On the feasibility of impulse reflection response data for the two-dimensional inverse scattering problem

Abstract

Abstruct-Layer stripping algorithms for inverse scattering problems are very fast but have the reputation of being numerically unstable, especially when applied to noisy data. The goal of this paper is to provide an explicitly discrete framework for layer stripping algorithms for the two-dimensional (2-D) Schrodinger equation inverse scattering problem. We determine when 2-D layer stripping algorithms are numerically stable, explain why they are stable, and specify exactly the (discrete) problem they solve when they are stable. We reformulate the 2- D Schrodinger equation as a multichannel two-component wave system by Fourier transforming the Schrodinger equation in the lateral spatial variable. Discretization results in new 2-D layer stripping algorithms which incorporate multichannel transmission effects; this leads to an important new feasibility condition onimpulse reflection response data for stability of these algorithms. A 2-D discrete Schrodinger equation is defined, and analogous results are obtained. Numerical examples illustrate the new results, especially how rendering noisy data feasible stabilizes layer stripping algorithms.

Time Domain Image Reconstruction for Homogenous Dielectric Objects by Dynamic Differential Evolution

“…However, the time domain scattering data is a potential alternative scheme for the inverse problem, because there is more available information about the scatterer than for single-frequency scattering data alone. Therefore, various time domain inversion approaches have been intensively proposed in recent years, which could be briefly classified into the layer-stripping approach (Yagle & Frolik, 1996) and iterative approaches, including the Born iterative method (BIM; Moghaddam et al, 1991), the distorted Born iterative method (DBIM; Weedon, 1994), and optimization approaches (Rekanos, 2003;Takenaka et al, 2000;He et al, 1996).…”

Computational Approach Based on a Differential Evolution with Self-Adaptive Concept for Microwave Imaging of Two-Dimensional Inverse Scattering Problem

“…However, the time-domain scheme is a potential alternative for inverse problems because the time-domain data contain more information about the scatterer than those in the scattered data of a single frequency. Therefore, various time-domain inversion approaches have been intensively proposed in recent years that could be briefly classified as the layer-stripping approach (Yagle & Frolik, 1996), the iterative approach, the distorted Born iterative method (DBIM) (Li et al, 2004), the optimization approach (Rekanos, 2003), and the forward-backward time-stepping method (Moriyama et al, 2011).…”

On the feasibility of impulse reflection response data from one-dimensional multilayered lossy media

“…These algorithms can be used to reconstruct stratified dielectric media, a problem that reduces to one dimension when the probing wave is assumed to be plane. In addition, layer stripping algorithms have been applied to lossless two-dimensional media [8]. The layer stripping approach recursively identifies the media by removing the effects of layers one at a time.…”