Inverse source problems in an inhomogeneous medium with a single far-field pattern

2019/07/19 by Guanghui Hu, Hu, Guanghui, Jingzhi Li +1 · 1 citation
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Microwave Imaging and Scattering Analysis #Numerical methods in inverse problems #Ultrasonics and Acoustic Wave Propagation

paper · pdf · doi:10.48550/arxiv.1907.08390

openalex publication_date 2019/07/19 · openalex created_date 2020/03/23 · openalex updated_date 2026/07/28

Abstract

This paper concerns time-harmonic inverse source problems with a single far-field pattern in two dimensions, where the source term is compactly supported in an a priori given inhomogeneous background medium. For convex-polygonal source terms, we prove that the source support together with the zeroth and first order derivatives of the source function at corner points can be uniquely determined. Further, we prove that an admissible set of source functions (including harmonic functions) having a convex-polygonal support can be uniquely identified by a single far-field pattern. A class of radiating sources is characterized and the extension of the radiated field across a corner point is proven impossible. The corner scattering theory leads to a data-driven inversion scheme for imaging an arbitrarily convex-polygonal source support.

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