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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)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Inverse Problems
volume
24
issue
2
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
2008-03-19 11:20:09
date last changed
2017-08-13 04:35:24
@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.},
  articleno    = {025027},
  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},
  volume       = {24},
  year         = {2008},
}