Stability estimates for the inverse source problem with passive measurements

TL;DR

This paper establishes stability estimates for an inverse source problem in a non-homogeneous medium using passive boundary measurements across multiple frequencies, demonstrating well-posedness under certain frequency conditions.

Contribution

It provides the first stability estimates for reconstructing sources from passive measurements in complex media, combining spectral analysis and unique continuation techniques.

Findings

Inverse problem is well-posed for sufficiently large frequency bands.

Stability estimates depend on the spectral properties of the medium.

The approach uses spectral decomposition and holomorphic continuation of the resolvent.

Abstract

We consider the multi-frequency inverse source problem in the presence of a non-homogeneous medium using passive measurements. Precisely, we derive stability estimates for determining the source from the knowledge of only the imaginary part of the radiated field on the boundary for multiple frequencies. The proof combines a spectral decomposition with a quantification of the unique continuation of the resolvent as a holomorphic function of the frequency. The obtained results show that the inverse problem is well posed when the frequency band is larger than the spatial frequency of the source.