In order to solve the “soft field” and uncertainty problems in electrical capacitance tomography, a homotopy extension regularization and selfscaling metric image reconstruction algorithm for electrical capacitance tomography is presentedOn the basis of ECT theory, the algorithm combines homotopy continuation with regularization method, and derives the corresponding correction formula combined with selftuning ratio Finally, the mathematical model of inverse problem of ECT Image reconstruction is derived.The algorithm is used in digital simulation experiment to verify its effectiveness The simulation results are compared with the classical Landweber algorithm, SD algorithm and other imaging algorithms The results show that the algorithm has the advantages of high image quality, fast convergence speed and less iteration times in ECT Image reconstruction It is an effective algorithm to solve ECT imaging problems

To solve the 'soft-field' nature and the ill-posed problem in electrical capacitance tomography technology, a modified sparse quasi-newton algorithm for electrical capacitance tomography is presented. The mathematical model of modified sparse quasi-newton is derived. The final iteration formula of modified sparse quasi-newton used to adjust the inverse problem solving of the capacitance tomography image reconstruction is given. An iterative formula for ECT inverse problem solving is used for digital simulation experiment. The simulation experiment results are compared with the results of LBP, Landweber, CG, SD, and so on. The results of the analysis show that both precision and speed of the algorithm are very good.

In electrical capacitance tomography technology, to solve the ‘soft-field’ nature and the typical ill-posed problem, a Broyden Correction image reconstruction algorithm is proposed for electrical capacitance tomography system. After the analysis of the basic principles of the ECT system, to solve the problem of electrical capacitance tomography system, we deduced a mathematical model of Broyden Correction algorithm and analyzed the convergence of the algorithm using the monotony of the iterative error. The feasibility of this algorithm solving ECT problems is also discussed. This algorithm meets the convergence condition and the error of image reconstruction is small. Simulation data and experimental results indicate that this algorithm can provide favorable stabilization and high quality images compared with SD, LBP, Landweber and CG and this new algorithm provides a feasible and effective way for ECT image reconstruction field.

A modified implicit type Landweber image reconstruction algorithm is presented for solving the'soft-field'nature and the ill-posed problem in Electrical Capacitance Tomography (ECT) technology.On analysis of the basic principles of the ECT system,the paper proposes a formula of the modified implicit type Landweber algorithm to solve the problem of electrical capacitance tomography,and finishes the iterative modification,and analyzes the convergence of the algorithm.Simulation experimental results show that compared with Landweber,LBP methods,both precision and speed of the modified implicit formula Landweber method are very good,and it is simple and stabilized.