2D and 3D reconstructions in acousto-electric tomography

TL;DR

This paper introduces stable algorithms for reconstructing internal conductivity in biological tissues using acousto-electric measurements, employing synthetic focusing with realistic acoustic wave propagation to produce accurate 2D and 3D images even with noisy data.

Contribution

The authors develop and validate a new reconstruction method that uses synthetic focusing with spherical acoustic waves, improving stability and accuracy over traditional approaches.

Findings

High-quality 2D and 3D images achieved

Method remains accurate with high noise levels

Local uniqueness and stability proven for the problem

Abstract

We propose and test stable algorithms for the reconstruction of the internal conductivity of a biological object using acousto-electric measurements. Namely, the conventional impedance tomography scheme is supplemented by scanning the object with acoustic waves that slightly perturb the conductivity and cause the change in the electric potential measured on the boundary of the object. These perturbations of the potential are then used as the data for the reconstruction of the conductivity. The present method does not rely on "perfectly focused" acoustic beams. Instead, more realistic propagating spherical fronts are utilized, and then the measurements that would correspond to perfect focusing are synthesized. In other words, we use \emph{synthetic focusing}. Numerical experiments with simulated data show that our techniques produce high quality images, both in 2D and 3D, and that they remain accurate in the presence of high-level noise in the data. Local uniqueness and stability for the problem also hold.