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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 Technical Report LUTEDX/(TEAT-7164)/1-23/(2008) TEAT-7164.
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)
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organization
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type
Book/Report
publication status
published
subject
in
Technical Report LUTEDX/(TEAT-7164)/1-23/(2008)
volume
TEAT-7164
pages
23 pages
publisher
[Publisher information missing]
external identifiers
  • scopus:42549158861
language
English
LU publication?
yes
id
ace062ea-9f61-4cb3-a32a-14c09a28e8f1 (old id 1049016)
date added to LUP
2008-03-18 12:47:01
date last changed
2017-01-01 08:18:58
@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},
  pages        = {23},
  series       = {Technical Report LUTEDX/(TEAT-7164)/1-23/(2008)},
  title        = {A systematic approach to robust preconditioning for gradient based inverse scattering algorithms},
  volume       = {TEAT-7164},
  year         = {2008},
}