A systematic approach to robust preconditioning for gradient based inverse scattering algorithms
(2008) In Technical Report LUTEDX/(TEAT7164)/123/(2008) TEAT7164. Abstract
 This paper presents a systematic approach to robust preconditioning for gradient based nonlinear inverse scattering algorithms. In particular, one and twodimensional 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 timedomain leastsquares formulation is employed and the inversion algorithm is based on a conjugate gradient, or
quasiNewton algorithm together with an FDTDelectromagnetic 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 nonlinear inverse scattering algorithms. In particular, one and twodimensional 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 timedomain leastsquares formulation is employed and the inversion algorithm is based on a conjugate gradient, or
quasiNewton algorithm together with an FDTDelectromagnetic 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 quasiNewton 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:
http://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/(TEAT7164)/123/(2008)
 volume
 TEAT7164
 pages
 23 pages
 publisher
 [Publisher information missing]
 external identifiers

 scopus:42549158861
 language
 English
 LU publication?
 yes
 id
 ace062ea9f614cb3a32a14c09a28e8f1 (old id 1049016)
 date added to LUP
 20080318 12:47:01
 date last changed
 20170813 04:51:46
@techreport{ace062ea9f614cb3a32a14c09a28e8f1, abstract = {This paper presents a systematic approach to robust preconditioning for gradient based nonlinear inverse scattering algorithms. In particular, one and twodimensional 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 timedomain leastsquares formulation is employed and the inversion algorithm is based on a conjugate gradient, or<br/><br> quasiNewton algorithm together with an FDTDelectromagnetic 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 quasiNewton 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/(TEAT7164)/123/(2008)}, title = {A systematic approach to robust preconditioning for gradient based inverse scattering algorithms}, volume = {TEAT7164}, year = {2008}, }