Simultaneous estimation of electrical conductivity and permittivity in quantitative thermoacoustic tomography

TL;DR

This paper develops a Bayesian framework for simultaneously estimating electrical conductivity and permittivity in quantitative thermoacoustic tomography, demonstrating the feasibility and challenges of the approach through numerical simulations.

Contribution

It introduces a Bayesian inverse problem approach for joint estimation of dielectric parameters in thermoacoustic tomography, incorporating Maxwell's equations and finite element methods.

Findings

Electrical conductivity and permittivity can be estimated simultaneously.

Multiple electromagnetic excitations improve estimation accuracy.

Non-uniqueness issues can be mitigated with additional excitations.

Abstract

In this work, the inverse problem of quantitative thermoacoustic tomography is studied. In quantitative thermoacoustic tomography, dielectric parameters of an imaged target are estimated from an absorbed energy density induced by an externally introduced electromagnetic excitation. In this work, simultaneous estimation of electrical conductivity and permittivity is considered. We approach this problem in the framework of Bayesian inverse problems. The dielectric parameters are estimated by computing maximum a posteriori estimates, and the reliability of the estimates is studied using the Laplace's approximation. The forward model to describe electromagnetic wave propagation is based on a vectorial Maxwell's equation, that is numerically approximated using a finite element method with edge elements. The proposed methodology is evaluated using numerical simulations utilising one or two electromagnetic excitations at multiple excitation frequencies. The results show that the electrical conductivity and permittivity can be simultaneously estimated in quantitative thermoacoustic tomography. However, the problem can suffer from non-uniqueness, which could be overcome using multiple electromagnetic excitations.