Recursive algorithms for computing the Cramer-Rao bound

Author

Hero, Alfred O. ; Usman, Mohammad ; Sauve, Anne C. ; Fessler, Jeffrey A.

Author_Institution

Dept. of Electr. Eng. & Comput. Sci., Michigan Univ., Ann Arbor, MI, USA

Volume

45

Issue

3

fYear

1997

fDate

3/1/1997 12:00:00 AM

Firstpage

803

Lastpage

807

Abstract

Computation of the Cramer-Rao bound (CRB) on estimator variance requires the inverse or the pseudo-inverse Fisher information matrix (FIM). Direct matrix inversion can be computationally intractable when the number of unknown parameters is large. In this correspondence, we compare several iterative methods for approximating the CRB using matrix splitting and preconditioned conjugate gradient algorithms. For a large class of inverse problems, we show that nonmonotone Gauss-Seidel and preconditioned conjugate gradient algorithms require significantly fewer flops for convergence than monotone “bound preserving” algorithms

Keywords

conjugate gradient methods; convergence of numerical methods; deconvolution; image restoration; inverse problems; iterative methods; matrix inversion; medical image processing; parameter estimation; positron emission tomography; recursive estimation; Cramer-Rao bound; deconvolution; direct matrix inversion; estimator variance; image restoration; inverse problems; iterative methods; matrix splitting; nonmonotone Gauss-Seidel algorithms; preconditioned conjugate gradient algorithms; pseudo-inverse Fisher information matrix; recursive algorithms; tomographic reconstruction; Chromium; Convergence; Covariance matrix; Equations; Gaussian processes; Inverse problems; Iterative algorithms; Iterative methods; Jacobian matrices; Signal processing algorithms;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.558511

Filename

558511