteration, where is the initial value of the iteration. This can be obtained using the Linear Back Projection (LBP) algorithm, i.e. S T S is the normalized sensitivity transpose matrix; α is the gain factor controlling the convergence rate, typically taken as α = 2 / λmax, where λmax is the square matrix S. T The maximum eigenvalue of S; P(·) is a 0 / 1 threshold operator that sets gray values ​​greater than 1 to 1 and gray values ​​less than 0 to 0.

[0042] Example 2: Analysis of the influence of actual medium distribution on sensitivity:

[0043] Since the sensitivity matrix of each electrode pair describes the distribution of the sensitive field of the ECT sensor, and the sensitivity matrix is ​​often used as prior knowledge during image reconstruction, the determination of the sensitivity matrix is ​​extremely important for the ECT system. The electric potential distribution is usually used to approximate the sensitive field. The sensitivity calculation formula based on the electric field strength in two-dimensional analysis is as follows (3):

[0044]

[0045] In the formula, E i (x,y) represents the voltage V applied to plate i. i The electric field distribution when the remaining plates are at zero potential; E j (x,y) represents the voltage V applied to plate j. j The electric field distribution when the remaining plates are at zero potential; Ω e This represents the region corresponding to pixel e.

[0046] Figure 1 The diagram shows the air field sensitivity of different electrode pairs according to embodiments of this application. Electrode 1 is the excitation electrode, and electrodes 2, 3, 4, and 5 are the measurement electrodes. Figure 1 It can be seen that: 1) The sensitivity of each pixel in each electrode pair is not uniform, and the values ​​differ greatly, especially the sensitivity values ​​of 1-2 adjacent electrodes differ greatly; 2) The sensitivity values ​​of the same pixel are also different in different electrode pairs; 3) The sensitivity of the pipe edge area is higher, while the sensitivity of the pipe center area is lower.

[0047] To analyze the influence of actual medium distribution on sensitivity, the space sensitivity matrix and actual sensitivity matrix under different medium distributions were summed, and the ratio R of the sum of each column of the actual sensitivity matrix to the sum of each column of the space sensitivity matrix, as well as the ratio R of the sum of the positive sensitivities in each column, were calculated for different medium distributions. 正 The ratio R to the sum of the negative sensitivities of each column 负 , where R, R 正 R 负The dimension of each is 1×N, where N is the number of pixels in the imaging region within the pipe. For ease of comparison, R and R under different medium distributions are compared. 正 R 负 Perform filtering, that is, set all elements greater than 2 to 2, and then apply the threshold-processed R and R'. 正 R 负 Spatial distribution mapping was performed, resulting in the following: Figure 2 The embodiments shown in this application provide R, R based on different media distributions. 正 R 负 The spatial distribution map is shown. In the map, distribution 1 and distribution 2 are used to represent different medium distributions.

[0048] Depend on Figure 2 It can be seen that, in addition to the unevenness of sensitivity values, the sensitivity is also affected by the actual medium distribution. The degree to which the sensitivity matrix is ​​affected varies depending on the medium distribution. Specifically:

[0049] 1) The magnitude of the ratio R can reflect the shape of the actual medium distribution; that is, the ratio R of the target is basically smaller than that of the background and basically less than 1. 2) The R of the target's location... 正 Most are less than 1, only a few are greater than or equal to 1, and the R value of the target location is... 正 The average value is less than 1; 3) The R value of the target location 负 Some are greater than 1, some are less than 1, but R 负 There are more values ​​less than 1 in R, and 负 The average value is less than 1; 4) The R value of the target location 负 The average value is greater than R. 正 average value.

[0050] Example 3: Based on the influence of actual medium distribution on sensitivity, a method for correcting the sensitivity matrix is ​​proposed, which is applied to the ECT image reconstruction process.

[0051] Please see Figure 3 The flowchart shown is a method for correcting the sensitivity matrix provided in an embodiment of this application.

[0052] like Figure 3 As shown, the method includes:

[0053] S101. Obtain an approximate medium distribution image using a linear back projection algorithm.

[0054] Specifically, based on the normalized capacitance vector and the normalized space-field sensitivity transpose matrix, an approximate medium distribution image is obtained using a linear back-projection algorithm.

[0055] In this step, an approximate medium distribution image is obtained using the following formula (4):

[0056]

[0057] In the formula, S is a grayscale vector; P(·) is a 0 / 1 thresholding operator that sets grayscale values ​​greater than 1 to 1 and grayscale values ​​less than 0 to 0 in the approximate medium distribution image; T C is the normalized space-field sensitivity transpose matrix; C is the normalized capacitance vector.

[0058] Before obtaining an approximate medium distribution image using a linear back-projection algorithm based on the normalized capacitance vector and the normalized space-field sensitivity transpose matrix, the method further includes:

[0059] Step 201: Measure the capacitance vector and field strength distribution, and calculate the space sensitivity matrix and the space sensitivity transpose matrix.

[0060] In this step, the field sensitivity matrix is ​​first calculated based on the field strength distribution using the above formula (3), and then the field sensitivity matrix is ​​transposed to obtain the field sensitivity transpose matrix.

[0061] Step 202: Normalize the capacitance vector and the transpose matrix of the air field sensitivity respectively to obtain the normalized capacitance vector and the normalized transpose matrix of the air field sensitivity.

[0062] S102. Determine the location of the target based on the grayscale values ​​of each pixel in the reconstructed image.

[0063] In practice, the location of the target is determined using the following methods:

[0064] Step 1021: For each pixel in the approximate medium distribution image, determine whether the pixel's location is the target or the background based on its grayscale value.

[0065] When the grayscale value of the pixel is 0, proceed to step 1022 and determine that the location of the pixel is the background.

[0066] If the grayscale value of the pixel is not 0, then step 1023 is executed to determine the location of the pixel as the target.

[0067] S103. Using positive and negative sensitivity correction coefficients, correct the positive and negative sensitivities of the target column in the air field sensitivity matrix respectively to obtain the corrected sensitivity matrix.

[0068] Wherein, the positive sensitivity repair coefficient is less than the negative sensitivity repair coefficient.

[0069] Specifically, based on the target index value vector, the positive and negative sensitivity correction coefficients are used to respectively correct the positive and negative sensitivities of the column corresponding to the target in the empty-field sensitivity matrix, and the corrected sensitivity matrix is obtained.

[0070] In this step, the following formula (5) is used to represent the target index vector:

[0071]

[0072] In the formula, find represents extracting the index value of the elements greater than zero in the gray vector among.

[0073] Furthermore, the following formula (6) is used to correct the positive and negative sensitivities of the column corresponding to the target in the empty-field sensitivity matrix:

[0074]

[0075] In the formula, SS q (i) is the i-th element in the q-th column of the empty-field sensitivity matrix, where q is an element in the target index vector Q; SS′ q (i) is the i-th element in the q-th column of the corrected sensitivity matrix; where i = 1, 2,..., M; a is the positive sensitivity correction coefficient, b is the negative sensitivity correction coefficient, a and b are constants, 0 < a < 1, 0 < b < 1, and a < b.

[0076] After obtaining the corrected sensitivity matrix, the method further includes:

[0077] Step 301: Transpose the corrected sensitivity matrix to obtain the corrected sensitivity transposed matrix.

[0078] Step 302: Normalize the corrected sensitivity matrix and the corrected sensitivity transposed matrix respectively to obtain the normalized sensitivity matrix and the normalized sensitivity transposed matrix.

[0079] Step 303: Based on the normalized capacitance vector and the normalized sensitivity transposed matrix, use the linear backprojection algorithm to obtain the initial reconstructed image.

[0080] Step 304: Take the initial reconstructed image as the iterative initial value, and use the Landweber iterative algorithm to obtain the reconstructed image according to the normalized sensitivity matrix and the normalized sensitivity transposed matrix.

[0081] Example 4: Simulation verification of the sensitivity matrix correction method:

[0082] To verify the effectiveness of the sensitivity matrix correction method proposed in this application, image reconstruction was performed under three conditions: no sensitivity correction, correction using the same coefficients in existing technologies (i.e., a = 0.5, b = 0.5), and correction using different coefficients (i.e., a = 0.5, b = 0.7) proposed in this application. The Landweber iterative algorithm was set to iterate 30 times, yielding the following results: Figure 4 and 5 The image shown is a comparison of reconstructed images and their quality indices obtained using different processing methods. Figure 5 The correlation coefficient (CC), relative image error (IE), and spatial image error (SIE) are used to quantitatively evaluate the quality of the reconstructed image. CC represents the correlation between the reconstructed image and the real distribution, and a CC value closer to 1 is better; IE represents the difference in dielectric constant between the reconstructed image and the real distribution, and a smaller IE value is better; SIE represents spatial error information, which includes errors in the reconstructed target such as shape, position, and area, and a smaller SIE value is better.

[0083] pass Figure 4 and Figure 5 It can be seen that:

[0084] 1) In terms of the visual effect of the reconstructed image, the visual effect of the reconstructed image using the same coefficient and the different coefficients of the sensitivity matrix are both better than the case where the sensitivity is not modified, and the visual effect of the reconstructed image using the different coefficients of the correction method of the present application is better than the case where the same coefficients are used.

[0085] 2) In terms of reconstruction quality indicators, the reconstruction quality indicators of the different coefficient correction methods in this application are basically optimal.

[0086] Example 5: Experimental verification of the sensitivity matrix correction method:

[0087] The measured capacitance data were obtained using a capacitance tomography system from ITS. The two-phase medium distribution within the pipe was simulated by placing a 20mm diameter acrylic rod inside the sensor. Figure 6 The images shown are photographs of test models for different media provided in the embodiments of this application, approximate prototype distribution images, and reconstructed images corresponding to the three sensitivity processing methods. Figure 6 In the diagram, the different media distributions are: media distribution 1, 2, and 3. The three sensitivity processing methods are: Landweber no correction, Landweber correction with the same coefficient, and Landweber correction with different coefficients. Through... Figure 6It can be seen that for distributions 1-3, the reconstruction images obtained by the different coefficient correction methods of this application have the best visual effect, and the reconstruction images obtained by the algorithm of this application have fewer artifacts and the reconstructed gray values ​​are closer to the original distribution.

[0088] The above content is only a preferred embodiment of the present invention. For those skilled in the art, many changes can be made in the specific implementation and application scope based on the ideas of the present invention. As long as these changes do not depart from the concept of the present invention, they all fall within the protection scope of this patent.

Claims

1. A method for correcting a sensitivity matrix, characterized in that, The method is applied to the ECT image reconstruction process, and the method includes: An approximate medium distribution image is obtained using a linear back projection algorithm; The location of the target is determined based on the gray values ​​of each pixel in the approximate medium distribution image. Positive and negative sensitivity correction coefficients are used to correct the positive and negative sensitivities of the target column in the air field sensitivity matrix, respectively, to obtain the corrected sensitivity matrix; wherein the positive sensitivity correction coefficient is less than the negative sensitivity correction coefficient, and both the positive and negative sensitivity correction coefficients are constants less than 1 and greater than 0.

2. The method as described in claim 1, characterized in that, The method of obtaining an approximate medium distribution image using a linear back-projection algorithm includes: Based on the normalized capacitance vector and the normalized space-field sensitivity transpose matrix, an approximate medium distribution image is obtained using a linear back-projection algorithm.

3. The method as described in claim 2, characterized in that, Before obtaining an approximate medium distribution image using a linear back-projection algorithm based on the normalized capacitance vector and the normalized space-field sensitivity transpose matrix, the method further includes: The capacitance vector and field strength distribution were measured, and the space field sensitivity matrix and the space field sensitivity transpose matrix were calculated. The capacitance vector and the transpose matrix of the space field sensitivity are normalized respectively to obtain the normalized capacitance vector and the normalized transpose matrix of the space field sensitivity.

4. The method as described in claim 1, characterized in that, Determining the target location based on the grayscale values ​​of each pixel in an approximate medium distribution image includes: For each pixel in an image with an approximate medium distribution, determine whether the pixel's location is the target or the background based on its grayscale value; When the grayscale value of a pixel is 0, the location of that pixel is determined to be the background. When the grayscale value of a pixel is not 0, the location of that pixel is determined to be the target.

5. The method as described in claim 1, characterized in that, The positive and negative sensitivity correction coefficients are used to correct the positive and negative sensitivities of the target column in the airfield sensitivity matrix, respectively, to obtain the corrected sensitivity matrix, including: Based on the target index value vector, positive and negative sensitivity correction coefficients are used to correct the positive and negative sensitivities of the target corresponding column in the air field sensitivity matrix, respectively, to obtain the corrected sensitivity matrix.

6. The method as described in claim 1, characterized in that, After obtaining the corrected sensitivity matrix, the method further includes: Transpose the modified sensitivity matrix to obtain the modified sensitivity transpose matrix; The modified sensitivity matrix and the modified sensitivity transpose matrix are normalized to obtain the normalized sensitivity matrix and the normalized sensitivity transpose matrix, respectively. Based on the normalized capacitance vector and the normalized sensitivity transpose matrix, the initial reconstructed image is obtained using a linear back projection algorithm; Using the initial reconstructed image as the initial value for iteration, the Landweber iterative algorithm is used to obtain the reconstructed image based on the normalized sensitivity matrix and the normalized sensitivity transpose matrix.

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