High resolution inverse scattering in two dimensions using recursive linearization
For researchers in inverse scattering and imaging, this provides a practical algorithm for high-resolution reconstruction in a nonlinear, ill-posed problem.
The paper presents a fast, stable algorithm for 2D inverse acoustic scattering, using recursive linearization to reconstruct sound speed at resolutions of thousands of square wavelengths in a nonlinear regime, solving up to 19,600 unknowns with ~1 million PDEs in ~2 days on a multi-core workstation.
We describe a fast, stable algorithm for the solution of the inverse acoustic scattering problem in two dimensions. Given full aperture far field measurements of the scattered field for multiple angles of incidence, we use Chen's method of recursive linearization to reconstruct an unknown sound speed at resolutions of thousands of square wavelengths in a fully nonlinear regime. 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 profile, each least squares calculation is well-conditioned and involves the solution of a large number of forward scattering problems, for which we employ a recently developed, spectrally accurate, fast direct solver. For the largest problems considered, involving 19,600 unknowns, approximately one million partial differential equations were solved, requiring approximately two days to compute using a parallel MATLAB implementation on a multi-core workstation.