Local electrical impedance tomography via projections
A. Jääskeläinen, A. Vavilov, J. Toivanen, A. Hänninen, V. Kolehmainen, N. Hyvönen
TL;DR
This work presents a projection-based framework for local electrical impedance tomography (EIT) that suppresses effects from conductivity changes outside a region of interest (ROI). By partitioning the domain into ROI and rest-of-domain (RONI) and constructing projections from a weighted nuisance Jacobian via left singular vectors, the method enables ROI-focused reconstructions from difference data. The approach integrates into a Bayesian linearized EIT solver with a smoothened total variation prior through a lagged diffusivity iteration, and is validated on three tank experiments including a head-shaped phantom to mimic stroke monitoring. Results show that partial projections onto the RONI can substantially reduce non-ROI artifacts and improve ROI localization, with performance depending on the chosen nuisance subspace and projection strategy. The framework offers a practical pathway to local EIT in clinical and industrial settings, while highlighting open issues in nuisance-subspace selection and nonlinear extensions.
Abstract
This paper introduces a method for approximately eliminating the effect that conductivity changes outside the region of interest have in electrical impedance tomography, allowing to form a local reconstruction in the region of interest only. The method considers the Jacobian matrix of the forward map, i.e., of the map that sends the discretized conductivity to the electrode measurements, at an initial guess for the conductivity. The Jacobian matrix is divided columnwise into two parts: one corresponding to the region of interest and a nuisance Jacobian corresponding to the rest of the domain. The leading idea is to project both the electrode measurements and the forward map onto the orthogonal complement of the span of a number of left-hand singular vectors for a suitably weighted nuisance Jacobian. The weighting can, e.g., account for the element sizes in a finite element discretization or to prior information on the conductivity outside the region of interest. The inverse problem is then solved by considering the projected relation between the measurements and the forward map, only reconstructing the conductivity in the region of interest. The functionality of the method is demonstrated by applying a reconstruction algorithm that combines lagged diffusivity iteration and total variation regularization to experimental data. In particular, data from a head-shaped water tank is considered, with the conductivity change in the region of interest mimicking growth of a hemorrhagic stroke and the changes outside the region of interest imitating physiological variations in the conductivity of the scalp.