Hybrid Inverse Problems for a System of Maxwell's Equations

TL;DR

This paper develops a method to uniquely and stably reconstruct optical properties in Thermo-acoustic Tomography by modeling radiation with Maxwell's equations, revealing differences from scalar models.

Contribution

It introduces a novel approach using Maxwell's equations for TAT inverse problems, demonstrating stability and uniqueness in reconstructing optical parameters.

Findings

Unique and stable reconstruction of optical properties from TAT data.

Reconstruction differs qualitatively from scalar Helmholtz models.

Linearization forms a redundant elliptic system.

Abstract

This paper concerns the quantitative step of the medical imaging modality Thermo-acoustic Tomography (TAT). We model the radiation propagation by a system of Maxwell's equations. We show that the index of refraction of light and the absorption coefficient (conductivity) can be uniquely and stably reconstructed from a sufficiently large number of TAT measurements. Our method is based on verifying that the linearization of the inverse problem forms a redundant elliptic system of equations. We also observe that the reconstructions are qualitatively quite different from the setting where radiation is modeled by a scalar Helmholtz equation as in [10].