Novel implementation of the extended sampling method for inverse biharmonic scattering

TL;DR

This paper introduces a new extended sampling method for inverse biharmonic scattering that improves obstacle detection from limited data, incorporating sound-hard and sound-soft reference disks, and demonstrates effectiveness through numerical experiments.

Contribution

Develops a novel extended sampling method based on factorization analysis for better shape and size reconstruction in biharmonic inverse problems.

Findings

Effective obstacle localization with limited incident waves

Sound-hard sampling disks enhance reconstruction accuracy

Method robust to noisy data and sensitive to reference disk radius

Abstract

This paper considers an inverse shape problem for recovering an unknown clamped obstacle in two dimensions from far--field measurements generated by a single incident wave or just a few incident waves for the biharmonic (flexural) wave equation. Here we will develop a new extended sampling method (ESM) that is derived using the analysis of the well--known factorization method. We will also consider an ESM using both sound--soft and sound--hard sampling disks to identify sampling points where the reference disk intersects the unknown cavity. The use of a sound--hard sampling disk has not been studied in the literature whereas the sound--soft sampling disk has been used in most recent works. Traditionally the ESM seeks to find the location of the scatterer from limited incident directional data. Here, our method acts more like the factorization method to obtain the location as well as the size (and possibly the shape) of the obstacle. We present numerical experiments with synthetic data that demonstrate how effective this new implementation is with respect to noisy data and illustrate the influence of the reference disk radius on the reconstruction.