# Adaptive Reconstruction for Electrical Impedance Tomography with a Piecewise Constant Conductivity

arXiv: https://arxiv.org/abs/1904.08837 · HTML: https://mlsanity.com/paper/1904.08837/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Apr 2019.

## Built on by (most cited first, 2 of 2)

- [Transformer Meets Boundary Value Inverse Problems](https://mlsanity.com/paper/2209.14977/) (2022)
- [Electrical Impedance Tomography: A Fair Comparative Study on Deep Learning and Analytic-based Approaches](https://mlsanity.com/paper/2310.18636/) (2023)

## Abstract (arXiv)

In this work we propose and analyze a numerical method for electrical impedance tomography of recovering a piecewise constant conductivity from boundary voltage measurements. It is based on standard Tikhonov regularization with a Modica-Mortola penalty functional and adaptive mesh refinement using suitable a posteriori error estimators of residual type that involve the state, adjoint and variational inequality in the necessary optimality condition and a separate marking strategy. We prove the convergence of the adaptive algorithm in the following sense: the sequence of discrete solutions contains a subsequence convergent to a solution of the continuous necessary optimality system. Several numerical examples are presented to illustrate the convergence behavior of the algorithm.