Stability in Conductivity Imaging from Partial Measurements of One Interior Current

TL;DR

This paper establishes a stability result for reconstructing electrical conductivity inside a body using partial interior current measurements, clarifying the conditions under which the reconstruction is reliably stable.

Contribution

It provides a new stability analysis for the inverse conductivity problem with partial interior current data, defining the region of stable reconstruction.

Findings

Stability region is characterized by data accuracy.

Partial interior current data suffices for stable conductivity recovery.

Theoretical bounds for reconstruction stability are derived.

Abstract

We prove a stability result in the hybrid inverse problem of recovering the electrical conductivity from partial knowledge of one current density field generated inside a body by an imposed boundary voltage. The region where interior data stably reconstructs the conductivity is well defined by a combination of the exact and perturbed data.