[Paper Review] Feasibility of Acousto-Electric Tomography

Bjørn Jensen, Adrian Kirkeby+1 more|arXiv (Cornell University)|Aug 9, 2019

Electrical and Bioimpedance Tomography31 references4 citations

TL;DR

This paper proposes a two-step computational framework for acousto-electric tomography (AET) to reconstruct internal electrical conductivity from boundary measurements, first recovering power density and then conductivity. Despite extremely low signal-to-noise ratios (SNR) due to weak acousto-electric coupling and Johnson-Nyquist noise, numerical experiments show robust feature reconstruction even at 1000% relative noise (SNR = -10 dB), indicating mathematical feasibility but practical infeasibility without signal enhancement.

ABSTRACT

In acousto-electric tomography the goal is to reconstruct the electric conductivity in a domain from electrostatic boundary measurements of corresponding currents and voltages, while the domain is penetrated by a time-dependent acoustic wave. We explicitly model the phenomena, and we propose a complete inversion framework for acousto-electric tomography in two steps: First the interior power density is obtained from boundary measurements by solving a linear, ill-posed problem; second the interior conductivity is reconstructed from the power density by solving a non-linear, fairly well-posed problem. We perform numerical experiments on synthetic data with realistically chosen parameters. We investigate how feasibility of reconstructing the electrical conductivity from boundary measurements depends on the acousto-electric coupling constant and measurement noise. Our findings are positive, and indicate that AET is indeed feasible for interesting applications in for example medical imaging. Finally, we consider a limited angle setup and show that the conductivity is well reconstructed near the measurement boundary.

Motivation & Objective

• To assess the feasibility of acousto-electric tomography (AET) for medical imaging using realistic physical parameters.
• To develop a complete computational inversion framework for AET, including signal modeling and noise analysis.
• To quantify the critical signal strength and Johnson-Nyquist noise levels in AET to evaluate practical usability.
• To investigate whether AET can achieve stable, high-quality conductivity reconstructions under realistic noise conditions.

Proposed method

• Model the acousto-electric effect using a linearized conductivity perturbation model: σₚ(x,t) = σ(x)(1 + ηp(x,t)), where η is the known coupling parameter.
• Simulate the acoustic wave propagation via the scalar wave equation with known sound speed and external source.
• Reconstruct the interior power density from boundary voltage and current measurements using a linear inverse problem solution.
• Reconstruct the conductivity distribution from the power density using a nonlinear, well-posed inverse problem approach.
• Apply truncated singular value decomposition (TSVD) to stabilize the reconstruction of the power density operator H.
• Perform numerical experiments on synthetic data with increasing levels of relative noise (up to 1000%) to test robustness.

Experimental results

Research questions

• RQ1 Can acousto-electric tomography achieve stable and accurate conductivity reconstructions under realistic noise conditions?
• RQ2 What is the signal-to-noise ratio (SNR) in a clinically plausible AET setup, and is it sufficient for diagnostic imaging?
• RQ3 How does data redundancy from multiple acoustic waves and boundary conditions affect reconstruction robustness under high noise?
• RQ4 To what extent does Johnson-Nyquist noise dominate the measurable signal in AET, and can it be mitigated?

Key findings

• The reconstruction of conductivity features remains observable even at a relative noise level of 1000% (SNR = -10 dB), indicating strong robustness to noise.
• The method demonstrates significant resilience to random noise due to data redundancy from multiple acoustic waves and boundary conditions.
• Johnson-Nyquist noise is estimated to be several orders of magnitude larger than the acousto-electric signal, making practical implementation extremely challenging.
• Despite favorable mathematical properties and robustness, the required signal-to-noise ratio remains infeasible for high-resolution medical imaging with current technology.
• The two-step inversion framework—first reconstructing power density, then conductivity—proves effective and stable under extreme noise conditions.
• The study concludes that AET may be useful for anomaly detection or low-resolution imaging in materials science, but not for high-resolution medical diagnostics without major SNR improvements.