Two-stage reconstruction of a circular anomaly in electrical impedance tomography

Abstract

In the electrical impedance tomography inverse problem, an unknown conductivity distribution in a given object is to be reconstructed from a set of noisy voltage measurements made on the boundary. This paper focuses on the development of effective reconstruction techniques for detection of a circular anomaly from an otherwise constant background. The goal is to investigate applicability of a two-stage reconstruction process in which a region of interest (ROI) containing the anomaly (e.g. a tumour) is determined in the first stage, and the actual reconstruction is found in the second stage by exploring the ROI. Bayesian inversion methods are applied. The conductivity distribution is modelled as a random variable that follows a posterior probability density proportional to the product of a prior density and a likelihood function. The investigated two-stage reconstruction strategy is, however, not fully Bayesian. In the first stage, the ROI is determined using a quasi-Newton optimization algorithm and a smoothness prior, and in the second stage, the reconstruction is found using Markov chain Monte Carlo sampling and an anomaly prior. Performances of white noise and enhanced noise models as well as performances of standard and linearized finite element forward simulations are compared.