Past Event: Oden Institute Seminar

High Resolution Solution of Inverse Scattering Problems

Carlos Borges, ICES, UT Austin

Abstract

I describe a fast, stable framework for the solution of the inverse acoustic scattering problem. Given full aperture far field measurements of the scattered field for multiple angles of incidence, the recursive linearization is used to obtain high resolution reconstructions of properties of the scatterer. Despite the fact that the underlying optimization problem is formally ill-posed and non-convex, recursive linearization requires only the solution of a sequence of linear least squares problems at successively higher frequencies. By seeking a suitably band-limited approximation of the sound speed prole, each least squares calculation is well-conditioned and involves the solution of a large number of forward scattering problems. For two dimension problems we employ spectrally accurate, fast direct solvers. For the largest problems considered, approximately one million partial differential equations were solved, requiring approximately two days to compute using a parallel MATLAB implementation on a multi-core workstation.