Selective focusing of multiple particles in a layered medium

TL;DR

This paper introduces a novel method for selectively focusing on multiple buried scatterers in layered media using time reversal and Bayesian inversion, improving identification and imaging accuracy in applications like geophysics and medical imaging.

Contribution

It develops a new asymptotic analysis-based focusing technique that distinguishes different types of particles and integrates Bayesian inversion for enhanced reconstruction.

Findings

Eigenvalues correspond to particle types, enabling selective focusing.

The method effectively identifies multiple scatterers with high resolution.

Numerical experiments confirm the method's efficiency and accuracy.

Abstract

Inverse scattering in layered media has a wide range of applications, examples including geophysical exploration, medical imaging, and remote sensing. In this paper, we develop a selective focusing method for identifying multiple unknown buried scatterers in a layered medium. The method is derived through the asymptotic analysis of the time reversal operator using the layered Green's function and limited aperture measurements. We begin by showing the global focusing property of the time reversal operator. Then we demonstrate that each small sound-soft particle gives rise to one significant eigenvalue of the time reversal operator, while each sound-hard particle gives three. The associated eigenfunction generates an incident wave focusing selectively on the corresponding unknown particle. Finally, we employ the time reversal method as an initial indicator and propose an effective Bayesian inversion scheme to reconstruct multiple buried extended scatterers for enhanced resolution. Numerical experiments are provided to demonstrate the efficiency.