Fast post-processing algorithm for improving electrical capacitance tomography image reconstruction

Abstract

Electrical tomography is the reconstruction of an image of the interior of a body, based on measurements made on its surface. Mathematically it can be described as a coefficient inverse problem for the Laplace equation, written in the divergent form. The coefficient is a function of the space variables and characterizes the electrical properties of the medium. One of the best-known and most developed approaches is electrical capacitance tomography (ECT). This method has some advantages, but because of the non-linear structure of the mathematical model, the results of the regularization procedures for image reconstruction are not perfect. We propose here a fast post-processing algorithm to improve the quality of the electrical tomography images, obtained by any method. This algorithm is based on the explicit spline-approximation method theoretically justified for restoring some classes of functions. Numerical experiments on simulated model problems confirm its good properties.