Direct sampling for recovering sound soft scatterers from point source measurements

TL;DR

This paper introduces and analyzes new direct sampling methods for recovering sound soft scatterers from point source measurements, providing explicit resolution bounds and demonstrating effectiveness through numerical examples.

Contribution

The paper proposes novel direct sampling techniques using far-field transformations and Funk-Hecke identities for improved scatterer imaging from known point source data.

Findings

Explicit resolution bounds derived for the imaging functional.

Effective recovery of sound soft scatterers demonstrated in 2D simulations.

New methods applicable to Cauchy data cases.

Abstract

In this paper, we consider the inverse problem of recovering a sound soft scatterer from the measured scattered field. The scattered field is assumed to be induced by a point source on a curve/surface that is known. Here we will propose and analyze new direct sampling methods for this problem. The first method we consider uses a far-field transformation of the near-field data which will allow us to derive explicit bounds in the resolution analysis for the direct sampling method's imaging functional. Two direct sampling methods will be studied using the far-field transformation. For these imaging functionals, we will use the Funk-Hecke identities to study the resolution analysis. We will also study a direct sampling method for the case of the given Cauchy data. Numerical examples are given to show the applicability of the new imaging functionals for recovering a sound soft scatterer in 2D.