# Discrete approximation and regularisation for the inverse conductivity problem

## TL;DR

This paper presents a combined regularisation and discretisation approach for solving the inverse conductivity problem with discontinuous conductivities, demonstrating convergence of solutions as measurement noise diminishes.

## Contribution

It introduces a novel variational method that simultaneously regularises and discretises the inverse conductivity problem with proven convergence properties.

## Key findings

- Discrete regularised solutions converge as noise decreases.
- Suitable parameter choices ensure convergence to the true solution.
- The approach effectively handles discontinuous conductivities.

## Abstract

We study the inverse conductivity problem with discontinuous conductivities. We consider, simultaneously, a regularisation and a discretisation for a variational approach to solve the inverse problem. We show that, under suitable choices of the regularisation and discretisation parameters, the discrete regularised solutions converge, as the noise level on the measurements goes to zero, to the looked for solution of the inverse problem.