Feasibility of acousto-electric tomography

Abstract

In acousto-electric tomography (AET) the goal is to reconstruct the electric conductivity in a domain from electrostatic boundary measurements of corresponding currents and voltages, while the domain is perturbed by a time-dependent acoustic wave, thus taking advantage of the acousto-electric effect. We approach the AET reconstruction in two steps: First, the interior power density is obtained from boundary measurements by solving a linear inverse and ill-posed problem; second, the interior conductivity is reconstructed from the power density by solving a non-linear and well-posed problem. Mathematically these inverse problems are fairly well understood, and reconstruction methods work well on synthetic data. This is in contrast to experimental findings. An effect can indeed be observed and data can be collected. However, the acousto-electric coupling is very weak, and consequently, the change in the measured voltage due to the acoustic perturbation might be too small compared to the background noise for viable reconstructions. In this paper, we take one step towards understanding the feasibility of AET. We provide an in-silico model of the coupled physics scenario based on standard models for the individual phenomena. Moreover, we formulate and implement numerically a full reconstruction method for the inverse problem via the two steps. We perform computational experiments with realistically chosen parameters from the context of medical imaging. The focus is on understanding the role of the acousto-electric coupling parameter and the signal-to-noise ratio (SNR). The critical signal strength is analyzed and the omnipresent Johnson-Nyquist noise is estimated. We obtain both positive and negative findings; we can reconstruct features even under severe noise conditions, but we also find that the SNR one is likely to face in practice is too low to obtain useful reconstructions.