Regularization Algorithm Study On Image Reconstruction For Electrical Capacitance Tomography

With the rapid development of modern science and technology, especially the developmentof atomic energy nuclear power station and aerospace industry, and the increasing emphasis onenvironmental protection, parameter measurement of two-phase flow for industrial productionand scientific research has important significance. Electrical capacitance tomography (ECT) is aprocess tomography technology based on the capacitance sensitivity mechanism. With its simplestructure, low cost, fast respond, non-invade and without radiation, applicable to a wide range, ithas a wide application prospect.This paper is based on the study of12-electrode sensor model. From the analysis of ECTtechnology research and the common method of image reconstruction, to improve the precisionand speed of image reconstruction, fast and stable algorithm of ECT based on regularization isstudied. The simulated experiment under the environment of MATLAB is made to test theeffectivity of the proposed method.The main study contents are as follows:1. The theoretical basis of the optimal Tikhonov regularization parameter selection is given byusing Morozov deviation principle when the error level is known, which solved uncertainproblem when the parameter selected by traditional experience method. According to theinfinitely differentiable properties of regularization solution and deviation function, and bycombining three-order convergence algorithm with two parameter model, a hybrid algorithm isconstructed to realized to get the optimal regularization parameter rapidly and reasonably.2. Using total variation regularization method, the regular solution was extended to a boundedvariation function space which broke the limitation that the Tikhonov regularization solution isonly confined to the continuous space; the nonlinear Euler equation is derived from the functional minimization of total variation regularization, and the fixed point iteration method isused to get the equation’s solution which improved the speed of ECT image reconstruction.3. According to the error level is known, Morozov deviation principle andδ~2-criterion of theTikhonov regularization were promotion to the total variation regularization method to improvethe accuracy of the reconstructed images. Priori strategy and posteriori strategy are given fordetermining the regularization parameter of total variation regularization.