Spline Smoothing Algorithms for Improving Capacitance Tomography Image Reconstruction

A Grebennikov

Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Av. San Claudio y Río verde, Ciudad Universitaria, CP 72570, Puebla, Pue., México, agrebe@fcfm.buap.mx

ABSTRACT

Electrical Tomography consists in reconstructing an image of 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 media. Know and the most developed approach is Electrical Capacitance Tomography. This method has some advantages, but because of the nonlinear 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 electric 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.

Keywords Image reconstruction, Electrical tomography, Spline, Regularization