Recovering coefficients in a system of semilinear Helmholtz equations from internal data

TL;DR

This paper investigates the inverse problem of reconstructing multiple coefficients in a coupled semilinear Helmholtz system from internal data, establishing uniqueness, stability, and demonstrating numerical reconstruction quality with noisy data.

Contribution

It introduces a novel approach using linearization techniques to prove uniqueness and stability in reconstructing coefficients from internal measurements.

Findings

Proved uniqueness and stability for small boundary data

Developed a linearization-based reconstruction method

Numerical simulations show effective reconstructions with noisy data

Abstract

We study an inverse problem for a coupled system of semilinear Helmholtz equations where we are interested in reconstructing multiple coefficients in the system from internal data measured in applications such as thermoacoustic imaging. We derive results on the uniqueness and stability of the inverse problem in the case of small boundary data based on the technique of first- and higher-order linearization. Numerical simulations are provided to illustrate the quality of reconstructions that can be expected from noisy data.