A direct imaging method for inverse scattering problem of biharmonic wave with phased and phaseless data

TL;DR

This paper introduces a direct imaging method based on reverse time migration for inverse biharmonic scattering problems, capable of reconstructing obstacle shapes using various measurement data types.

Contribution

A novel imaging technique utilizing reverse time migration for inverse biharmonic problems with phased and phaseless data, effective with limited measurement types.

Findings

Imaging functions show contrast near and far from obstacle boundaries.

Numerical experiments confirm accurate reconstruction of complex geometries.

Method demonstrates robustness to noise.

Abstract

This paper investigates the inverse biharmonic scattering problems of identifying the shape and location of the obstacle with phased and phaseless measurement data. A direct imaging method based on reverse time migration is proposed for reconstructing the extended obstacle with one of four types of boundary conditions on the obstacle. The newly developed imaging functions are constructed by utilizing merely one of various measurement data, including the scattered field, its normal derivative, the bending moment, the transverse force, its far-field and the phaseless total field. Our resolution analysis demonstrates that these imaging functions have a contrast when sampling points are near or far from the boundary of the obstacle. Numerical experiments are further presented to show the algorithm's efficiency to accurately reconstruct complex scatter geometries and its robustness to noise.