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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)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Progress In Electromagnetics Research B
volume
16
pages
407 - 432
publisher
EMW Publishing
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
2009-08-05 11:41:28
date last changed
2016-10-16 04:14:52
@misc{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    = {ARRAY(0x99d3990)},
  series       = {Progress In Electromagnetics Research B},
  title        = {A priori modeling for gradient based inverse scattering algorithms},
  url          = {http://dx.doi.org/10.2528/PIERB09060805},
  volume       = {16},
  year         = {2009},
}