Abstract
This paper introduces a constructive method for approximating relative continuum measurements in two-dimensional electrical impedance tomography based on data originating from either the point electrode model or the complete electrode model. The upper bounds for the corresponding approximation errors explicitly depend on the number (and size) of the employed electrodes as well as on the regularity of the continuum current that is mimicked. In particular, if the input current and the object boundary are infinitely smooth, the discrepancy associated with the point electrode model converges to zero faster than any negative power of the number of electrodes. The results are first proven for the unit disk via trigonometric interpolation and quadrature rules, and they are subsequently extended to more general domains with the help of conformal mappings.
Highlights
In electrical impedance tomography (EIT) the goal is to reconstruct an unknown conductivity distribution inside a physical body
According to the idealized continuum model (CM) of EIT, such measurements correspond to knowing the infinite-dimensional Neumann-to-Dirichlet (ND) boundary map for the conductivity equation that models the behavior of the electric potential
The point-like electrodes of the point electrode model (PEM) cannot completely accurately model the finite-sized ones used in practical EIT measurements, it has been shown that the discrepancy between relative measurements modeled by the complete electrode model (CEM) and the PEM behave asymptotically as O(d2) in the maximal diameter d > 0 of the electrodes [17]
Summary
In electrical impedance tomography (EIT) the goal is to reconstruct an unknown conductivity distribution inside a physical body. We tackle mimicking relative continuum data by electrode measurements in two-dimensional EIT as a problem of (hardware) algorithm design: our aim is to choose (optimal) positions for the employed electrodes based on the shape of the imaged domain and the net electrode currents as functions of the continuum current pattern one would like to drive through the object boundary. M for the discrepancy between the relative measurements of the CM and suitably postprocessed PEM or CEM data (provided the width of the electrodes decay appropriately in M for the CEM) This result is first proven for the PEM in the unit disk with equiangular electrodes, and subsequently it is extended to more general domains with the help of conformal mappings. An appendix clarifies how the constants appearing in the estimates of [17] depend on the number of electrodes
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
