A priori modeling for gradient based inverse scattering algorithms

Summary, in English

This paper presents a Fisher information based Bayesian approach to analysis and design of the regularization and preconditioning parameters used with gradient based inverse scattering algorithms. In particular, a one-dimensional inverse problem is considered where the permittivity and conductivity profiles are unknown and the input data consist of the scattered field over a certain bandwidth. A priori parameter modeling is considered with linear, exponential and arctangential parameter scalings and robust preconditioners are obtained by choosing the related scaling parameters based on a Fisher information analysis of the known background. The Bayesian approach and a principal parameter (singular value) analysis of the stochastic Cramer-Rao bound provide a natural interpretation of the regularization that is necessary to achieve stable inversion, as well as an indicator to predict the feasibility of achieving successful reconstruction in a given problem set-up. In particular, the Tikhonov regularization scheme is put into a Bayesian estimation framework. A time-domain least-squares inversion algorithm is employed which is based on a quasi-Newton algorithm together with an FDTD-electromagnetic solver. Numerical examples are included to illustrate and verify the analysis.

• Författare: Sven Nordebo; Mats Gustafsson
• Avdelning/ar: Institutionen för elektro- och informationsteknik
• Publiceringsår: 2009
• Språk: Engelska
• Sidor: 407-432
• Publikation/Tidskrift/Serie: Progress In Electromagnetics Research B
• Volym: 16
• Länkar: http://dx.doi.org/10.2528/PIERB09060805
• Dokumenttyp: Artikel i tidskrift
• Förlag: Electromagnetics Academy
• Ämne: Electrical Engineering, Electronic Engineering, Information Engineering
• Status: Published
• Forskningsgrupp: Electromagnetic theory
• ISBN/ISSN/Övrigt: ISSN: 1937-6472