On the robustness of inverse scattering for penetrable, homogeneous objects with complicated boundary

TL;DR

This paper compares boundary-based and volumetric approaches for acoustic inverse obstacle scattering, finding the volumetric method more robust despite higher degrees of freedom, through systematic numerical analysis.

Contribution

It extends shape optimization methods to penetrable objects and systematically compares boundary and volumetric approaches in inverse scattering.

Findings

Volumetric approach shows greater robustness.

Boundary approach is less stable with complex boundaries.

Numerical experiments validate the superiority of volumetric methods.

Abstract

The acoustic inverse obstacle scattering problem consists of determining the shape of a domain from measurements of the scattered far field due to some set of incident fields (probes). For a penetrable object with known sound speed, this can be accomplished by treating the boundary alone as an unknown curve. Alternatively, one can treat the entire object as unknown and use a more general volumetric representation, without making use of the known sound speed. Both lead to strongly nonlinear and nonconvex optimization problems for which recursive linearization provides a useful framework for numerical analysis. After extending our shape optimization approach developed earlier for impenetrable bodies, we carry out a systematic study of both methods and compare their performance on a variety of examples. Our findings indicate that the volumetric approach is more robust, even though the number of degrees of freedom is significantly larger. We conclude with a discussion of this phenomenon and potential directions for further research.