Sensitivity Theorem Based Inverse Solution Using Conjugate Gradients Methods for Electrical Impedance Tomography

M. Wang

School of Process, Environmental and Materials Engineering, University of Leeds, LS2 9JT Tel: +44 (0) 113 2435, Fax: +44 (0) 113 246 7310, Email: minmw@leeds.ac.uk

ABSTRACT

To deal with the divergence problem due to the errors introduced from the electrode modelling and instrument noise a multi-step inverse solution is developed in the paper. This is based on a normalised linear approximation of the mutual impedance change in use of the mutual impedance derived from sensitivity theorem and a method of error vector decomposition. An algebraic solution of the linear equations using a generalised conjugate gradients method is reported. The solution of the non-linear problem is approached with multi-step inversions. Comparisons between the multi-step algorithms and other algorithms based on sensitivity coefficient backprojection and Newton-Raphson methods are given. Examples for 3-dimensionally imaging a gas-liquid mixing and a human hand in brine are demonstrated.

Keyword electrical impedance tomography, sensitivity theorem, inverse solution, conjugate gradients method.