Frequency content of randomly scattered signals. II: Inversion
type: Item
instance of: scholarly article
title: Frequency content of randomly scattered signals. II: Inversion
zbMATH Open document ID: 0727.73020
DOI: 10.1016/0165-2125(90)90023-W
author: Marie Postel
author: Ping Sheng
author: Benjamin S. White
author: George Papanicolaou
published in: Wave Motion
publication date: 1990-01-01T00:00:00Z
review text: 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)].
Mathematics Subject Classification ID: 74J99
Mathematics Subject Classification ID: 74H50
Mathematics Subject Classification ID: 74J25
Mathematics Subject Classification ID: 74A40
Mathematics Subject Classification ID: 60G35
zbMATH DE Number: 4201765
zbMATH Keywords: one-dimensional inverse scattering problem
zbMATH Keywords: noisy data
zbMATH Keywords: small scale random microstructure superimposed on large scale smooth macroscopic variations
zbMATH Keywords: asymptotic theory
Wikidata QID: Q61761134
MaRDI profile type: Publication
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full work available at URL: 0165-2125(90)90023-w
OpenAlex ID: W2092004500
description: scientific article; zbMATH DE number 4201765