A Multilevel Sampling Algorithm for Locating Inhomogeneous Media

TL;DR

This paper introduces a multilevel sampling algorithm that efficiently locates inhomogeneous media in inverse scattering problems, reducing computational effort and improving robustness and convergence.

Contribution

The paper presents a novel multilevel sampling method for accurately locating inhomogeneous media, enabling more efficient subsequent shape reconstruction.

Findings

Robustness against noise demonstrated

Requires fewer incident measurements

Fast convergence observed

Abstract

In the reconstruction process of unknown multiple scattering objects in inverse medium scattering problems, the first important step is to effectively locate some approximate domains that contain all inhomogeneous media. Without such an effective step, one may have to take a much larger computational domain than actually needed in the reconstruction of all scattering objects, thus resulting in a huge additional computational efforts. In this work we propose a simple and efficient multilevel reconstruction algorithm to help locate an accurate position and shape of each inhomogeneous medium. Then other existing effective but computationally more demanding reconstruction algorithms may be applied in these initially located computational domains to achieve more accurate shapes of the scatter and the contrast values over each medium domain. The new algorithm exhibits several strengths: robustness against noise, requiring less incidences, fast convergence, flexibility to deal with scatterers of special shapes, and advantages in computational complexity.