Nonlinear Inverse Problems in Imaging

Chapter 7

Electrical Impedance Tomography

Electrical impedance tomography (EIT) produces cross-sectional images of an admittivity distribution inside an electrically conducting object. It has a wide range of applications in biomedicine, geophysics, non-destructive testing and so on. Considering the fact that structural imaging modalities such as X-ray CT and MRI provide images with a superior spatial resolution to EIT, the primary goal of biomedical EIT is to supply functional diagnostic information of organs with a high temporal resolution. It may provide diagnostic information on functional and pathological conditions of biological tissues and organs. Following a brief introduction to EIT, we summarize bioimpedance measurement methods, on which an EIT system is based, to acquire data for image reconstruction. Its forward problem is introduced in the context of a practically feasible measurement setting. Modeling of the forward problem and sensitivity analysis will be the key to understanding and designing an inversion method. Three kinds of EIT inverse problems, including static imaging, time-difference imaging and frequency-difference imaging, will be described.

7.1 Introduction

The material properties of electrical conductivity and permittivity may produce image contrast in EIT. The conductivity (σ) and permittivity () values of a biological tissue are determined by its ion concentrations ...