On the robustness of inverse scattering for penetrable, homogeneous objects with complicated boundary. (1st March 2023)

• Record Type: Journal Article
• Authors: Borges, Carlos; Rachh, Manas; Greengard, Leslie
• Is Part Of: Inverse problems. Volume 39:Number 3(2023)
• Publication Date: 2023-03-01
• Subjects: inverse scattering -- transmission problem -- Helmholtz equation -- boundary integral equations -- recursive linearization; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/acb2ec
• Languages: English
• ISSNs: 0266-5611

Abstract

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.