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A PRIORI MODELING FOR GRADIENT BASED INVERSE SCATTERING ALGORITHMS

By S. Nordebo and M. Gustafsson

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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:
S. Nordebo and M. 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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