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Cramer-Rao Lower Bounds for Inverse Scattering Problems of Multilayer Structures
Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.ORCID iD: 0000-0002-7018-6248
2006 (English)In: Inverse Problems, Vol. 22, p. 1359-1380Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2006. Vol. 22, p. 1359-1380
Keywords [en]
Inverse problems, Cramer-Rao bound
National Category
Other Physics Topics Signal Processing
Research subject
Physics, Electrotechnology
Identifiers
URN: urn:nbn:se:vxu:diva-3076OAI: oai:DiVA.org:vxu-3076DiVA, id: diva2:203032
Available from: 2006-08-21 Created: 2006-08-21 Last updated: 2017-01-10Bibliographically approved

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Nordebo, Sven

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