A Survey of Approaches to Solving Inverse Problems for Lossless Layered Media Systems

In this paper, we survey approaches to solving inverse problems for lossless layered systems. Such systems can be modeled in two different ways, by nonparametric or parametric models. We review both models, but concentrate our attention on inverse and estimation procedures for parametric models. Algebraic inverse procedures are described for determining the reflection coefficient parameters when measurements are noise free. An extension of these procedures to the case of noisy data is also discussed; but, resulting reflection coefficient values are suboptimal. Finally, we describe two procedures for estimating reflection coefficients from noisy data. One of these, which is very promising, is a maximum-likelihood procedure, which is not only able to provide estimates of reflection coefficients, but is also able to provide estimates of another set of parameters, layer travel times. These maximum-likelihood estimates are optimal.