Title: Cramér-Rao lower bounds for inverse scattering problems of multilayer structures
Abstract:In this paper, the inverse scattering problem of a multilayer structure is analyzed with the Fisher information matrix and the Cramer-Rao lower bound. The Cramer-Rao lower bound quanti es the ill-pose...In this paper, the inverse scattering problem of a multilayer structure is analyzed with the Fisher information matrix and the Cramer-Rao lower bound. The Cramer-Rao lower bound quanti es the ill-posedness of the inverse scattering problem in terms of resolution contra estimation accuracy based on the observation of noisy data. The limit for feasible inversion is identi ed by an asymptotic eigenvalue analysis of the Toeplitz Fisher information matrix and an application of the sampling theorem. It is shown that the resolution is inversely proportional to the bandwidth of the re ection data and that the Cramer-Rao lower bound increases linearly with the number of slabs. The transmission data gives a rank one Fisher information matrix which can approximately reduce the Cramer-Rao lower bound a factor of four. Moreover, the e ect of dispersive material parameters and simultaneous estimation of two material parameters are analyzed. The results are illustrated with numerical examples.Read More
Publication Year: 2006
Publication Date: 2006-01-01
Language: en
Type: article
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