Non-Iterative Reconstruction for Electrical Tomography using Optimal First and Second Order Approximations

H. Zangl, D. Watzenig, G. Steiner, A. Fuchs, and H. Wegleiter

Institute of Electrical Measurement and Measurement Signal Processing, Graz University of Technology, Austria, Kopernikusgasse 24/IV, A-8010 Graz, Austria

Email: Hubert.Zangl@tugraz.at

ABSTRACT

For the reconstruction of the cross-sectional profile in Electrical Capacitance Tomography, several methods are commonly used. They differ in speed and performance. Up to now, the best performance in terms of speed is provided by simple non-iterative algorithms such as Linear Back-Projection, Offline Iteration/Online Reconstruction and Singular Value Decomposition, whereas best reconstruction results are obtained by more complex approaches, e.g. iterative methods in particular in conjunction with statistical methods. In this paper we investigate optimal first and second order approximations as a fast alternative. The idea is that it should be possible in general to approximate an algorithm by a series of orthogonal functions, e.g. a polynomial series or a Fourier series. The higher efforts to find the approximation pay off in a very fast reconstruction. Experimental results for piecewise constant permittivities demonstrate that Optimal First and Second Order Approximations can provide results comparable to the Gauss-Newton method whereas the speed of the algorithms is in the range of Linear Back-Projection.

Keywords Capacitance Tomography, Optimal First Order Approximation, Optimal Second Order Approximation, Non-Iterative Algorithm