# Stability of Current Density Impedance Imaging

## TL;DR

This paper proves that current density impedance imaging (CDII) is stable against measurement errors, confirming previous numerical observations and enhancing understanding of its reliability in reconstructing conductivity from interior current measurements.

## Contribution

The paper provides a rigorous mathematical proof of the stability of CDII, which was previously supported only by numerical evidence.

## Key findings

- CDII is stable with respect to interior measurement errors
- Reconstruction stability is mathematically confirmed
- Supports previous numerical stability observations

## Abstract

We study stability of reconstruction in current density impedance imaging (CDII), that is, the inverse problem of recovering the conductivity of a body from the measurement of the magnitude of the current density vector field in the interior of the object. Our results show that CDII is stable with respect to errors in interior measurements of the current density vector field, and confirm the stability of reconstruction which was previously observed in numerical simulations, and was long believed to be the case.