Fast, non-linear inversion for electrical impedance tomography

Abstract

Electrical Impedance Tomography, (EIT), is a non-invasive imaging technique which aims to image the impedance within a test volume from electrical measurements made on the surface. The reconstruction of impedance images is an ill-posed problem which is both extremely sensitive to noise and highly computationally intensive. This paper defines an experimental measurement in EIT and calculates optimal experiments which maximise the distinguishability between the region to be imaged and a best estimate conductivity distribution. These optimal experiments can be derived from measurements made on the boundary. A reconstruction algorithm, known as POMPUS, based on the use of optimal experiments is derived. It is proved to converge given some mild constraints and is demonstrated to be many times faster than standard, Newton based, reconstruction algorithms. Results using synthetic data indicate that the images produced by POMPUS are comparable to those produced by these standard algorithms.