# Sparse reconstruction of log-conductivity in current density impedance tomography

## TL;DR

This paper introduces a novel non-linear optimization method for sparse reconstruction of log-conductivities in current density impedance tomography, combining $L^1$ regularization and anisotropic diffusion to improve image resolution.

## Contribution

It presents a new framework that enhances image quality in impedance tomography by integrating sparsity promotion and edge enhancement techniques.

## Key findings

- Demonstrates superior reconstruction quality over existing methods.
- Effectively captures high-contrast conductivity patterns.
- Numerical experiments validate the approach's robustness.

## Abstract

A new non-linear optimization approach is proposed for the sparse reconstruction of log-conductivities in current density impedance imaging. This framework comprises of minimizing an objective functional involving a least squares fit of the interior electric field data corresponding to two boundary voltage measurements, where the conductivity and the electric potential are related through an elliptic PDE arising in electrical impedance tomography. Further, the objective functional consists of a $L^1$ regularization term that promotes sparsity patterns in the conductivity and a Perona-Malik anisotropic diffusion term that enhances the edges to facilitate high contrast and resolution. This framework is motivated by a similar recent approach to solve an inverse problem in acousto-electric tomography. Several numerical experiments and comparison with an existing method demonstrate the effectiveness of the proposed method for superior image reconstructions of a wide-variety of log-conductivity patterns.