# Imaging point sources in heterogeneous environments

## TL;DR

This paper studies how uncertainties in the environment's refractive index affect the accuracy of imaging point sources using boundary or far-field measurements, providing stability results and numerical validation.

## Contribution

It extends existing imaging theories by analyzing the impact of environment uncertainty on source reconstruction stability in heterogeneous media.

## Key findings

- Reconstruction stability is maintained under measurement errors.
- Smooth variations in the environment have limited impact on imaging accuracy.
- Numerical simulations confirm theoretical stability results.

## Abstract

Imaging point sources in heterogeneous environments from boundary or far-field measurements has been extensively studied in the past. In most existing results, the environment, represented by the refractive index function in the model equation, is assumed known in the imaging process. In this work, we investigate the impact of environment uncertainty on the reconstruction of point sources inside it. Following the techniques developed by El Badia and El Hajj (C. R. Acad. Sci. Paris, Ser. I, 350 (2012), 1031-1035), we derive stability of reconstructing point sources in heterogeneous media with respect to measurement error as well as smooth changes in the environment, that is, the refractive index. Numerical simulations with synthetic data are presented to further explore the derived stability properties.