Frequency content of randomly scattered signals. II: Inversion
In this paper we formulate and solve a one-dimensional inverse scattering problem using noisy data. In our model, we assume that a pulse is reflected from an acoustic medium with material properties which vary on two distinct spatial scales. In particular, we assume that the medium consists of a small scale random microstructure superimposed on large scale smooth macroscopic variations. We consider the problem of determining the macroscopic variation from the backscattered data, when its effects are obscured by random multiple scattering from the microstructure. To this end, the medium is probed with a pulse whose width is intermediate between the two spatial scales. To our knowledge, this is the first time a tractable problem of this type has been formulated in which signal and noise are modeled from first principles as generated by the same physical process of wave scattering. The asymptotic theory for randomly reflected signals on which we base our inversion scheme is described in part I [see the foregoing entry Zbl 0727.73019)].
one-dimensional inverse scattering problem
small scale random microstructure superimposed on large scale smooth macroscopic variations
scientific article; zbMATH DE number 4201765
scientific article