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

Carlos Borges, Manas Rachh, Leslie Greengard

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number035004
JournalInverse Problems
Issue number3
StatePublished - Mar 2023


  • Helmholtz equation
  • boundary integral equations
  • inverse scattering
  • recursive linearization
  • transmission problem

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Mathematical Physics
  • Computer Science Applications
  • Applied Mathematics


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