Inverse scattering by a continuation method with initial guesses from a direct imaging algorithm

Authors:
Gang Bao;Songming Hou;Peijun Li
Affiliations:
Department of Mathematics, Michigan State University, East Lansing, MI 48824, United States;Department of Mathematics and Statistics, Louisiana Tech University, Ruston, LA 71272, United States;Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, United States
Venue:
Journal of Computational Physics
Year:
2007

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Abstract

A novel continuation method is presented for solving the inverse medium scattering problem of the Helmholtz equation, which is to reconstruct the shape of the inhomogeneous medium from boundary measurements of the scattered field. The boundary data is assumed to be available at multiple frequencies. Initial guesses are chosen from a direct imaging algorithm, multiple signal classification (MUSIC), along with a level set representation at a certain wavenumber, where the Born approximation may not be valid. Each update via recursive linearization on the wavenumbers is obtained by solving one forward and one adjoint problem of the Helmholtz equation.