Magneto-Acousto-Electric Tomography with Magnetic Field Measurements: Modeling, Inversion and Stability

TL;DR

This paper develops a mathematical model and inversion method for magneto-acousto-electric tomography (MAET) using magnetic field data, demonstrating stable conductivity recovery under specific conditions.

Contribution

It introduces a rigorous quasi-static model for MAET with magnetic measurements and a two-step inversion process with stability analysis.

Findings

Conductivity can be stably recovered under smallness assumptions.

The model decouples the hybrid inverse problem into two steps.

Lipschitz stability is proven in various geometries.

Abstract

Magneto-acousto-electric tomography (MAET) combines ultrasound with a static magnetic field to infer the electrical conductivity of an object. In this paper, we present a rigorous quasi-static mathematical model for MAET with magnetic field measurements and introduce an adjoint problem to decouple the resulting hybrid inverse problem. This yields a two-step inversion procedure: solving an acoustic inverse source problem and then recovering the conductivity from an internal current density. We prove that, under explicit smallness assumptions on the conductivity and coil geometry, the conductivity can be recovered with Lipschitz stability in both bounded and half-space geometries.