Increasing stability for the inverse source scattering problem with multi-frequencies

TL;DR

This paper demonstrates that using multi-frequency Dirichlet boundary data significantly enhances the stability of reconstructing a compactly supported source in inverse Helmholtz scattering problems in 2D and 3D.

Contribution

It provides a new stability analysis showing that multi-frequency data improves the inverse source reconstruction stability.

Findings

Stability increases with multiple frequencies

Multi-frequency data improves reconstruction accuracy

Applicable to 2D and 3D Helmholtz equations

Abstract

Consider the scattering of the two- or three-dimensional Helmholtz equation where the source of the electric current density is assumed to be compactly supported in a ball. This paper concerns the stability analysis of the inverse source scattering problem which is to reconstruct the source function. Our results show that increasing stability can be obtained for the inverse problem by using only the Dirichlet boundary data with multi-frequencies.