A priori modeling for gradient based inverse scattering algorithms

• 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.

Subject headings

TEKNIK OCH TEKNOLOGIER  -- Elektroteknik och elektronik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Electrical Engineering, Electronic Engineering, Information Engineering (hsv//eng)

Keyword

Electrical engineering, electronics and photonics

Elektroteknik, elektronik och fotonik

Electrotechnology

Elektroteknik alt Electrical engineering

Publication and Content Type

ref (subject category)

art (subject category)