H\"older Stability for an Inverse Medium Problem with Internal Data

TL;DR

This paper establishes a H"older stability estimate for an inverse medium problem with internal data, focusing on the Helmholtz equation, which enhances understanding of the problem's well-posedness in imaging applications.

Contribution

The work provides the first H"older stability estimate for an inverse medium problem with internal data, specifically for Helmholtz equations with bounded potentials.

Findings

Proved H"older stability estimate for the inverse problem

Demonstrated well-posedness under boundary conditions

Focused on Helmholtz equations with bounded potential

Abstract

We are interested in an inverse medium problem with internal data. This problem is originated from multi-waves imaging. We aim in the present work to study the well-posedness of the inversion in terms of the boundary conditions. We precisely show that we have actually a stability estimate of H\"older type. For sake of simplicity, we limited our study to the class of Helmholtz equations $\Delta$+V with bounded potential V.