Abstract
In the image reconstruction of the electrical capacitance tomography (ECT) system, the application of the total least squares theory transforms the ill-posed problem into a nonlinear unconstrained minimization problem, which avoids calculating the matrix inversion. But in the iterative process of the coefficient matrix, the ill-posed problem is also produced. For the effect on the final image reconstruction accuracy of this problem, combined with the principle of the ECT system, the coefficient matrix is targeted and updated in the overall least squares iteration process. The new coefficient matrix is calculated, and then, the regularization matrix is corrected according to the adaptive targeting singular value, which can reduce the ill-posed effect. In this study, the total least squares iterative method is improved by introducing the mathematical model of EIV to deal with the errors in the measured capacitance data and coefficient matrix. The effect of noise interference on the measurement capacitance data is reduced, and finally, the high-quality reconstructed images are calculated iteratively.
Highlights
To better solve the ill-posed nature of the inverse problem in the image reconstruction process and reduce the impact of complex noise on the reconstructed images, our work proposes an image reconstruction algorithm based on a combination of improved total least squares and EIV models, conducts simulation experiments on four flow types, and analyzes the impact of the noise environment on the imaging quality
In order to verify the feasibility of this study’s algorithm in Electrical capacitance tomography (ECT) image reconstruction, two evaluation metrics are introduced: image error and correlation coefficient. e calculation formula is shown in equation (29) as well as equation (30), and the correlation coefficient can reflect the similarity between the reconstruction result and the actual prototype
To verify the adaptability of the algorithm to noise, experiments are conducted for four flow types: core flow, laminar flow, circulation flow, and multidrop flow, and random noise is added to the normalized capacitance C and coefficient matrix S, respectively, eL ∼ N(0, σ2Im), eA ∼ N(0, σ2Im ⊗ In), σ 0.1, random noise generated by Matlab
Summary
Electrical capacitance tomography (ECT) is a typical method for multiphase flow detection. e principle is to collect data through the electrode array installed on the outside of the pipe to make real-time visualization of the dielectric constant distribution inside the pipe, to process, collect, filter, and amplify the capacitance data between the electrode pairs acquired by the sensor through the data acquisition unit, and to reconstruct the image through the image reconstruction algorithm to carry out the image output to obtain the final image process. e ECT system has been gradually applied in the field of multiphase flow because of its noninvasive, fast response, simple structure, no radiation, wide range of applications, and good real-time performance [1,2,3]. e image reconstruction algorithm is the most critical step in the whole process of implementing capacitance tomography, which directly affects the clarity and accuracy of imaging, and is a key point that needs to be addressed effectively. E ECT system has a “soft field” effect, which makes the image reconstruction more difficult, and the obtained solution is only an approximate solution of the system, which has a certain error compared with the exact solution [4].Typical direct algorithms include the LBP algorithm, Tikhonov regularization algorithm, and so on [5]. E typical algorithm of the iterative class is the Landweber algorithm, which is simple in principle and has high image accuracy, but is not suitable for applications with high real-time requirements [6]. Computational Intelligence and Neuroscience projection sparse reconstruction algorithm is used to address the problem of poor image accuracy when the medium is distributed close together in a two-phase flow [10]. To better solve the ill-posed nature of the inverse problem in the image reconstruction process and reduce the impact of complex noise on the reconstructed images, our work proposes an image reconstruction algorithm based on a combination of improved total least squares and EIV models, conducts simulation experiments on four flow types, and analyzes the impact of the noise environment on the imaging quality
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