Computational inverse scattering with internal sources: a reproducing kernel Hilbert space approach

TL;DR

This paper introduces a novel method using reproducing kernel Hilbert spaces and regularization to reconstruct the dielectric susceptibility of inhomogeneous media from internal source data, demonstrated with numerical examples.

Contribution

It applies RKHS theory to inverse scattering with internal sources, providing a new regularization-based reconstruction approach for 2D and 3D media.

Findings

Effective reconstruction demonstrated through numerical examples

Applicable to both two- and three-dimensional scattering media

Shows improved stability and accuracy over existing methods

Abstract

We present a method to reconstruct the dielectric susceptibility (scattering potential) of an inhomogeneous scattering medium, based on the solution to the inverse scattering problem with internal sources. We employ the theory of reproducing kernel Hilbert spaces, together with regularization to recover the susceptibility of two- and three-dimensional scattering media. Numerical examples illustrate the effectiveness of the proposed reconstruction method.