A direct imaging method for inverse scattering by unbounded rough surfaces

TL;DR

This paper introduces a fast, accurate, and noise-robust direct imaging method for reconstructing unbounded rough surfaces in inverse scattering problems using near-field data.

Contribution

It proposes a novel direct imaging algorithm applicable to both penetrable and impenetrable rough surfaces, with theoretical analysis and numerical validation.

Findings

The method is fast and accurate.

It is robust against noise in the data.

Applicable to various boundary conditions.

Abstract

This paper is concerned with the inverse scattering problem by an unbounded rough surface. A direct imaging method is proposed to reconstruct the rough surface from the scattered near-field Cauchy data generating by point sources and measured on a horizontal straight line segment at a finite distance above the rough surface. Theoretical analysis of the imaging algorithm is given for the case of a penetrable rough surface, but the imaging algorithm also works for impenetrable surfaces with Dirichlet or impedance boundary conditions. Numerical experiments are presented to show that the direct imaging algorithm is fast, accurate and very robust with respect to noise in the data.