A Novel Image Reconstruction Algorithm for Electrical Capacitance Tomography Based on Variational Methods and Green’s Functions

A Fraguela, J Oliveros and S Gomez

BUAP, Puebla, Mexico, IMP Mexico, IIMAS UNAM Mexico

ABSTRACT

A novel method is described to solve the 2D inverse parameter identification problem, for image reconstruction of permittivity distribution in the cross section of a pipeline, using Electrical Capacitance Tomography. This method takes into account the important characteristics of the problem: its non- linearity, its ill-posednes and the need to perform a theoretically justified regularization, the limitations of the measurement equipment that produce data errors and that may not allow to get the images with all the desired precision. These difficulties have not yet been solved completely by any of the existing methods as will be discussed in the introduction. Even in the case of complicated geometries, the novel method presented here, allows the decomposition of the inverse problem in several simpler problems, and each one of them can be solved with a numerically stable procedure, with the necessary theoretical justification. In the present method, it is not necessary to solve the direct problem at each iteration, as the resulting optimization problem is a linear least squares subject to quadratic constraints. The low computational cost will then allow the solution of this problem in real time for industrial applications.

Keywords Electrical Capacitance Tomography, Identification of Permittivity Distribution, Ill-Posed Problem, Regularization.