Three-dimensional inverse scattering: layer-stripping formulas and ill-posedness results
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1039254
- author
- Cheney, Margaret and Kristensson, Gerhard LU
- organization
- publishing date
- 1988
- 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
- 2016-04-04 07:34:49
- date last changed
- 2021-01-03 09:35:14
@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}}, doi = {{10.1088/0266-5611/4/3/007}}, volume = {{4}}, year = {{1988}}, }