Quantification of measurement error effects on conductivity reconstruction in electrical impedance tomography

Electrical impedance tomography (EIT) is a boundary measurement inverse technique targeting reconstruction of the conductivity distribution of the interior of a physical body based on boundary measurement data. Typically, the measured data are uncertain because of various error sources; thus, there are many uncertainties in the reconstructed image. This study attempts to quantify the effects of these measurement errors on EIT reconstruction. A comprehensive framework that combines uncertainty quantification techniques and EIT reconstruction techniques is proposed. In this framework, a polynomial chaos expansion method is used to construct a surrogate model of the conductivity field with respect to the measurement errors. Two shape detection indices are introduced to show the EIT reconstruction quality. Finally, under certain detection index constraints, statistical and sensitivity analyses are performed using the properties of the surrogate model. Several EIT problems are examined in this study, involving one or two anomalies in a circular domain or two asymmetric anomalies in a body-like domain. The results show that the proposed framework can quantify the effects of measurement errors on EIT reconstruction at reasonable cost. Further, for the test cases, the measurement errors at the electrodes close to the anomalies are shown to have the greatest influence on the image reconstruction.