Carlos Borges
College of Sciences
University of Central Florida (UCF)

"Inverse Scattering Problems: A framework for high-resolution parameter reconstruction"

Wednesday, Dec 06, 2023

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Abstract:

We present a fast, accurate, and stable algorithm for the solution of the inverse acoustic scattering problems. Given full aperture far field measurements of the scattered field for multiple angles of incidence, we use a continuation-in-frequency scheme based in Chen's method of recursive linearization to reconstruct unknown parameters of a domain with high resolution in a fully nonlinear regime. Despite the fact that the underlying optimization problem is formally ill-posed, non-linear, and non-convex, our scheme 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 parameters, the solution of each iteration of the nonlinear optimization method is well-conditioned and involves the solution of forward scattering problems, for which we employ fast analysis-based solvers to solve integral representations to a PDE. We present compelling results obtained through the application of our framework to various manifestations of the inverse scattering problem, encompassing both penetrable and impenetrable obstacles in two dimensions. Our findings underscore the adaptability of the framework, showcasing its potential extension to three-dimensional problems—an exciting avenue for future exploration in our ongoing research endeavors.