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

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.