On the robustness of inverse scattering for penetrable, homogeneous objects with complicated boundary
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Feb 01, 2023
- Source ID
- 10.1088/1361-6420/acb2ec
Entities
People
- Carlos F. Borges
- Leslie Greengard
- Manas Rachh
Organizations
- Office of Naval Research