Cramer-Rao lower bounds for inverse scattering problems of multilayer structures
Gustafsson, Mats LU
and Nordebo, Sven
LU
(2006)
In Inverse Problems
22(4).
p.1359-1380
- Abstract
- In this paper, the inverse scattering problem of amultilayer structure is analysed with the Fisher information matrix and the Cramer-Rao lower bound (CRLB). The CRLB quantifies the ill-posedness of the inverse scattering problem in terms of resolution versus estimation accuracy based on the observation of noisy data. The limit for feasible inversion is identified by an asymptotic eigenvalue analysis of the Toeplitz Fisher information matrix and an application of the sampling theorem. It is shown that the resolution is inversely proportional to the bandwidth of the reflection data and that the CRLB increases linearly with the number of slabs. The transmission data give a rank-1 Fisher information matrix which can approximately reduce the... (More)
- In this paper, the inverse scattering problem of amultilayer structure is analysed with the Fisher information matrix and the Cramer-Rao lower bound (CRLB). The CRLB quantifies the ill-posedness of the inverse scattering problem in terms of resolution versus estimation accuracy based on the observation of noisy data. The limit for feasible inversion is identified by an asymptotic eigenvalue analysis of the Toeplitz Fisher information matrix and an application of the sampling theorem. It is shown that the resolution is inversely proportional to the bandwidth of the reflection data and that the CRLB increases linearly with the number of slabs. The transmission data give a rank-1 Fisher information matrix which can approximately reduce the CRLB by a factor of 4. Moreover, the effect of dispersive material parameters and simultaneous estimation of two material parameters are analysed. The results are illustrated with numerical examples. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/401364
- author
- Gustafsson, Mats
LU
and Nordebo, Sven
LU
- organization
- publishing date
- 2006
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Inverse Problems
- volume
- 22
- issue
- 4
- pages
- 1359 - 1380
- publisher
- IOP Publishing
- external identifiers
-
- wos:000239164600015
- scopus:33746295326
- ISSN
- 0266-5611
- DOI
- 10.1088/0266-5611/22/4/014
- language
- English
- LU publication?
- yes
- id
- 99aefa4e-8f29-414d-b87c-be6cf824b83d (old id 401364)
- date added to LUP
- 2016-04-01 11:45:14
- date last changed
- 2022-01-26 17:45:30
@article{99aefa4e-8f29-414d-b87c-be6cf824b83d,
abstract = {{In this paper, the inverse scattering problem of amultilayer structure is analysed with the Fisher information matrix and the Cramer-Rao lower bound (CRLB). The CRLB quantifies the ill-posedness of the inverse scattering problem in terms of resolution versus estimation accuracy based on the observation of noisy data. The limit for feasible inversion is identified by an asymptotic eigenvalue analysis of the Toeplitz Fisher information matrix and an application of the sampling theorem. It is shown that the resolution is inversely proportional to the bandwidth of the reflection data and that the CRLB increases linearly with the number of slabs. The transmission data give a rank-1 Fisher information matrix which can approximately reduce the CRLB by a factor of 4. Moreover, the effect of dispersive material parameters and simultaneous estimation of two material parameters are analysed. The results are illustrated with numerical examples.}},
author = {{Gustafsson, Mats and Nordebo, Sven}},
issn = {{0266-5611}},
language = {{eng}},
number = {{4}},
pages = {{1359--1380}},
publisher = {{IOP Publishing}},
series = {{Inverse Problems}},
title = {{Cramer-Rao lower bounds for inverse scattering problems of multilayer structures}},
url = {{http://dx.doi.org/10.1088/0266-5611/22/4/014}},
doi = {{10.1088/0266-5611/22/4/014}},
volume = {{22}},
year = {{2006}},
}