A priori modeling for gradient based inverse scattering algorithms

Nordebo, Sven,1963-Lund University,Lunds universitet,Växjö universitet,Matematiska och systemtekniska institutionen,Institutionen för elektro- och informationsteknik,Institutioner vid LTH,Lunds Tekniska Högskola,Department of Electrical and Information Technology,Departments at LTH,Faculty of Engineering, LTH (author)

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.

TEKNIK OCH TEKNOLOGIER Elektroteknik och elektronik hsv//swe
ENGINEERING AND TECHNOLOGY Electrical Engineering, Electronic Engineering, Information Engineering hsv//eng
Electrical engineering, electronics and photonics
Elektroteknik, elektronik och fotonik
Electrotechnology
Elektroteknik alt Electrical engineering

Gustafsson, MatsLund University,Lunds universitet,Institutionen för elektro- och informationsteknik,Institutioner vid LTH,Lunds Tekniska Högskola,Department of Electrical and Information Technology,Departments at LTH,Faculty of Engineering, LTH(Swepub:lu)tde-mgu (author)
Växjö universitetMatematiska och systemtekniska institutionen (creator_code:org_t)

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