Analysis of the Magneto-acoustic Tomography with Magnetic Induction (MAT-MI)

TL;DR

This paper analyzes the mathematical foundations of Magneto-acoustic Tomography with Magnetic Induction (MAT-MI), demonstrating that conductivity can be uniquely and stably reconstructed from internal data, and proposing a numerical recovery method.

Contribution

It provides a rigorous mathematical analysis of the second step in MAT-MI, including uniqueness, stability, and a numerical approach for conductivity reconstruction.

Findings

Single internal data determines conductivity uniquely.

A global Lipschitz stability estimate is established.

Numerical experiments demonstrate the effectiveness of the proposed method.

Abstract

Magnetoacoustic tomography with magnetic induction (MAT-MI) is a coupled-physics medical imaging modality for determining conductivity distribution in biological tissue. The capability of MAT-MI to provide high resolution images has been demonstrated experimentally. MAT-MI involves two steps. The first step is a well-posed inverse source problem for acoustic wave equation, which has been well studied in the literature. This paper concerns mathematical analysis of the second step, a quantitative reconstruction of the conductivity from knowledge of the internal data recovered in the first step, using techniques such as time reversal. The problem is modeled by a system derived from Maxwell's equations. We show that a single internal data determines the conductivity. A global Lipschitz type stability estimate is obtained. A numerical approach for recovering the conductivity is proposed and results from computational experiments are presented.