# Optimal depth-dependent distinguishability bounds for electrical impedance tomography in arbitrary dimension

## TL;DR

This paper derives and proves optimal bounds on how well electrical impedance tomography can distinguish inclusions at different depths within a domain, extending previous 2D results to higher dimensions.

## Contribution

It extends depth-dependent distinguishability bounds for electrical impedance tomography from 2D to arbitrary dimensions, using Kelvin transformations and proving their optimality.

## Key findings

- Depth-dependent distinguishability bounds are established for any dimension.
- The bounds are proven to be optimal.
- Results generalize previous 2D findings to higher dimensions.

## Abstract

The inverse problem of electrical impedance tomography is severely ill-posed. In particular, the resolution of images produced by impedance tomography deteriorates as the distance from the measurement boundary increases. Such depth dependence can be quantified by the concept of distinguishability of inclusions. This paper considers the distinguishability of perfectly conducting ball inclusions inside a unit ball domain, extending and improving known two-dimensional results to an arbitrary dimension $d \geq 2$ with the help of Kelvin transformations. The obtained depth-dependent distinguishability bounds are also proven to be optimal.