Imaging of isotropic and anisotropic conductivities from power densities in three dimensions

TL;DR

This paper develops improved algorithms for reconstructing three-dimensional isotropic and anisotropic conductivities from power density measurements, addressing issues like vanishing determinants, with numerical validation.

Contribution

It advances previous methods by enhancing algorithm robustness for 3D conductivity imaging, including anisotropic cases, and tackles the problem of vanishing determinants.

Findings

Successful numerical reconstructions demonstrated

Enhanced algorithm stability and accuracy

Addressed vanishing determinant issues

Abstract

We present numerical reconstructions of anisotropic conductivity tensors in three dimensions, from knowledge of a finite family of power density functionals. Such a problem arises in the coupled-physics imaging modality Ultrasound Modulated Electrical Impedance Tomography for instance. We improve on the algorithms previously derived in [Bal et al, Inverse Probl Imaging (2013), pp.353-375, Monard and Bal, Comm. PDE (2013), pp.1183-1207] for both isotropic and anisotropic cases, and we address the well-known issue of vanishing determinants in particular. The algorithm is implemented and we provide numerical results that illustrate the improvements.