A mathematical model and inversion procedure for Magneto-Acousto-Electric Tomography (MAET)

TL;DR

This paper introduces a mathematical model and an efficient inversion algorithm for Magneto-Acousto-Electric Tomography (MAET), demonstrating its stability and high-resolution imaging capabilities through analytical and numerical analysis.

Contribution

It proposes a new general inversion procedure for MAET, including an explicit series solution for cubic regions, enhancing reconstruction speed and stability.

Findings

MAET provides high-resolution images with noise resilience.

The explicit series solution enables fast reconstruction for cubic regions.

Both analytical and numerical results confirm the method's stability.

Abstract

Magneto-Acousto-Electric Tomography (MAET), also known as the Lorentz force or Hall effect tomography, is a novel hybrid modality designed to be a high-resolution alternative to the unstable Electrical Impedance Tomography. In the present paper we analyze existing mathematical models of this method, and propose a general procedure for solving the inverse problem associated with MAET. It consists in applying to the data one of the algorithms of Thermo-Acoustic tomography, followed by solving the Neumann problem for the Laplace equation and the Poisson equation. For the particular case when the region of interest is a cube, we present an explicit series solution resulting in a fast reconstruction algorithm. As we show, both analytically and numerically, MAET is a stable technique yilelding high-resolution images even in the presence of significant noise in the data.