A fully non-linear optimization approach to acousto-electric tomography

TL;DR

This paper introduces a non-linear optimization method for acousto-electric tomography, improving image reconstruction by addressing the non-linear inverse problem with a conjugate gradient scheme and revealing trade-offs between resolution and contrast.

Contribution

It formulates the inverse problem as a regularized non-linear optimization, proves existence of solutions, and develops a conjugate gradient algorithm for improved reconstructions.

Findings

Reconstruction quality depends on regularization choice.

Non-linear effects significantly influence image resolution and contrast.

The method generalizes to other hybrid imaging techniques.

Abstract

This paper considers the non-linear inverse problem of reconstructing an electric conductivity distribution from the interior power density in a bounded domain. Applications include the novel tomographic method known as acousto-electric tomography, in which the measurement setup in Electrical Impedance Tomography is modulated by ultrasonic waves thus giving rise to a method potentially having both high contrast and high resolution. We formulate the inverse problem as a regularized non-linear optimization problem, show the existence of a minimizer, and derive optimality conditions. We propose a non-linear conjugate gradient scheme for finding a minimizer based on the optimality conditions. All our numerical experiments are done in two-dimensions. The experiments reveal new insight into the non-linear effects in the reconstruction. One of the interesting features we observe is that, depending on the choice of regularization, there is a trade-off between high resolution and high contrast in the reconstructed images. Our proposed non-linear optimization framework can be generalized to other hybrid imaging modalities.