A Two-stage Method for Inverse Medium Scattering

TL;DR

This paper introduces a two-stage numerical method for inverse medium scattering that accurately detects and resolves scatterer properties from near-field data using a combination of sampling and regularization techniques.

Contribution

The paper proposes a novel two-stage approach combining direct sampling and mixed regularization for improved inverse scattering reconstruction.

Findings

Accurate detection of scatterer support in the first stage.

Precise resolution of scatterer sizes and intensities in the second stage.

Method is efficient, robust, and effective in noisy data scenarios.

Abstract

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