Inverse scattering by a random periodic structure

TL;DR

This paper introduces a novel numerical approach combining Monte Carlo, continuation, and Karhunen-Loève expansion to efficiently reconstruct statistical properties of a random periodic structure from boundary scattering data.

Contribution

It presents a new computational method for inverse scattering problems involving random periodic structures, integrating multiple advanced techniques for improved reconstruction.

Findings

Method accurately reconstructs statistical properties

Demonstrates high efficiency and reliability

Applicable to complex random structures

Abstract

This paper develops an efficient numerical method for the inverse scattering problem of a time-harmonic plane wave incident on a perfectly reflecting random periodic structure. The method is based on a novel combination of the Monte Carlo technique for sampling the probability space, a continuation method with respect to the wavenumber, and the Karhunen-Lo$\grave{e}$ve expansion of the random structure, which reconstructs key statistical properties of the profile for the unknown random periodic structure from boundary measurements of the scattered fields away from the structure. Numerical results are presented to demonstrate the reliability and efficiency of the proposed method.