A two-stage method for inverse medium scattering

Authors:
Kazufumi Ito;Bangti Jin;Jun Zou
Affiliations:
Department of Mathematics and Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695, USA;Department of Mathematics and Institute for Applied Mathematics and Computational Science, Texas A&M University, College Station, TX 77843-3368, USA;Department of Mathematics, Chinese University of Hong Kong, Shatin, N.T., Hong Kong
Venue:
Journal of Computational Physics
Year:
2013

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Abstract

We present a novel numerical method to the time-harmonic inverse medium scattering problem of recovering the refractive index from noisy near-field scattered data. The approach consists of two stages, one pruning step of detecting the scatterer support, and one resolution enhancing step with nonsmooth mixed regularization. The first step is strictly direct and of sampling type, and it faithfully detects the scatterer support. The second step is an innovative application of nonsmooth mixed regularization, and it accurately resolves the scatterer size as well as intensities. The nonsmooth model can be efficiently solved by a semi-smooth Newton-type method. Numerical results for two- and three-dimensional examples indicate that the new approach is accurate, computationally efficient, and robust with respect to data noise.