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2009-08-03
A Priori Modeling for Gradient Based Inverse Scattering Algorithms
By
Progress In Electromagnetics Research B, Vol. 16, 407-432, 2009
Abstract
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.
Citation
Sven Nordebo, and Mats Gustafsson, "A Priori Modeling for Gradient Based Inverse Scattering Algorithms," Progress In Electromagnetics Research B, Vol. 16, 407-432, 2009.
doi:10.2528/PIERB09060805
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