Inverse Problems Seminar - Recovering point sources for the inhomogeneous Helmholtz equation

The talk 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 background 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 local Carleman estimates and an ad-hoc technique for proving uniqueness of the Cauchy problem.