Non Iterative Inversion Method for Electrical Resistance, Capacitance and Inductance Tomography for Two Phase Materials

A Tamburrino1, G Rubinacci1, M Soleimani2, W R B Lionheart2

1 Department of Engineering University of Cassino Italy, Email: tamburrino@unicas.it

2 Department of Mathematics UMIST, Manchester, UK, Email: m.soleimani@umist.ac.uk

ABSTRACT

This paper focuses on the application of a recently proposed non-iterative inversion method for three different imaging techniques for two phases materials. Specifically, two techniques concern the retrieval of the resistivity of a conductor (electrical resistance tomography and magnetic induction tomography) and one technique concerns the retrieval of the permittivity of a dielectric material (electrical capacitance tomography). All have in common a monotonicity property that is the mathematical basis for the non-iterative inversion method. This quantitative non-iterative inversion method requires a modest computational effort. Specifically, it requires the solution of a number of forward problems increasing linearly with the number of pixels (voxels) used to discretize the unknown.

Keywords Monotonocity property, Shape identification, Two phase material