Modified sampling method with near field measurements

TL;DR

This paper introduces modified sampling methods for inverse scattering problems using near field measurements, applicable to obstacle and cavity problems, with theoretical support and numerical validation for full and limited data scenarios.

Contribution

It proposes novel sampling techniques that do not rely on asymptotic assumptions and includes a data completion algorithm for limited-aperture measurements.

Findings

Effective in reconstructing scatterers with full near field data.

Accurate results even with limited-aperture measurements.

Theoretical justification via near field operator factorization.

Abstract

This paper investigates the inverse scattering problems using sampling methods with near field measurements. The near field measurements appear in two classical inverse scattering problems: the inverse scattering for obstacles and the interior inverse scattering for cavities. We propose modified sampling methods to treat these two classical problems using near field measurements without making any asymptotic assumptions on the distance between the measurement surface and the scatterers. We provide theoretical justifications based on the factorization of the near field operator in both symmetric factorization case and non-symmetric factorization case. Furthermore, we introduce a data completion algorithm which allows us to apply the modified sampling methods to treat the limited-aperture inverse scattering problems. Finally numerical examples are provided to illustrate the modified sampling methods with both full- and limited- aperture near field measurements.