A systematic approach to robust preconditioning for gradient based inverse scattering algorithms
Nordebo, Sven LU ; Fhager, Andreas ; Gustafsson, Mats LU
and Persson, Mikael
(2008)
In Technical Report LUTEDX/(TEAT-7164)/1-23/(2008)
- Abstract
- This paper presents a systematic approach to robust preconditioning for gradient based non-linear inverse scattering algorithms. In particular, one- and two-dimensional inverse problems are considered where the permittivity and conductivity profiles are unknown and the input data consists of the scattered field over a certain bandwidth. A time-domain least-squares formulation is employed and the inversion algorithm is based on a conjugate gradient, or
quasi-Newton algorithm together with an FDTD-electromagnetic solver. A Fisher information analysis is used to estimate the Hessian of the error functional. A robust preconditioner is then obtained by incorporating a parameter scaling such that the scaled Fisher information has a unit... (More) - This paper presents a systematic approach to robust preconditioning for gradient based non-linear inverse scattering algorithms. In particular, one- and two-dimensional inverse problems are considered where the permittivity and conductivity profiles are unknown and the input data consists of the scattered field over a certain bandwidth. A time-domain least-squares formulation is employed and the inversion algorithm is based on a conjugate gradient, or
quasi-Newton algorithm together with an FDTD-electromagnetic solver. A Fisher information analysis is used to estimate the Hessian of the error functional. A robust preconditioner is then obtained by incorporating a parameter scaling such that the scaled Fisher information has a unit diagonal. By improving the conditioning of the Hessian, the convergence rate of the conjugate gradient or quasi-Newton methods are improved. The preconditioner is robust
in the sense that the scaling, i.e., the diagonal Fisher information is virtually invariant to the numerical resolution and the discretization model that is employed. Numerical examples of image reconstruction are included to illustrate the efficiency of the proposed technique. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1049016
- author
- Nordebo, Sven
LU
; Fhager, Andreas
; Gustafsson, Mats
LU
and Persson, Mikael
- organization
- publishing date
- 2008
- type
- Book/Report
- publication status
- published
- subject
- in
- Technical Report LUTEDX/(TEAT-7164)/1-23/(2008)
- pages
- 23 pages
- publisher
- [Publisher information missing]
- report number
- TEAT-7164
- external identifiers
-
- scopus:42549158861
- language
- English
- LU publication?
- yes
- additional info
- Published version: Inverse problems, Vol. 24, No. 2, pp. 025027-, 2008.
- id
- ace062ea-9f61-4cb3-a32a-14c09a28e8f1 (old id 1049016)
- date added to LUP
- 2016-04-04 14:30:59
- date last changed
- 2022-01-30 02:06:29
@techreport{ace062ea-9f61-4cb3-a32a-14c09a28e8f1,
abstract = {{This paper presents a systematic approach to robust preconditioning for gradient based non-linear inverse scattering algorithms. In particular, one- and two-dimensional inverse problems are considered where the permittivity and conductivity profiles are unknown and the input data consists of the scattered field over a certain bandwidth. A time-domain least-squares formulation is employed and the inversion algorithm is based on a conjugate gradient, or<br/><br>
quasi-Newton algorithm together with an FDTD-electromagnetic solver. A Fisher information analysis is used to estimate the Hessian of the error functional. A robust preconditioner is then obtained by incorporating a parameter scaling such that the scaled Fisher information has a unit diagonal. By improving the conditioning of the Hessian, the convergence rate of the conjugate gradient or quasi-Newton methods are improved. The preconditioner is robust<br/><br>
in the sense that the scaling, i.e., the diagonal Fisher information is virtually invariant to the numerical resolution and the discretization model that is employed. Numerical examples of image reconstruction are included to illustrate the efficiency of the proposed technique.}},
author = {{Nordebo, Sven and Fhager, Andreas and Gustafsson, Mats and Persson, Mikael}},
institution = {{[Publisher information missing]}},
language = {{eng}},
number = {{TEAT-7164}},
series = {{Technical Report LUTEDX/(TEAT-7164)/1-23/(2008)}},
title = {{A systematic approach to robust preconditioning for gradient based inverse scattering algorithms}},
url = {{https://lup.lub.lu.se/search/files/6378229/1049266}},
year = {{2008}},
}