Full Newton method for inverse transmission line problems, utilising explicit second order derivatives
2007 (English)In: Inverse Problems in Science and Engineering, ISSN 1741-5977, E-ISSN 1741-5985, Vol. 15, no 8, 827-853 p.Article in journal (Refereed) Published
The full Newton's method is considered as,in optimisation approach to the inverse transmission line problem in the frequency-domain. For the sake of accuracy and computational efficiency, the gradient and the Hessian of the cost-functional, with respect to parameter functions in the L-2-space, are derived explicitly by means of the adjoint transmission line problem and the first and second order Frechet differentials of the cost-functional. The numerical implementation, when reducing to a finite dimensional parameter space, and a regularisation technique for the resulting ill-conditioned Hessian matrix are presented. For the reconstruction of one or two parameters, the algorithm is tested oil synthetic reflection data contaminated with gaussian noise. The algorithm is also tested oil measured reflection data to reconstruct a piecewise constant shunt-capacitance. The generalisation to the three-dimensional inverse scattering problem for bianisotropic media is presented.
Place, publisher, year, edition, pages
2007. Vol. 15, no 8, 827-853 p.
inverse problem, transmission line, optimisation, Newton method, Hessian, image-reconstruction, optimization approach, frequency-domain, parameter, object
IdentifiersURN: urn:nbn:se:kth:diva-17210DOI: 10.1080/17415970601030734ISI: 000252669300004ScopusID: 2-s2.0-37149038890OAI: oai:DiVA.org:kth-17210DiVA: diva2:335253
QC 201005252010-08-052010-08-05Bibliographically approved