The factorization method for the inverse acoustic scattering problems with limited aperture data

TL;DR

This paper extends the factorization method to inverse acoustic scattering problems with limited aperture data by developing a new functional analytic framework that handles non-symmetric factorizations.

Contribution

It introduces a novel theoretical approach for the factorization method applicable to limited aperture data where symmetry is absent.

Findings

Provides a new characterization of the unknown domain

Develops a functional analytic theorem for non-symmetric factorizations

Enables application of the factorization method to limited aperture scenarios

Abstract

We study the factorization method for the inverse acoustic scattering problems in the case of limited aperture data. In this case, the factorization of the far field operator is not symmetric. So, we can not apply the original factorization method which requires the symmetricity of the factorization. In this paper, we provide a new functional analytic theorem corresponding to the case of limited aperture data, and by applying it, we give the characterizations of the unknown domain.