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 Inverse Problems
24(2).
- Abstract
- This paper presents a systematic approach to robust preconditioning for gradient-based nonlinear 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 consist 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.... (More)
- This paper presents a systematic approach to robust preconditioning for gradient-based nonlinear 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 consist 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/1049419
- author
- Nordebo, Sven
LU
; Fhager, Andreas
; Gustafsson, Mats
LU
and Persson, Mikael
- organization
- publishing date
- 2008
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Inverse Problems
- volume
- 24
- issue
- 2
- article number
- 025027
- publisher
- IOP Publishing
- external identifiers
-
- wos:000254375500028
- scopus:42549158861
- ISSN
- 0266-5611
- DOI
- 10.1088/0266-5611/24/2/025027
- language
- English
- LU publication?
- yes
- id
- 68b5ce0a-5265-4469-b782-68d439ee7de7 (old id 1049419)
- date added to LUP
- 2016-04-04 08:21:57
- date last changed
- 2022-01-29 03:21:26
@article{68b5ce0a-5265-4469-b782-68d439ee7de7,
abstract = {{This paper presents a systematic approach to robust preconditioning for gradient-based nonlinear 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 consist 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.}},
author = {{Nordebo, Sven and Fhager, Andreas and Gustafsson, Mats and Persson, Mikael}},
issn = {{0266-5611}},
language = {{eng}},
number = {{2}},
publisher = {{IOP Publishing}},
series = {{Inverse Problems}},
title = {{A systematic approach to robust preconditioning for gradient-based inverse scattering algorithms}},
url = {{http://dx.doi.org/10.1088/0266-5611/24/2/025027}},
doi = {{10.1088/0266-5611/24/2/025027}},
volume = {{24}},
year = {{2008}},
}