Factorization method with one plane wave: from model-driven and data-driven perspectives. (1st December 2021)

• Record Type: Journal Article
• Authors: Ma, Guanqiu; Hu, Guanghui
• Is Part Of: Inverse problems. Volume 38:Number 1(2022)
• Publication Date: 2021-12-01
• Subjects: factorization method -- inverse scattering -- inverse source problem -- single far-field pattern -- polygonal scatterers -- corner scattering; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ac38b5
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: The factorization method provides a necessary and sufficient condition for characterizing the shape and position of an unknown scatterer by using far-field patterns of infinitely many time-harmonic plane waves at a fixed frequency (which are also called the multistatic data response matrix). This paper is concerned with the factorization method with a single far-field pattern to recover an arbitrary convex polygonal scatterer/source. Its one-wave version relies on the absence of analytical continuation of the scattered/radiated wave-fields in corner domains. It can be regarded as a domain-defined sampling method and does not require forward solvers. In this paper we provide a rigorous mathematical justification of the one-wave factorization method and present some preliminary numerical examples. In particular, the proposed method can be interpreted as a model-driven and data-driven imaging scheme, and it shows how to incorporate a priori knowledge about the unknown target into the test scatterers for the purpose of detecting obstacles/sources with specific features.