# The Calder\'on problem with corrupted data

## TL;DR

This paper addresses the inverse Calderón problem with noisy data, proposing theoretical formulas for reconstructing conductivity and its derivatives, and analyzing the convergence rate of the method under measurement errors.

## Contribution

It introduces a theoretical, stochastic approach to reconstruct conductivity from corrupted data and provides formulas and convergence analysis for the method.

## Key findings

- Formulas for reconstructing conductivity and its normal derivative from noisy data.
- Analysis of the convergence rate of the reconstruction method.
- Theoretical framework accommodating measurement errors in the Calderón problem.

## Abstract

We consider the inverse Calder\'on problem consisting of determining the conductivity inside a medium by electrical measurements on its surface. Ideally, these measurements determine the Dirichlet-to-Neumann map and, therefore, one usually assumes the data to be given by such map. This situation corresponds to having access to infinite-precision measurements, which is totally unrealistic. In this paper, we study the Calder\'on problem assuming the data to contain measurement errors and provide formulas to reconstruct the conductivity and its normal derivative on the surface. Additionally, we state the rate convergence of the method. Our approach is theoretical and has a stochastic flavour.