Electrical capacitance tomography image reconstruction method based on damping spectrum iteration method

Abstract

According to the electrical capacitance tomography image reconstruction method based on the damping spectrum iteration method, an ill-conditioned nonlinear equation set is converted into a solvable linear equation set, the complexity of the solving process is greatly reduced, and meanwhile the accuracy and stability of understanding are remarkably improved. By means of the algorithm, artifacts in the electrical capacitance tomography reconstructed image are effectively reduced, the image quality is remarkably improved, and the reconstructed image is closer to the original flow pattern. Compared with a traditional method, the algorithm has the advantages that the imaging speed is remarkably increased while the imaging precision is improved, and the key problem that the imaging quality and the calculation efficiency are difficult to consider in an existing image reconstruction algorithm is successfully solved.

Description

Technical Field

[0001] The present invention belongs to the field of capacitance tomography (ECT) image reconstruction methods, and particularly relates to the field of image reconstruction technology in the field of multiphase fluid measurement. Specifically, it relates to an ECT image reconstruction method based on a damped spectral iteration method. Background Art

[0002] As an important process tomography technology, capacitance tomography has the advantages of non-invasiveness, high sensitivity, and good spatio-temporal resolution. It can achieve on-line non-destructive measurement in multiphase flows such as gas-solid, liquid-solid, and gas-liquid without disturbing the flow field. Currently, ECT technology has been widely applied to the real-time monitoring and fault diagnosis of the internal flow fields of industrial equipment such as fluidized beds, mixers, and chemical reactors.

[0003] The basic principle of ECT technology is based on the difference in the dielectric constants of media. Capacitance measurements are carried out by arranging multiple electrodes around the measured area. Its basic measurement process includes the following steps: First, an alternating voltage is applied to excite an electric field. The electric field propagates in different media, and the difference in the conductivity of the media will cause changes in the electric field distribution, thereby affecting the capacitance value between the electrodes. Then, the capacitance values between electrode pairs are measured one by one, and capacitance data reflecting the media distribution is collected. Finally, the collected capacitance data is processed using an appropriate image reconstruction algorithm to inversely obtain the media distribution inside the measured area, that is, the concentration field distribution, so as to achieve real-time monitoring. The selection and performance of the reconstruction algorithm directly affect the reconstruction quality of the ECT image and its calculation speed, and thus determine the measurement accuracy and efficiency.

[0004] According to different mathematical principles and calculation strategies, ECT image reconstruction algorithms can generally be divided into several categories such as non-iterative methods, iterative methods, optimization methods, and machine learning methods. Non-iterative methods, such as the linear backprojection method (LBP), are suitable for situations with simple calculations and fast speeds, but are very sensitive to noise and have low reconstruction accuracy; iterative methods, such as the Landweber iteration method, are suitable for more complex systems and can gradually optimize the reconstruction results, but have a slow convergence speed and may be relatively dependent on the initial value and algorithm parameters; optimization methods, such as genetic algorithms, have strong global search capabilities and can avoid local optimal solutions, but have a large amount of calculation and a slow convergence speed; machine learning methods, especially deep learning, show strong modeling capabilities when dealing with complex non-linear problems, can automatically extract features and adapt to different media distributions, but require a large amount of labeled data for training and have high computational resource requirements. It can be seen that the image reconstruction quality and computational efficiency (i.e., reconstruction speed) are usually contradictory. Therefore, the selection of an appropriate reconstruction algorithm needs to comprehensively consider multiple factors such as specific application requirements, data characteristics, and computational resources. Summary of the Invention

[0005] Based on the above technical status quo, the object of the present invention is to provide an ECT image reconstruction method based on the damped spectral iteration method, which can improve the imaging speed and imaging accuracy, and solve the problem that the existing image reconstruction algorithms often have an inverse relationship between the image reconstruction quality and the calculation efficiency.

[0006] The technical solution adopted by the present invention is as follows: an ECT image reconstruction method based on the damped spectral iteration method, and the specific solution process is as follows:

[0007] S1.1 Construct an indefinite system of equations: Sg = C (1)

[0008] In the formula, C is a column vector containing the capacitance measurement values of all capacitance sensors, g is the dielectric constant, S is the sensitivity field matrix, expressed as C ∈ R m , g ∈ R n , S ∈ R m×n , m is the number of capacitances measured by the ECT sensor, n is the number of pixels in the imaging area, and R is the set of real numbers;

[0009] S1.2 Multiply both sides of equation (1) by S T , and unify the coefficient matrix into a real symmetric matrix, which is transformed into:

[0010] S T Sg = S T C (2)

[0011] Let B = S T S and H = S T C, equation (2) becomes:

[0012] Bg = H (3)

[0013] Using the least squares solution, its solution is:

[0014] g = B -1 H (4)

[0015] S1.3 Add a damping factor λ, and add λg to both sides of equation (3), which becomes:

[0016] (B + λI)g = H + λg (5)

[0017] Construct an iterative method numerical solution formula through equation (5):

[0018] (B + λI)g k = H + λg k-1 (6)

[0019] In the formula, g k represents the k-th iteration result, and g k-1 represents the (k - 1)-th iteration result;

[0020] The iteration format is:

[0021] g k =(B + λI) -1 (H + λg k-1 ) (7)

[0022] S1.4 Perform LU decomposition on (B + λI), which generates a lower triangular matrix L, an upper triangular matrix U, and a permutation matrix P, such that:

[0023] LU = P(B + λI) (8)

[0024] Multiply both sides of equation (6) by P to obtain:

[0025] P(B + λI)g k = PH + λPg k-1 (9)

[0026] Combining equations (8) and (9), we get:

[0027] LUg k = P(H + λg k-1 ) (10)

[0028] Let

[0029] Y = Ug k , W = P(H + λg k-1 ) (11)

[0030] Equation (10) becomes

[0031] LY = W (12)

[0032] S1.5 Solve for Y:

[0033]

[0034] After that, solve for g:

[0035]

[0036] S1.6 Determine whether the iteration result g i meets the requirements. If it does, output it as the dielectric constant g; otherwise, update g i as the new dielectric constant into equation (4) and continue the iterative calculation.

[0037] In equations (13) and (14), i represents the number of rows of the matrix, j represents the number of columns of the matrix, and g i represents the result of the i-th iteration.

[0038] The selection of the initial value is crucial for image reconstruction. To improve the accuracy of the reconstructed image and reduce the number of iterations, after obtaining the capacitance measurement values of the capacitance sensor, the dielectric constant solved by the LBP algorithm is used as the initial g of the damping spectrum iteration algorithm. 0 .

[0039] In the above step S1.3, when selecting the damping factor, first set a fixed number of iterations. Within the set number of iterations, the minimum value of the norm ||Sg - C|| of the matrix [Sg - C] 2 is used as the damping factor λ.

[0040] In the above step S1.6, set the error ε; let Error = ||Sg - C|| 2 , and after obtaining g i in each iterative calculation, substitute g i into the calculation of the value of Error. If Error is greater than or equal to ε, then update the g obtained in this iteration i to Equation (4) for continued calculation. If Error is less than ε, then terminate the iteration and output the result of this iteration as the dielectric constant g. Then, generate an image with the help of an image reconstruction program according to the dielectric constant g obtained by iterative calculation.

[0041] The present invention also claims protection for an ECT image reconstruction device based on the damping spectrum iteration method, including:

[0042] Multiple capacitance sensors for obtaining capacitance measurement values of the image in the shooting area;

[0043] At least one processor for performing image reconstruction according to the capacitance measurement values obtained by the capacitance sensors;

[0044] At least one memory for storing at least one program;

[0045] When the at least one program is executed by the at least one processor, the at least one processor executes the above-mentioned ECT image reconstruction method based on the damping spectrum iteration method.

[0046] The present invention also claims protection for a computer storage medium storing a program executable by a processor. When the program executable by the processor is executed by the processor, the above-mentioned ECT image reconstruction method based on the damping spectrum iteration method is implemented.

[0047] The advantages of the technical solution of the present invention are:

[0048] 1. An algorithm based on the damped spectral iteration method is adopted. By transforming the ill-conditioned nonlinear equations into solvable linear equations, the complexity of the solution is reduced. This method effectively improves the accuracy and stability of the solution, reduces the artifacts in the ECT reconstructed image, significantly enhances the image quality, and makes the reconstructed image of ECT closer to the original flow pattern.

[0049] 2. The number of iterations is significantly reduced. By using the damped spectral iteration algorithm of the present invention, usually only 2 - 3 iterations are required to obtain the best imaging result, while the traditional Landweber iteration method usually requires dozens to hundreds of iterations to achieve a relatively accurate reconstruction effect.

[0050] 3. There is a prominent problem in traditional ECT measurement, that is, the sensitive field at the center position of the measurement area is relatively sparse, resulting in difficult accurate measurement of the medium distribution in the central area, thus affecting the imaging quality. The algorithm based on the damped spectral iteration method proposed by the present invention significantly improves this soft-field characteristic, improves the imaging accuracy in the central area, and enables ECT to achieve a wider application in the real-time measurement of large-scale industrial production flow parameters.

[0051] 4. It has higher robustness and can maintain stable imaging quality in environments with large humidity changes or complex environments. Even in different humidity environments, the algorithm can still maintain high-quality imaging results, showing good adaptability, and is especially suitable for harsh environments in industrial production.

[0052] 5. The ECT device based on the new algorithm significantly improves the calculation efficiency and accuracy, and shows high stability under different operating conditions. This breakthrough lays a solid foundation for the application of ECT technology in the field of flow parameter detection of large-scale and complex equipment, and promotes its wide application and further development in the industrial field. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 is the flow chart of the ECT image reconstruction method based on the damped spectral iteration method of the present invention;

[0054] Figure 2 is the relationship diagram between the damping factor λ and the correlation coefficient Cof, relative error RE in the method of the present invention;

[0055] Figure 3 is the imaging quality comparison diagram between the damped spectral iteration algorithm of the present invention and the LBP and Landweber algorithms;

[0056] Figure 4a is the relationship diagram between the number of iterations of the Landweber algorithm and the correlation coefficient Cof;

[0057] Figure 4bIt is a graph showing the relationship between the number of iterations of the damping spectrum iteration algorithm of the present invention and the correlation coefficient Cof;

[0058] Figure 5a It is a graph showing the relationship between the number of iterations of the Landweber algorithm and the relative error RE;

[0059] Figure 5b It is a graph showing the relationship between the number of iterations of the damping spectrum iteration algorithm of the present invention and the relative error RE;

[0060] Figure 6 It is a comparison graph of the calculation time consumption of the damping spectrum iteration algorithm of the present invention, LBP, and the Landweber algorithm under multiple manifolds;

[0061] Figure 7 It is a diagram of the test device arranged based on the method of the present invention;

[0062] Figure 8 It is a comparison graph of the specific test results of the image reconstruction quality of the damping spectrum iteration algorithm of the present invention, LBP, and the Landweber algorithm. Detailed implementation manners

[0063] In order to make the objectives, technical solutions, and advantages of the present application clearer, the present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0064] It should be noted that although functional module division is performed in the system schematic diagram and the logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in a different order from the module division in the system or the order in the flowchart. Terms such as "first" and "second" in the specification, claims, and the above-mentioned drawings are used to distinguish similar objects and do not necessarily need to describe a specific order or sequence.

[0065] In subsequent descriptions, suffixes such as "module", "component", or "unit" used to represent elements are only for the convenience of describing the present invention and have no specific meaning by themselves. Therefore, "module", "component", or "unit" can be used interchangeably.

[0066] The following combines the attached Figure 1 The ECT image reconstruction method based on the damping spectrum iteration method of the present invention will be further introduced in detail, which includes the following steps:

[0067] S1: Based on the capacitance measurement values obtained by the capacitance sensor, construct an indefinite equation set: Sg = C (1)

[0068] Let \(C\) be a column vector containing the capacitance measurement values of all capacitance sensors, \(g\) be the dielectric constant, and \(S\) be the sensitive field matrix. \(C\in R\) m , \(g\in R\) n , \(S\in R\) m×n , where \(m\) is the number of capacitances measured by the ECT sensor and \(n\) is the number of pixels in the imaging area. Multiple capacitance sensors are often set up to measure the flow field. Taking the common setting of 12 capacitance sensors as an example, \(C\) is a \(66\times1\) vector containing all capacitance measurement values; \(g\) is a \(4096\times1\) vector containing all pixel dielectric constant values; \(S\) is a \(66\times4096\) sensitive field matrix. It can be seen that the system of equations has 4096 unknowns and 66 equations, so it belongs to a typical underdetermined problem and cannot be directly solved. The problem solved by the present invention lies in the process of finding the optimal solution for the underdetermined system of equations, and the algorithm process is as follows.

[0069] Still taking the case of arranging 12 capacitance sensors to measure the flow field as a specific example, unify the coefficient matrix into a real symmetric matrix, and multiply both sides of the above formula by \(S\) T \(S\) T , and it is transformed into:

[0070] \(S\) T \(Sg = S\) T \(C\) (2)

[0071] Let \(B = S\) T \(S\) and \(H = S\) T \(C\), then \(B\) is a \(4096\times4096\) real symmetric matrix and \(H\) is a \(4096\times1\) vector, and formula (2) becomes:

[0072] \(Bg = H\) (3)

[0073] Using the least squares method to solve, its solution is:

[0074] \(g = B\) -1 \(H\) (4)

[0075] To improve its ill-conditioning, a damping factor \(\lambda\) is added, and \(\lambda g\) is added to both sides of formula (3) to become:

[0076] \((B + \lambda I)g = H + \lambda g\) (5)

[0077] Construct an iterative method numerical solution formula through the above formula:

[0078] \((B + \lambda I)g\) k \(= H + \lambda g\) k-1 (6)

[0079] In the formula: \(g\) k represents the result of the \(k\)th iteration, and \(g\) k-1 represents the result of the \((k - 1)\)th iteration.

[0080] The iterative format is as follows:

[0081] g k =(B + λI) -1 (H + λg k-1 ) (7)

[0082] In numerical calculations, the inverse operation of large matrices will have a greater impact on the solution of linear equations. To avoid inverting numerical matrices, LU factorization is introduced to solve (B + λI), and a lower triangular matrix L, an upper triangular matrix U, and a permutation matrix P are generated, satisfying:

[0083] LU = P(B + λI) (8)

[0084] Multiply both sides of equation (6) by P to obtain:

[0085] P(B + λI)g k = PH + λPg k-1 (9)

[0086] Combining equations (8) and (9), we get:

[0087] LUg k = P(H + λg k-1 ) (10)

[0088] Let

[0089] Y = Ug k , W = P(H + λg k-1 ) (11)

[0090] Therefore, equation (10) becomes

[0091] LY = W (12)

[0092] Solve for Y:

[0093]

[0094] After that, solve for g:

[0095]

[0096] In equations (13) and (14), i represents the number of rows of the matrix, j represents the number of columns of the matrix, and their value ranges are both related to the initial data of the capacitance measurement values. Taking the example of setting 12 capacitance sensors in this embodiment, since g is a 4096×1 vector, then both i and j take values (1, 2, 3,..., 4096), and W is a 4096×1 matrix, and L is a 4096×4096 lower triangular matrix.

[0097] Thus, an iteration is completed, and the obtained g from the iteration is i updated as the new dielectric constant value g into Equation (4), and subsequent iterations are continued until a dielectric constant that fully meets the error requirements is obtained.

[0098] S2: Set the initial value; The selection of the initial value is crucial for image reconstruction. To improve the accuracy of the reconstructed image and reduce the number of iterations, the dielectric constant distribution solved by the LBP algorithm is selected as the initial g of the damped spectral iteration algorithm. 0 With the advantage of simple calculation and fast speed of the non-iterative method, the initial value can be quickly obtained.

[0099] S3: Set the algorithm parameter λ.

[0100] Refer to Figure 1 , the initial settings of the algorithm are mainly the initial value of the iteration, the LU decomposition of matrix D, and the setting of the damping factor. Matrix D = S T S + λA, where A is the identity matrix and λ is the damping factor. The initial value of the iteration is the g obtained in step S2. 0 , the key lies in the setting of the damping factor. In the damped spectral iteration algorithm, the selection of the damping factor plays a key role in problem solving. If the damping factor is too small, it will exacerbate the ill-conditioning in the solution of the inverse problem. If it is too large, it is difficult to achieve the accuracy of the problem solution. Based on the characteristics of the damped spectral iteration algorithm in ECT applications, the present invention takes the damping factor corresponding to the minimum value of ||Sg - C|| 2 as the optimal damping factor. The basis for the selection is as follows: The smaller the norm of a matrix, usually it indicates that the matrix has some specific properties or constraints in terms of its nature or characteristics. Specifically, a smaller norm of a matrix may indicate the following situations: the matrix is close to the zero matrix; the matrix is a low-rank matrix; orthogonality. In the solution of the ECT inverse problem, the smaller the norm ||Sg - C|| 2 of the matrix [Sg - C], it only means that the matrix is closer to the zero matrix, that is, the difference between Sg and the capacitance value C is smaller, and the solution is more accurate. Based on this, first set a fixed number of iterations initially. Among the iterative results of multiple times, take the minimum value of ||Sg - C|| 2 as the damping factor λ. Note that the g 0 used in the first iteration is the dielectric constant value obtained by the LBP algorithm.

[0101] S4: Calculate the dielectric constant distribution value g

[0102] After obtaining g in each iterative calculation i , compare the magnitude of ||Sg - C|| 2 with the set error ε, that is, Figure 1 judge the magnitude of Error and ε in 2Use the size of Error as the error for the iteration termination condition. If Error is greater than or equal to ε, update the g obtained in this iteration into Equation (4) for continued calculation. If Error is less than ε, terminate the iteration and output the result of this iteration as the dielectric constant g. i Update it into Equation (4) for continued calculation. If Error is less than ε, terminate the iteration and output the result of this iteration as the dielectric constant g.

[0103] S5: Use the dielectric constant distribution value g and generate an image with the aid of an image reconstruction program.

[0104] To evaluate the imaging effect, two parameters, the correlation coefficient (Cof) and the relative error (RE), are introduced, which respectively reflect the correlation degree and the deviation degree between the reconstructed image and the actual dielectric constant. The calculation formulas are as follows:

[0105]

[0106] In the formula, g, are the true dielectric constant and the dielectric constant of the reconstructed image respectively, are the averages of g, respectively. m represents the total number of capacitance measurement values obtained by the capacitance sensors of ECT, and i = (1, 2,..., m).

[0107] The larger the correlation coefficient, the closer the reconstructed image is to the true image. The larger the relative error, the more deviated the reconstructed image is from the true image. See Figure 2 , which is the relationship between the damping factor λ and Cof, RE. It can be seen from the figure that ||Sg - C|| 2 is positively correlated with the relative error, and the damping factors corresponding to the peak points of the three curves are the same. Therefore, take the damping factor corresponding to the minimum value of ||Sg - C|| 2 as the optimal damping factor. Under one working condition, the optimal damping factor does not change significantly with the number of iterations, and the optimal damping factor only shows a slight change in the case of the same sensor, the same sensitive field, and different dielectric constant distributions, without affecting the accuracy of the solution. Therefore, on the premise of ensuring the solution accuracy, select the optimal damping factor and perform the LU decomposition of (B + λI) before the iteration. The optimal damping factor is selected by the least square norm of the residual [Sg - C] mentioned above. Then substitute the damping factor into the formula for LU decomposition.

[0108] Based on the algorithm of the present invention, specific verification is carried out by numerical simulation.

[0109] First, in terms of the image reconstruction quality, the damping spectrum iteration algorithm of the present invention has higher imaging accuracy compared with the traditional algorithm.

[0110] During the numerical simulation process, a 12-electrode ECT sensor with an inner diameter of 16 cm was used. Air was set as the low-dielectric-constant medium and corn kernels as the high-dielectric-constant medium, which were represented as blue and red respectively in the ECT reconstructed images. Eight different gas-solid two-phase flow patterns were set, and the damping spectrum iteration algorithm proposed in the present invention was compared with the conventional LBP and the imaging quality of Landweber. The imaging effects of the three image reconstruction algorithms for different flow patterns were focused on. The imaging results are as Figure 3 shown. For case1-case5, that is, flow patterns 1-5, although there are large deviations between the dielectric constant values in the imaging area and the real distribution, the LBP and Landweber algorithms can basically reconstruct the flow state. However, for the more complex case6-case8, that is, flow patterns 6-8, neither the LBP nor the Landweber algorithm can accurately reconstruct the real flow pattern distribution. Compared with the first two algorithms, all the reconstructed images of the damping spectrum iteration algorithm are very close to the real flow pattern distribution. In terms of the central flow (i.e., flow pattern 5) and complex flow patterns (i.e., flow patterns 6-8), the improvement in imaging accuracy is particularly obvious, reflecting the ability of this algorithm to reconstruct complex flow patterns.

[0111] Secondly, in terms of calculation speed, on the premise of comprehensively ensuring the imaging quality, the damping spectrum iteration algorithm of the present invention consumes less time than the traditional algorithm.

[0112] In addition to the advantages of image reconstruction quality, imaging speed is also another important factor for judging the quality of the algorithm.

[0113] To analyze the influence of the number of iterations on the imaging quality of the two iterative methods, Figures 4 and 5 respectively show the laws of the correlation coefficient and relative error changing with the increase in the number of iterations. From Figure 4a it can be seen that the correlation coefficient of the Landweber algorithm first increases with the increase in the number of iterations and reaches the peak within the range of 300 to 500 iterations for all 8 flow patterns, and then decreases with the further increase in the number of iterations. Compared with the Landweber algorithm, as Figure 4b shown, the damping spectrum iteration algorithm obtains a higher correlation coefficient from the first iteration and can reach the peak with only 2 to 3 iterations. Therefore, using the damping spectrum iteration algorithm can significantly reduce the calculation cost. From Figure 5a and Figure 5b it can be seen that with the increase in the number of iterations, the relative errors of the two algorithms decrease slightly or almost remain unchanged. Compared with the Landweber algorithm, the damping spectrum iteration algorithm requires fewer iterations to reach a lower relative error. Specifically, the Landweber algorithm needs 300 to 500 iterations to reach the lowest relative error, while the damping spectrum iteration algorithm only needs 2 or 3 iterations to achieve a similar result.

[0114] Figure 6 The computation times of different flow patterns under three algorithms were compared. As can be seen from the table, due to its non-iterative nature, the LBP algorithm has the shortest computation time (i.e., the fastest computation speed). The computation time of the Landweber algorithm exceeds 2 seconds, and its imaging speed is slow, making it unsuitable for real-time imaging applications. Compared with the Landweber algorithm, the computation speed of the damped spectral iteration algorithm has been significantly improved. This method transforms simple numerical iteration into iteration for solving linear equations, greatly reducing the required number of iterations. Usually, only 2 to 3 iterations are needed to obtain the best imaging effect. Therefore, the computation time is significantly shortened, and it can be applied to real-time imaging in industrial production. The damped spectral iteration algorithm proposed in the present invention is superior to the traditional LBP and Landweber algorithms in terms of imaging quality and computation time.

[0115] In addition, the image reconstruction method based on the damped spectral iteration algorithm provided by the present invention can significantly improve the "soft field effect" in ECT technology. The existing image reconstruction technology has poor imaging quality in large-scale sensors and cannot effectively solve the soft field effect in the central region of ECT measurement. To verify the imaging quality of the method of the present invention for large-scale sensors, see Figure 7 , and three plexiglass tubes with inner diameters of 16 cm, 20 cm, and 24 cm were respectively used for static tests. Based on the capacitance measurement values measured by the test device, the damped spectral iteration algorithm, LBP algorithm, and Landweber algorithm of the present invention were respectively used for image reconstruction. Through the result comparison diagrams of the three algorithms, see Figure 8 , it can be seen that as the inner diameter of the sensor increases from 16 cm to 24 cm, the ECT imaging quality continuously decreases, which is mainly due to the serious "soft field" problem in large-scale ECT sensors. Among them, for the 24-cm sensor, LBP completely fails to reconstruct the core flow pattern and significantly deviates from the true flow patterns of the edge dual-core flow and edge quad-core flow. In contrast, the damped spectral iteration algorithm can generate the highest-quality reconstructed images for all flow patterns. This shows that the damped spectral iteration algorithm has important potential in improving the imaging quality of large-scale ECT sensors, especially in the central region of the imaging area, and can effectively solve the "soft field" problem of ECT measurement.

[0116] Combined with the specific implementation manner of the present application and the content in the given embodiments, it can be seen that the method of the present application can be stored or loaded with computer program instructions onto a computer or other programmable data processing device, and these computer programs can be specified to the computer or other programmable data processing device to generate a machine, and the machine can execute the functions specified in one or more processes of the flowchart by the instructions.

[0117] The method of the present application can be stored or loaded with computer program instructions onto a computer or other programmable data processing device, so that the computer or other programmable data processing device executes a series of operation steps by reading the instructions to generate a computer-implemented process, thereby providing steps for implementing the functions specified in one or more of the processes of the flowchart when the instructions are executed in the computer or other programmable data processing device.

[0118] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the processes or functions according to the embodiments of the present invention are generated in whole or in part. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. The computer instructions may be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another computer-readable storage medium. For example, the computer instructions may be transmitted from one website, computer, server, or data center to another website, computer, server, or data center by wire (such as coaxial cable, optical fiber, digital subscriber line (DSL)) or wirelessly (such as infrared, wireless, microwave, etc.). The computer-readable storage medium may be any available medium that can be accessed by a computer or a data storage device such as a server or a data center that includes one or more integrated available media. The available medium may be a magnetic medium (such as a floppy disk, hard disk, magnetic tape), an optical medium (such as a DVD), or a semiconductor medium (such as a solid state disk (SSD)), etc.

Claims

1. A capacitance tomography image reconstruction method based on damping spectrum iteration method, the specific solution process is as follows: S1.1 Construct an indeterminate system of equations: Sg = C (1) Where C is the column vector containing the capacitance measurement values ​​of all capacitive sensors, g is the dielectric constant, and S is the sensitive field matrix, expressed as C∈R m ,g∈R n ,S∈R m×n , m is the capacitance measured by the ECT sensor, n is the number of pixels in the imaging area, and R is a set of real numbers; S1.2 Multiply both sides of equation (1) by S T , unify the coefficient matrix into a real symmetric matrix and transform it into: S T Sg=S T C (2) Let B = S T S and H = S T C, formula (2) becomes: Bg=H (3) Using least squares solution, the solution is: g=B -1 H (4) S1.3 Add the damping factor λ, and add λg to both sides of equation (3), which becomes: (B+λI)g=H+λg (5) The iterative numerical solution formula is constructed through formula (5): (B+λI)g k =H+λg k-1 (6) In the formula, g k represents the result of the kth iteration, g k-1 Indicates the result of the k-1th iteration; The iteration format is: g k =(B+λI) -1 (H+λg k-1 ) (7) S1.4 Perform LU decomposition on (B+λI) to generate a lower triangular matrix L, an upper triangular matrix U and a permutation matrix P, so that they satisfy: LU=P(B+λI) (8) Multiply both sides of equation (6) by P to obtain: P(B+λI)g k =PH+λPg k-1 (9) Formula (8) and (9) are combined to obtain: LUg k =P(H+λg k-1 ) (10) make Y=And k ,W=P(H+λg k-1 ) (11) Formula (10) becomes LY=W (12) S1.5 solves for Y: Afterwards, solve for g: S1.6 Determine the iteration result g i Whether the requirements are met, if they are met, the dielectric constant g is output, otherwise g i The new dielectric constant is updated into equation (4) and the iterative calculation is continued. In formulas (13) and (14), i represents the number of rows in the matrix, j represents the number of columns in the matrix, and g i Represents the result of the i-th iteration.

2. The image reconstruction method according to claim 1, further characterized in that: After obtaining the capacitance measurement value of the capacitive sensor, the dielectric constant solved by the LBP algorithm is used as the initial g0 of the damping spectrum iterative algorithm.

3. The image reconstruction method according to claim 2, further characterized in that: In step S1.3, when selecting the damping factor, first set a fixed number of iterations, and the minimum value of the norm ||Sg-C||2 of the matrix [Sg-C] within the set number of iterations is used as the damping factor λ.

4. The image reconstruction method according to claim 2 or 3, further characterized in that: In step S1.6, set the error ε; set Error = ||Sg-C||2, and calculate g in each iteration i After that, g i Substitute the value of the calculated Error into the value. If Error is greater than or equal to ε, then the g obtained in this iteration is i Update to equation (4) and continue the calculation. If Error is less than ε, the iteration is terminated and the result of this iteration is output as the dielectric constant g.

5. The image reconstruction method according to claim 4, further characterized in that: Generate an image based on the dielectric constant g obtained by iterative calculation.

6. A capacitance tomography image reconstruction device based on damping spectrum iteration method, characterized in that: include: a plurality of capacitive sensors for obtaining capacitive measurements of an image of a captured area; at least one processor configured to reconstruct an image based on capacitance measurements obtained by the capacitance sensor; at least one memory for storing at least one program; When the at least one program is executed by at least one processor, the at least one processor executes the capacitance tomography image reconstruction method based on the damping spectrum iteration method as described in any one of claims 1 to 5.

7. A computer storage medium storing a program executable by a processor, characterized in that: When the processor is executed, the program executable by the processor implements the capacitance tomography image reconstruction method based on the damping spectrum iteration method as described in any one of claims 1 to 5.

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