Recovering a polyhedral obstacle by a few backscattering measurements

TL;DR

This paper introduces a method to recover polyhedral obstacles in 2D and 3D using only a few high-frequency backscattering measurements, by determining face normals and positions from phaseless data.

Contribution

It presents a novel inverse scattering scheme that reconstructs obstacle geometry with minimal measurements by analyzing local maxima in backscattering data.

Findings

The method accurately determines face normals from local maxima in backscattering data.

It reduces obstacle reconstruction to a finite-dimensional problem of locating the obstacle and its faces.

Numerical experiments confirm the effectiveness of the proposed approach.

Abstract

We propose an inverse scattering scheme of recovering a polyhedral obstacle in $\mathbb{R}^n$, $n=2,3$, by only a few high-frequency acoustic backscattering measurements. The obstacle could be sound-soft or sound-hard. It is shown that the modulus of the far-field pattern in the backscattering aperture possesses a certain local maximum behavior, from which one can determine the exterior normal directions of the front sides/faces. Then by using the phaseless backscattering data corresponding to a few incident plane waves with suitably chosen incident directions, one can determine the exterior unit normal vector of each side/face of the obstacle. After the determination of the exterior unit normals, the recovery is reduced to a finite-dimensional problem of determining a location point of the obstacle and the distance of each side/face away from the location point. For the latter reconstruction, we need make use of the far-field data with phases. Numerical experiments are also presented to illustrate the effectiveness of the proposed scheme.