Recovering point sources for the inhomogeneous Helmholtz equation * *The work of GB is supported in part by a NSFC Innovative Group Fund (No. 11621101). The work of FT is supported in part by the Grant ANR-17-CE40-0029 of the French National Research Agency ANR (project MultiOnde).

Abstract

The paper is concerned with an inverse point source problem for the Helmholtz equation. It consists of recovering the locations and amplitudes of a finite number of radiative point sources inside a given inhomogeneous medium from the knowledge of a single boundary measurement. The main result of the paper is a new Hölder type stability estimate for the inversion under the assumption that the point sources are well separated. The proof of the stability is based on a combination of Carleman estimates and a technique for proving uniqueness of the Cauchy problem.