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. © 2012 Elsevier Inc.
|Original language||English (US)|
|Number of pages||13|
|Journal||Journal of Computational Physics|
|State||Published - Mar 2013|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: We are grateful to two anonymous referees for their thoughtful comments, which have improved the quality of the paper. The work of BJ is supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST), and that of JZ is substantially supported by Hong Kong RGC grants (projects 405110 and 404611).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.