Direct Sampling for Recovering Sound Soft Scatterers from Point Source Measurements

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 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 allows us to derive explicit bounds in the resolution analysis for the direct sampling method’s imaging functional. Two direct sampling methods are studied, using the far-field transformation. For these imaging functionals, we use the Funk–Hecke identities to study the resolution analysis. We 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 with full and partial aperture data.

Keywords

• direct sampling method
• sound soft scatterer
• factorization method