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

TL;DR

This paper develops and justifies a novel factorization method using a single plane wave to identify convex polygonal scatterers, combining model-driven and data-driven approaches without needing forward solvers.

Contribution

It provides a rigorous mathematical foundation for a one-wave factorization method and demonstrates its potential through preliminary numerical examples.

Findings

The method accurately recovers convex polygonal scatterers from a single far-field pattern.

It does not require forward solvers, simplifying computational procedures.

The approach combines model-driven and data-driven techniques for improved robustness.

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}.