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Three-dimensional inverse scattering: layer-stripping formulas and ill-posedness results

Cheney, Margaret and Kristensson, Gerhard LU (1988) In Inverse Problems 4(3). p.625-642
Abstract
The authors consider the three-dimensional direct and inverse scattering problems for the Schrodinger equation and for the reduced wave equation with variable velocity. The scatterer is probed with either point sources or plane waves of fixed frequency. They ask the question, 'How does the wave field change when the scatterer is truncated?' Simple formulae for the derivative of the wave field with respect to the truncation parameter are obtained. Similar formulae are obtained for the scattering amplitudes. These formulae are used to derive ill-posedness results for various inverse scattering problems. The ill-posedness results apply when data are collected over a range of frequencies.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Inverse Problems
volume
4
issue
3
pages
625 - 642
publisher
IOP Publishing
external identifiers
  • scopus:0039417022
ISSN
0266-5611
DOI
10.1088/0266-5611/4/3/007
language
English
LU publication?
yes
id
a8184dbe-1d53-4459-8dbc-ce0e2fb5aec2 (old id 1039254)
date added to LUP
2008-02-28 12:08:44
date last changed
2017-01-01 07:32:10
@article{a8184dbe-1d53-4459-8dbc-ce0e2fb5aec2,
  abstract     = {The authors consider the three-dimensional direct and inverse scattering problems for the Schrodinger equation and for the reduced wave equation with variable velocity. The scatterer is probed with either point sources or plane waves of fixed frequency. They ask the question, 'How does the wave field change when the scatterer is truncated?' Simple formulae for the derivative of the wave field with respect to the truncation parameter are obtained. Similar formulae are obtained for the scattering amplitudes. These formulae are used to derive ill-posedness results for various inverse scattering problems. The ill-posedness results apply when data are collected over a range of frequencies.},
  author       = {Cheney, Margaret and Kristensson, Gerhard},
  issn         = {0266-5611},
  language     = {eng},
  number       = {3},
  pages        = {625--642},
  publisher    = {IOP Publishing},
  series       = {Inverse Problems},
  title        = {Three-dimensional inverse scattering: layer-stripping formulas and ill-posedness results},
  url          = {http://dx.doi.org/10.1088/0266-5611/4/3/007},
  volume       = {4},
  year         = {1988},
}