Bounds on the accuracy of estimating the parameters of discrete homogeneous random fields with mixed spectral distributions

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Abstract

This paper considers the achievable accuracy in jointly estimating the parameters of a real-valued two-dimensional (2-D) homogeneous random field with mixed spectral distribution, from a single observed realization of it. On the basis of a 2-D Wold-like decomposition, the field is represented as a sum of mutually orthogonal components of three types: purely indeterministic, harmonic, and evanescent. An exact form of the Cramer-Rao lower bound on the error variance in jointly estimating the parameters of the different components is derived. It is shown that the estimation of the harmonic component is decoupled from that of the purely indeterministic and the evanescent components. Moreover, the bound on the parameters of the purely indeterministic and the evanescent components is independent of the harmonic component. Numerical evaluation of the bounds provides some insight into the effects of various parameters on the achievable estimation accuracy.

Original languageEnglish
Pages (from-to)908-922
Number of pages15
JournalIEEE Transactions on Information Theory
Volume43
Issue number3
DOIs
StatePublished - 1 Dec 1997

Keywords

  • 2-D Wold decomposition
  • 2-D mixed spectral distributions
  • Cramer-Rao bound
  • Evanescent fields
  • Fisher information
  • Harmonic fields
  • Purely indeterministic fields

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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