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Cramer-Rao lower bounds for inverse scattering problems of multilayer structures

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Author

Summary, in English

In this paper, the inverse scattering problem of amultilayer structure is analysed with the Fisher information matrix and the Cramer-Rao lower bound (CRLB). The CRLB quantifies the ill-posedness of the inverse scattering problem in terms of resolution versus estimation accuracy based on the observation of noisy data. The limit for feasible inversion is identified 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 reflection data and that the CRLB increases linearly with the number of slabs. The transmission data give a rank-1 Fisher information matrix which can approximately reduce the CRLB by a factor of 4. Moreover, the effect of dispersive material parameters and simultaneous estimation of two material parameters are analysed. The results are illustrated with numerical examples.

Publishing year

2006

Language

English

Pages

1359-1380

Publication/Series

Inverse Problems

Volume

22

Issue

4

Document type

Journal article

Publisher

IOP Publishing

Topic

  • Electrical Engineering, Electronic Engineering, Information Engineering

Status

Published

ISBN/ISSN/Other

  • ISSN: 0266-5611