# Uniqueness and factorization method for inverse elastic scattering with a single incoming wave

## TL;DR

This paper proves the uniqueness of identifying polygonal obstacles in elastic scattering from a single wave and introduces a new factorization method for reconstructing elastic bodies using minimal data.

## Contribution

It establishes the first uniqueness result for inverse elastic scattering with one incident wave and develops a revisited factorization method for elastic body recovery.

## Key findings

- Unique identification of polygonal obstacles from a single far-field pattern
- Development of a new reflection principle for the Navier equation
- A revisited factorization method for elastic body reconstruction

## Abstract

The first part of this paper is concerned with the uniqueness to inverse time-harmonic elastic scattering from bounded rigid obstacles in two dimensions. It is proved that a connected polygonal obstacle can be uniquely identified by the far-field pattern over all observation directions corresponding to a single incident plane wave. Our approach is based on a new reflection principle for the first boundary value problem of the Navier equation. In the second part, we propose a revisited factorization method to recover a rigid elastic body with a single far-field pattern.