Image Reconstruction Algorithm In Electrical Capacitance Tomography Based On Statistics Methods

Electrical Capacitance Tomography (ECT), based on capacitance sensing principle, is a promising technique of process tomography. It has the advantage of being non-intrusive, fast response and low cost, which can acquire image information of process parameters. It has a broad application for the detection and control of industrial process.The traditional way of image reconstruction algorithms in ECT is only to find a single estimate, but the statistical methods can obtain the full statistical description of the information that is immersed in the prior information and the measurements. The paper mainly discussed the image reconstruction algorithms of ECT based on statistics methods. The main work of this paper is shown as follows:1,In order to solve the forward problem, a simulation software was designed. The model is constructed automatically according to given parameters and the finite element computation is done based on the dissection models.2,The image reconstruction algorithms in ECT were analyzed from starting point of statistical theory. According to the theory of Bayesian statistics, using the standard Tikhonov regularization as the prior information, the posterior distribution of the permittivity parameters is obtained.3,The maximum a posteriori (MAP) estimate based on conjugate gradient method was implemented. The investigation on two preconditioned conjugate gradient methods shows that excellent images are reconstructed after one-step iteration with these methods. The rationality of this result was proved by theory analysis which also validated that the better images can be reconstructed with one iteration step than with linear back projection.4,A posteriori uncertainties were estimated by Markov chain Monte Carlo(MCMC) and Gibbs sampling method. The conditional expectations could be used to reconstruct images and images could be reconstructed for different credibility interval.