Approximation of continuous EIT data from electrode measurements with Bayesian methods

Abstract

The electrical impedance tomography (EIT) in its classical formulation seeks to estimate the electric conductivity distribution inside the body from the knowledge of the Dirichlet-to-Neumann (DtN) map of the conductivity equation at the boundary. Numerical methods for the solution of the EIT problem have been developed based on this formulation, most notably the d-bar method and the layer stripping algorithm. In practice, however, the EIT data (electrode data), collected by using a fixed number of contact electrodes, is tantamount to knowledge of the resistance matrix, a mapping between given current configuration and the corresponding vector of measured electrode voltages. Forward models corresponding to the DtN data and the electrode data differ in terms of the boundary values and no direct connection between them has been established. In this article, we analyze the relation between the two boundary data types, and propose to approximate the DtN data from the measured resistance matrix for solving the EIT inverse problem within the Bayesian framework, leveraging a sample based prior and a principal component model reduction.