Research On Image Reconstruction Of Electrical Capacitance Tomography For The Multiphase Flow

Electrical capacitance tomography (ECT) is a visualization technology that can be applied to concentration measurement for the multiphase flow. It attempts to image the permittivity distribution of an object by measuring the electrical capacitances between sets of electrodes placed around its periphery. ECT is considered as a promising tomography technology due to its advantages such as high speed, high safety, non-intrusive sensing and low cost. Successful applications of ECT technology depend on the speed and precision of the image reconstruction algorithms. A main motivation for this dissertation is to investigate image reconstruction algorithms for ECT, and the main contents are as follows:The principles of ECT technique and the mathematics theory of the inverse problem are reviewed. Three typical regularization methods, such as the Landweber iteration algorithm, the Tikhonov regularization method and the truncated singular value decomposition method, are discussed in detail. Seven kinds of iterative algorithms of solving the generalized inverse are introduced and compared.The image reconstruction problem for ECT is often transformed into an optimization problem. In this dissertation, three kinds of unconstrained optimization algorithms, such as the steepest descent algorithm, the conjugate gradient algorithm and the Newton algorithm, are analyzed in detail. Especially, owing to the advantages such as the simplicity, smaller storage and faster convergence when compared with the steepest descent method, larger convergence domain, the conjugate gradient algorithms are detailedly discussed and improved according to the prior information of a solution. At the same time, four kinds of typical conjugate gradient algorithms are compared and evaluated by numerical simulations.The Tikhonov regularization method is an effective method to solve the inverse problems. A Tikhonov regularization solution is a result of balancing the precision and stabilization of a solution. Two generalized Tikhonov functionals are deduced according to the ill posed characteristics of ECT image reconstruction problem. In the first objective functional, the standard Tikhonov functional is improved using a combination robust estimation technique. In the second objective functional, the standard Minimax estimation is developed by the Tikhonov regularization technique. The numerical results indicate that the both algorithms are feasible and effectively overcome the numerical instability of ECT image reconstruction process. The spatial resolution of the reconstructed images is remarkably enhanced. The distortion of the reconstructed images is relative small, and the artifacts in the reconstructed images can be eliminated effectively. At the same time, the reconstructed results by the noise-contaminated capacitance data also show that the proposed algorithms hold a good robustness to the noises in the capacitance data.Traditional image reconstruction algorithms for ECT only consider the noises in the measured capacitance data; however, the inaccurate characteristics in the sensitivity matrix are not to be considered. In fact, the sensitivity matrix may be inaccurate due to the linearization approximation of the image reconstruction model. Therefore, considering the inaccurate nature in the measured capacitance data and the sensitivity matrix in the process of image reconstruction is reasonable. Based on the regularized total least squares method that has been developed using the robust estimation technique, an image reconstruction algorithm that considers the inaccurate nature in the measured capacitance data and the sensitivity matrix is proposed. The numerical results indicate that the proposed algorithm is feasible and effectively overcomes the numerical instability of ECT image reconstruction process. The spatial resolution of the reconstructed images is remarkably enhanced. The distortion of the reconstructed images is relatively small, and the artifacts in the reconstructed images can be eliminated effectively.A multiscale objective functional based on the wavelet multiscale analysis technique and the total least squares method is deduced. The homotopy algorithm is employed to solve the objective functional. The homotopy equation is designed by the fixed-point homotopy and is solved by the fixed-point iterative algorithm. The numerical results indicate that the proposed algorithm is feasible and effectively overcomes the numerical instability of ECT image reconstruction process. The spatial resolution of the reconstructed images is remarkably enhanced. The distortion of the reconstructed images is relatively small, and the artifacts in the reconstructed images can be eliminated effectively.Post-processing techniques for ECT images, such as the multiscale image enhancing, the multiscale image de-noising and the multiscale image fusion, have been carried out using the wavelet-based multiscale method. Numerical results indicate that the processed images can better highlight the detailed characteristics of the reconstructed objects and the explanatory ability and reliability of ECT images are increased, which provide necessary elements for the sequent quantitative analysis.Traditional ECT image reconstruction algorithms often consider the linearized model, which has obtained many successful applications when the difference between the high permittivity and low permittivity in the measured region is not large. However, the linearized model may bring large error when the difference between the high permittivity and low permittivity in the measured region is large. Therefore, considering the errors that linearization process brings is reasonable in the process of image reconstruction. A new objective functional based on the semiparametric method that considers the noises in the measured capacitance data and the linearization error is established. The homotopy algorithm is employed to solve this objective functional. Numerical results indicate that this algorithm is feasible, and quality of the reconstructed images is enhanced remarkably.