Imaging point sources in heterogeneous environments. (24th October 2019)

• Record Type: Journal Article
• Authors: Ren, Kui; Zhong, Yimin
• Is Part Of: Inverse problems. Volume 35:Number 12(2019)
• Publication Date: 2019-10-24
• Subjects: inverse source problems -- Helmholtz equation -- point sources -- stability estimates -- inverse problems -- numerical reconstructions; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ab3497
• Languages: English
• ISSNs: 0266-5611

Abstract

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 (2012 C. R. Acad. Sci. Paris I 350 1031–5), 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.