Method for correcting sensitivity matrix

Abstract

The invention provides a method for correcting a sensitivity matrix, and the method is applied to an ECT image reconstruction process, and comprises the steps: obtaining an approximate medium distribution image through employing a linear back projection algorithm; determining the position of the target based on the gray value of each pixel in the approximate medium distribution image; respectively correcting the positive sensitivity and the negative sensitivity of the column where the target is located in the empty field sensitivity matrix by using the positive sensitivity repair coefficient and the negative sensitivity repair coefficient 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 the reconstructed image can be obtained, the reconstructed image has fewer artifacts, and the reconstructed gray value is closer to actual distribution.

Description

Technical Field

[0001] The present application belongs to the technical field of electrical capacitance tomography, and in particular to a correction method for a sensitivity matrix. Background Art

[0002] Electrical capacitance tomography (ECT) is a process tomography technique that uses the capacitance between the plates to image the medium distribution inside a pipeline or equipment. ECT technology has a good development prospect because it has non-invasive and non-destructive measurement characteristics. In addition, its low cost, fast response and safe measurement are also its significant advantages. Therefore, ECT has a wide range of potential applications, such as visualization of pipeline oil and gas two-phase flow, swirl burner flame detection, estimation of bubble size and bubble rise velocity in gas-solid fluidized beds, and material defect detection.

[0003] The successful application of ECT technology depends largely on the accuracy and speed of the image reconstruction algorithm. The pathological and soft field characteristics of the ECT inverse problem (the sensitivity distribution of the sensor is uneven and changes with the distribution of the measured medium) make it difficult for ECT to obtain high-quality reconstructed images. At present, the image reconstruction algorithm in the ECT system usually uses a fixed sensitivity matrix when the medium is uniformly distributed (such as the sensitivity matrix when the pipe is empty, referred to as empty field sensitivity) for image reconstruction. However, the fixed sensitivity matrix assumes that the sensitivity matrix is ​​independent of the distribution changes of the medium inside the entire pipe, which is obviously an unrealistic assumption. Therefore, it is necessary to correct the sensitivity matrix according to the changes in the medium distribution.

[0004] Existing methods for correcting the sensitivity matrix include the following: 1) The nonlinear Landweber iterative algorithm that updates the ECT sensitivity matrix during the iteration process. The basic idea of ​​this method is that the Landweber iterative algorithm performs image reconstruction based on the empty field sensitivity matrix to obtain the approximate distribution of the medium, and then re-solves the ECT positive problem based on this distribution to update the sensitivity matrix. This method needs to re-solve the positive problem and update the sensitivity in each iteration process, so it is time-consuming and the reconstruction speed is slow. 2) The ECT nonlinear iterative reconstruction algorithm based on the regularization method, in which the sensitivity matrix is ​​only updated a small number of times, and a special numerical method is used to accelerate the relevant calculations of the sensitivity matrix. The core idea of ​​the above algorithms is to calculate the positive problem based on the approximate medium distribution. Although the use of the updated sensitivity matrix improves the quality of the reconstructed image, the process of recalculating the positive problem is time-consuming, so the reconstruction speed is slow. Summary of the invention

[0005] In view of this, the purpose of this application is to provide a correction method for the sensitivity matrix, using different repair coefficients for the positive and negative sensitivities of the target column in the empty field sensitivity matrix, and making the negative sensitivity repair coefficient greater than the positive sensitivity repair coefficient. Based on this method, a better visual effect of the reconstructed image can be obtained, the reconstructed image has fewer artifacts, and the reconstructed gray value is closer to the actual distribution.

[0006] The present application provides a sensitivity matrix correction method, which is applied to an ECT image reconstruction process, and comprises:

[0007] The linear back-projection algorithm is used to obtain an approximate medium distribution image;

[0008] Determine the location of the target based on the gray value of each pixel in the approximate medium distribution image;

[0009] The positive and negative sensitivity repair coefficients are used to respectively correct the positive and negative sensitivities of the columns where the targets are located in the empty field sensitivity matrix to obtain a corrected sensitivity matrix; wherein the positive sensitivity repair coefficient is smaller than the negative sensitivity repair coefficient.

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

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

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

[0013] The capacitance vector and field intensity distribution are measured, and the empty field sensitivity matrix and the empty field sensitivity transposed matrix are calculated;

[0014] The capacitance vector and the empty field sensitivity transposed matrix are normalized respectively to obtain a normalized capacitance vector and a normalized empty field sensitivity transposed matrix.

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

[0016] For each pixel in the approximate medium distribution image, determine whether the location of the pixel is a target or background according to the gray value of the pixel;

[0017] When the gray value of the pixel is 0, the location of the pixel is determined to be the background;

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

[0019] Furthermore, the positive and negative sensitivity repair coefficients are used to respectively correct the positive and negative sensitivities of the columns where the targets are located in the empty field sensitivity matrix to obtain a corrected sensitivity matrix, including:

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

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

[0022] Transposing the modified sensitivity matrix to obtain a modified sensitivity transposed matrix;

[0023] The corrected sensitivity matrix and the corrected sensitivity transposed matrix are normalized respectively to obtain a normalized sensitivity matrix and a normalized sensitivity transposed matrix;

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

[0025] The initial reconstructed image is used as an iteration initial value, and a Landweber iterative algorithm is used to obtain a reconstructed image according to a normalized sensitivity matrix and a normalized sensitivity transposed matrix.

[0026] The sensitivity matrix correction method provided in the present application adopts different repair coefficients for the positive and negative sensitivities of the target column in the empty field sensitivity matrix, and makes the negative sensitivity repair coefficient greater than the positive sensitivity repair coefficient. Based on this method, a better visual effect of the reconstructed image can be obtained, the reconstructed image has fewer artifacts, and the reconstructed grayscale value is closer to the actual distribution. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 The empty field sensitivity diagrams under different electrode plate pairs provided in the embodiments of the present application are shown;

[0028] Figure 2 The R and R based on different medium distributions provided in the embodiment of the present application are shown. 正 , R 负 Spatial distribution map of

[0029] Figure 3 A flow chart showing a method for correcting a sensitivity matrix provided in an embodiment of the present application is shown;

[0030] Figure 4 shows the reconstructed images obtained by using different processing methods provided in the embodiments of the present application;

[0031] Figure 5 A comparison chart of reconstructed image quality indicators obtained using different processing methods provided in an embodiment of the present application is shown;

[0032] Figure 6 Photos of test models of different media provided in the embodiments of the present application, approximate prototype distribution images, and reconstructed images corresponding to three sensitivity processing methods are shown. DETAILED DESCRIPTION

[0033] In order to make the purpose, technical solution and advantages of the technical solution more clear, the technical solution is further described in detail below in conjunction with specific implementation methods. It should be understood that these descriptions are only exemplary and are not intended to limit the scope of the technical solution.

[0034] Embodiment 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 consists of electrodes surrounding the pipeline, and any two electrodes form a capacitor. Changes in the distribution of the two-phase flow in the pipeline will cause changes in the capacitance value of the capacitor. The data acquisition unit measures the capacitance value of the capacitor and transmits it to the imaging computer. The imaging computer reconstructs the dielectric constant distribution (i.e., medium distribution) image of the cross-sectional area of ​​the pipeline through a reconstruction algorithm.

[0036] ECT image reconstruction belongs to the inverse problem research, which is usually realized with the help of the ECT forward problem model. The ECT forward problem is to find the capacitance value based on the known medium distribution. The discretized and linearized forward problem model can be expressed as formula (1):

[0037] C=Sg; (1)

[0038] Wherein, C is the normalized capacitance value vector of M×1 dimension; g is the normalized dielectric constant vector (i.e., grayscale vector) of N×1 dimension; and S is the normalized sensitivity matrix of M×N dimension.

[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, is the grayscale vector of the kth iteration, is the grayscale vector of the k+1th iteration, where the initial value of the iteration It can be obtained by using the Linear Back Projection (LBP) algorithm, that is, S T is the normalized sensitivity transposed matrix; α is the gain factor that controls the convergence rate, generally α = 2 / λmax, where λmax is the square matrix S T The maximum eigenvalue of S; P(·) is a 0, 1 threshold processing 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 a priori knowledge during image reconstruction, the determination of the sensitivity matrix is ​​extremely important for the ECT system. The 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 field intensity distribution when the other plates are at zero potential; E j (x,y) represents the voltage V applied to plate j. j , the field intensity distribution when the other plates are at zero potential; Ω e Represents the area corresponding to pixel e.

[0046] Figure 1 The figure shows the empty field sensitivity diagram under different electrode pairs provided in the embodiment of the present application. Among them, electrode 1 is the excitation electrode, and electrodes 2, 3, 4, and 5 are respectively the measurement electrodes. Figure 1 It can be seen that: 1) The sensitivity of each pixel in each electrode pair is uneven, and the values ​​vary greatly, especially the sensitivity values ​​of 1-2 adjacent electrodes vary greatly; 2) The sensitivity values ​​of the same pixel in different electrode pairs are also different; 3) The sensitivity of the edge area of ​​the pipeline is higher, while the sensitivity of the central area of ​​the pipeline is lower.

[0047] In order to analyze the influence of actual medium distribution on sensitivity, the empty field sensitivity matrix and the actual sensitivity matrix under different medium distributions are summed respectively, and the ratio R of the sum of each column of the actual sensitivity matrix under different medium distributions to the sum of each column of the empty field sensitivity matrix and the ratio R of the sum of each column of positive sensitivity are calculated. 正 The ratio of the sum of the negative sensitivities of each column R 负 , where R, R 正 , R 负The dimensions of are all 1×N, where N is the number of pixels in the imaging area of ​​the pipeline. 正 , R 负 Perform filtering, that is, set the elements greater than 2 to 2, and use the threshold value R and R 正 , R 负 By plotting the spatial distribution, we can obtain Figure 2 The embodiment of the present application shown in the figure provides R and R based on different medium distributions. 正 , R 负 In the figure, 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 uneven sensitivity values, the sensitivity is also affected by the actual medium distribution. When the medium distribution is different, the sensitivity matrix is ​​affected to different degrees. Specifically:

[0049] 1) The size 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 the background, and basically less than 1; 2) The R at the target location 正 Most of them are less than 1, and only a few are greater than or equal to 1. 正 The average value is less than 1; 3) R at 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 负 The average value is less than 1; 4) R of the target location 负 The average value is greater than R 正 average value.

[0050] Embodiment 3: Based on the influence of actual medium distribution on sensitivity, a sensitivity matrix correction method is proposed, and the method is applied to the ECT image reconstruction process.

[0051] See also Figure 3 The flowchart of the sensitivity matrix correction method provided in the embodiment of the present application is shown.

[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 empty field sensitivity transposed matrix, a linear back-projection algorithm is used to obtain an approximate medium distribution image.

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

[0056]

[0057] In the formula, is a grayscale vector; P(·) is a 0, 1 threshold processing operator that sets grayscale values ​​greater than 1 to 1 and grayscale values ​​less than 0 to 0 in the medium distribution image used for approximation; S T is the normalized empty field sensitivity transposed matrix; C is the normalized capacitance vector.

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

[0059] Step 201: Measure and obtain the capacitance vector and field intensity distribution, and calculate the empty field sensitivity matrix and the empty field sensitivity transposed matrix.

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

[0061] Step 202: Normalize the capacitance vector and the empty field sensitivity transposed matrix respectively to obtain a normalized capacitance vector and a normalized empty field sensitivity transposed matrix.

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

[0063] In specific implementation, the target location is determined by the following method:

[0064] Step 1021 : for each pixel in the approximate medium distribution image, determine whether the location of the pixel is a target or background according to the gray value of the pixel.

[0065] When the gray value of the pixel is 0, step 1022 is executed to determine that the location of the pixel is the background;

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

[0067] S103, using positive and negative sensitivity repair coefficients, respectively correcting the positive and negative sensitivities of the column where the target is located in the empty field sensitivity matrix to obtain a corrected sensitivity matrix.

[0068] Among them, the positive sensitivity repair coefficient is smaller 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 correct the positive and negative sensitivities of the corresponding column of the target in the empty field sensitivity matrix, respectively, to obtain the corrected sensitivity matrix.

[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 element 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 corresponding column of 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 the 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: Use 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] In order to verify the effectiveness of the sensitivity matrix correction method of the present application, the Landweber iterative algorithm is used to correct the sensitivity without correction, the correction method using the same coefficient (i.e., a=0.5, b=0.5) in the prior art, and the correction method using different coefficients (i.e., a=0.5, b=0.7) proposed in the present application. Image reconstruction is performed under three conditions, wherein the number of iterations of the Landweber iterative algorithm is set to 30, and the following is obtained: Figure 4 and 5 The comparison chart of reconstructed images and reconstructed image quality indicators obtained using different processing methods is shown in FIG. 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 true distribution. The closer CC is to 1, the better. IE represents the difference in dielectric constant between the reconstructed image and the true distribution. The smaller the IE value, the better. SIE represents spatial error information, which includes the errors in the reconstructed target such as shape, position, and area. The smaller the SIE value, the better.

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

[0084] 1) As far as the visual effect of the reconstructed image is concerned, the visual effect of the reconstructed image using the correction method of the sensitivity matrix with the same coefficient and the correction method of the different coefficients of the present application is better than the case where the sensitivity is not corrected, and the visual effect of the reconstructed image using the correction method of the different coefficients of the present application is better than the case with the same coefficients.

[0085] 2) As far as reconstruction quality indicators are concerned, the reconstruction quality indicators of the correction methods of different coefficients in this application are basically optimal.

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

[0087] The measured capacitance data were obtained using the capacitance tomography system of ITS. A 20 mm diameter organic glass rod was placed inside the sensor to simulate the distribution of two-phase media in the pipeline. Figure 6 Shown are photos of test models of different media provided in the embodiments of the present application, approximate prototype distribution images, and reconstructed images corresponding to three sensitivity processing methods. Figure 6 In the figure, different media distributions are: media distribution 1, 2, 3, and three sensitivity processing methods are: Landweber without correction, Landweber with same coefficient correction, and Landweber with different coefficient correction. Figure 6It can be seen that for distributions 1-3, the reconstructed image visual effects of the correction methods of different coefficients of the present application are optimal, and the reconstructed image artifacts of the algorithm of the present application are fewer, and the reconstructed grayscale values ​​are closer to the prototype distribution.

[0088] The above contents are only preferred embodiments of the present invention. For ordinary technicians in this field, many changes can be made in the specific implementation methods and application scopes based on the ideas of the present technical content. As long as these changes do not deviate from the concept of the present invention, they all fall within the scope of protection 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 comprises: The linear back-projection algorithm is used to obtain an approximate medium distribution image; Determine the location of the target based on the gray value of each pixel in the approximate medium distribution image; The positive and negative sensitivity repair coefficients are used to respectively correct the positive and negative sensitivities of the columns where the targets are located in the empty field sensitivity matrix to obtain a corrected sensitivity matrix; wherein the positive sensitivity repair coefficient is smaller than the negative sensitivity repair coefficient.

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

3. The method according to claim 2, characterized in that Before obtaining an approximate medium distribution image by using a linear back-projection algorithm based on the normalized capacitance vector and the normalized empty field sensitivity transposed matrix, the method further includes: The capacitance vector and field intensity distribution are measured, and the empty field sensitivity matrix and the empty field sensitivity transposed matrix are calculated; The capacitance vector and the empty field sensitivity transposed matrix are normalized respectively to obtain a normalized capacitance vector and a normalized empty field sensitivity transposed matrix.

4. The method according to claim 1, characterized in that The step of determining the location of the target based on the grayscale value of each pixel in the approximate medium distribution image includes: For each pixel in the approximate medium distribution image, determine whether the location of the pixel is a target or background according to the gray value of the pixel; When the gray value of the pixel is 0, the location of the pixel is determined to be the background; When the gray value of the pixel is not 0, the location of the pixel is determined to be the target.

5. The method according to claim 1, characterized in that The positive and negative sensitivity repair coefficients are used to respectively correct the positive and negative sensitivities of the columns where the targets are located in the empty field sensitivity matrix to obtain a corrected sensitivity matrix, including: Based on the target index value vector, the positive and negative sensitivity repair coefficients are used to respectively correct the positive and negative sensitivities of the target corresponding columns in the empty field sensitivity matrix to obtain a corrected sensitivity matrix.

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

Images