Application of Charge Simulation Method (CSM) for ECT Imaging in Forward Problem and Sensitivity Matrix Calculation

R. Banasiak, L. Mazurkiewicz, and R. Wajman

Computer Engineering Department, Technical University of Lodz, Poland, Email: rbanasi@kis.p.lodz.pl

ABSTRACT

Typically, a forward problem in ECT tomography has been solved using finite elements method. The basis of this technique is a discretisation of reconstructed process space into a finite number of faces each of them with homogenous material permittivity. Alternatively the authors propose a new approach which defines material permittivity for nodes and approximates permittivity distribution inside finite elements with linear function. This idea aims to reconstruct material permittivity only for the nodes. As a result, the size of matrices used for solving the forward and backward problems is significantly reduced in comparison to the FEM method with the same mesh (the number of rows in the sensitivity matrix is reduced by a factor of 3-5). Additionally, the reconstructed permittivity distribution is smoother thanks to use of linear approximation in contrast to granularity obtained with traditional FEM based algorithms. The authors present algorithms for the forward solution and sensitivity matrix calculation based on the Charge Simulation Method, which is well suited to the presented assumption about permittivity distribution.

Keywords electrical capacitance tomography, ECT, Charge Simulation Method, sensitivity matrix, forward problem, calculation cost reduction