Research On Inverse Problems Solving And Image Reconstruction Algorithm For Electrical Capacitance Tomography System

Electrical Capacitance Tomography (ECT) is a new computer tomography, which could calculate the spatial distribution of internal dielectric constant by measuring the capacitance around the electrode surface, mainly used for the Multiphase Flow Measurement inside the industrial pipe. Capacitance tomography technology has wide application, non-invasive, safe and good performance, and provides a better way to solve the problem of measuring the Multiphase Flow . Successful application of ECT technology mainly depends on the accuracy and speed of solving inverse problem and the quality of imaging reconstruction, this paper mainly researchs the problem such as the the solving of inverse problems and the algorithm of the imaging reconstruction ,the main research contents are as follows:This paper describes the fundamental principles of ECT technique, definition of the problem, definition of the inverse problem and ill-posedness of solving the inverse problem, and proposes the theory of finite-dimensional approximation for solving the ECT inverse problem.For the convergence of Landweber algorithm is slow, so propose polynomial acceleration algorithm to solve the inverse problem of ECT. At the same time the solving of Rust Region's sub-problem is a very complex problem, here conjugate gradient algorithm is used to solve them, denoted by the trust region - conjugate gradient(TR-CG) algorithm. Experimental results show that two kinds of algorithms have shown good imaging results and able to overcome instability of image reconstruction for ECT inverse problem.The distortion of the reconstructed images is relative small and very close to the original flow pattern. At the same time, the reconstructed results by the noise-contaminated capacitance data show that two kinds of algorithms have strong anti-noise.Application of Gauss-Newton to solve the inverse problem of ECT may be a very slow convergence , so it is proposed that the weighted and amended Gauss-Newton algorithm, known as WAGN algorithm. Basing on the analyzing the principle of the residual nonlinear least squares problem, proposed a NL2SOL quasi-Newton algorithm for ECT image reconstruction. Experimental results show that both algorithms are better solutions of the inverse problems, imaging with high precision and little error. Comparison of two algorithms show that NL2SOL algorithm has better imaging results about the large residual flow pattern, at same time weighted and modified Gauss-Newton algorithm has better imaging results about the small residual flow pattern.For the flow pattern identification of ECT inverse problem, described the ECT flow pattern identification method of BP neural network based on feature extraction. Analyzed the basic reasons for affect the flow pattern recognition accuracy, proposed an flow pattern identification algorithm of feature extraction based on adaptive principal component analysis (PCA-FE) for ECT, and proposed symmetric sub-space network model and the generalized Hebb network model for adaptive solving main components of capacitance value for ECT.Base on explaining progressive optimal-order theory of electrical capacitance tomography for solving the inverse problem, elaborated on necessity of using edge gray compensation algorithm after solving the inverse problem of ECT and propose an edge gray compensation algorithm of adaptive weighted particle swarm optimization (AWPSO) for electrical capacitance tomography. The experimental results show that the algorithm is very effective, and can greatly improve the stability of image reconstruction and improve the quality of image reconstruction. compensated image quality is much better than the LBP algorithm and conjugate gradient algorithm and provides a new and effective ways for ECT.