English

Factorization method with one plane wave: from model-driven and data-driven perspectives

Numerical Analysis 2025-08-25 v1 Numerical Analysis

Abstract

The factorization method by Kirsch (1998) 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. This paper is concerned with the factorization method with a single far-field pattern to recover a 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 scheme can be interpreted as a model-driven and data-driven method, because it essentially depends on the scattering model and a priori given \emph{sample data}.

Keywords

Cite

@article{arxiv.2101.09664,
  title  = {Factorization method with one plane wave: from model-driven and data-driven perspectives},
  author = {Guanqiu Ma and Guanghui Hu},
  journal= {arXiv preprint arXiv:2101.09664},
  year   = {2025}
}
R2 v1 2026-06-23T22:27:46.220Z