A priori modeling for gradient based inverse scattering algorithms
Nordebo, Sven LU and Gustafsson, Mats LU
(2009)
In Progress In Electromagnetics Research B
16.
p.407-432
- Abstract
- This paper presents a Fisher information based Bayesian approach to analysis and design of the regularization and preconditioning parameters used with gradient based inverse scattering algorithms. In particular, a one-dimensional inverse problem is considered where the permittivity and conductivity profiles are unknown and the input data consist of the scattered field over a certain bandwidth. A priori parameter modeling is considered with linear, exponential and arctangential parameter scalings and robust preconditioners are obtained by choosing the related scaling parameters based on a Fisher information analysis of the known background. The Bayesian approach and a principal parameter (singular value) analysis of the stochastic... (More)
- This paper presents a Fisher information based Bayesian approach to analysis and design of the regularization and preconditioning parameters used with gradient based inverse scattering algorithms. In particular, a one-dimensional inverse problem is considered where the permittivity and conductivity profiles are unknown and the input data consist of the scattered field over a certain bandwidth. A priori parameter modeling is considered with linear, exponential and arctangential parameter scalings and robust preconditioners are obtained by choosing the related scaling parameters based on a Fisher information analysis of the known background. The Bayesian approach and a principal parameter (singular value) analysis of the stochastic Cramer-Rao bound provide a natural interpretation of the regularization that is necessary to achieve stable inversion, as well as an indicator to predict the feasibility of achieving successful reconstruction in a given problem set-up. In particular, the Tikhonov regularization scheme is put into a Bayesian estimation framework. A time-domain least-squares inversion algorithm is employed which is based on a quasi-Newton algorithm together with an FDTD-electromagnetic solver. Numerical examples are included to illustrate and verify the analysis. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1453959
- author
- Nordebo, Sven
LU
and Gustafsson, Mats
LU
- organization
- publishing date
- 2009
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Progress In Electromagnetics Research B
- volume
- 16
- pages
- 407 - 432
- publisher
- Electromagnetics Academy
- external identifiers
-
- scopus:76249086648
- ISSN
- 1937-6472
- DOI
- 10.2528/PIERB09060805
- language
- English
- LU publication?
- yes
- id
- fab4b3f3-341f-4204-8cfe-9e198198ce57 (old id 1453959)
- date added to LUP
- 2016-04-04 09:41:34
- date last changed
- 2022-04-23 21:49:35
@article{fab4b3f3-341f-4204-8cfe-9e198198ce57,
abstract = {{This paper presents a Fisher information based Bayesian approach to analysis and design of the regularization and preconditioning parameters used with gradient based inverse scattering algorithms. In particular, a one-dimensional inverse problem is considered where the permittivity and conductivity profiles are unknown and the input data consist of the scattered field over a certain bandwidth. A priori parameter modeling is considered with linear, exponential and arctangential parameter scalings and robust preconditioners are obtained by choosing the related scaling parameters based on a Fisher information analysis of the known background. The Bayesian approach and a principal parameter (singular value) analysis of the stochastic Cramer-Rao bound provide a natural interpretation of the regularization that is necessary to achieve stable inversion, as well as an indicator to predict the feasibility of achieving successful reconstruction in a given problem set-up. In particular, the Tikhonov regularization scheme is put into a Bayesian estimation framework. A time-domain least-squares inversion algorithm is employed which is based on a quasi-Newton algorithm together with an FDTD-electromagnetic solver. Numerical examples are included to illustrate and verify the analysis.}},
author = {{Nordebo, Sven and Gustafsson, Mats}},
issn = {{1937-6472}},
language = {{eng}},
pages = {{407--432}},
publisher = {{Electromagnetics Academy}},
series = {{Progress In Electromagnetics Research B}},
title = {{A priori modeling for gradient based inverse scattering algorithms}},
url = {{http://dx.doi.org/10.2528/PIERB09060805}},
doi = {{10.2528/PIERB09060805}},
volume = {{16}},
year = {{2009}},
}