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

Abstract

Solving inverse scattering problems using layer stripping algorithms is known to be fast and effective when the data are noise-free. However, layer stripping algorithms have a reputation of being unstable when applied to noisy time-domain reflection response data. The reason is that the noisy data may be infeasible; i.e., could not have been produced by an actual media. In this paper, three feasibility conditions are introduced for data from absorbing (lossy) one-dimensional (1-D) media. Satisfying these conditions is both necessary and sufficient for the data to have been produced by an actual lossy media. That is, layer stripping algorithms applied such noisy but feasible data are stable. A methodology for correcting infeasible data is also proposed. Numerical examples illustrate key points and the correction method.

A Layer Stripping Approach for EM Reconstruction of Stratified Media

“…This is an intrinsic drawback of the LS approach due to its recursive formulation. In fact, as the number of layers increases, more iterations are required, so performances experience a general worsening due to the error spreading from one layer to the subsequent one, resulting in a divergent reconstruction [31].…”

Determination of the Fresnel Reflection Coefficient of a Half-Space for Medium Estimation Purposes

“…The first one is based on transmission and/or reflection coefficient measurements of material samples allocated, for instance, in wave-guide [2][3][4]. The other class of techniques, of major interest for this work, is based on the measurement of the reflection/transmission coefficients in free space conditions [5][6][7][8][9][10] mainly under plane wave incidence assumption.…”