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On estimation of noise variance in two-dimensional signal processing

Published online by Cambridge University Press:  01 July 2016

Peter Hall ,
J. W. Kay  and
D. M. Titterington
Peter Hall*
Affiliation:
University of Glasgow
J. W. Kay*
Affiliation:
University of Glasgow
D. M. Titterington*
Affiliation:
University of Glasgow
*
∗Present address: Department of Statistics, Faculty of Economics and Commerce, Australian National University, GPO Box 4, Canberra ACT 2601, Australia.
∗∗Postal address: Department of Statistics, University of Glasgow, University Gardens, Glasgow G12 8QW, UK.
∗∗Postal address: Department of Statistics, University of Glasgow, University Gardens, Glasgow G12 8QW, UK.
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Abstract

Estimation of noise variance is an important component of digital signal processing, in particular of image processing. In this paper we develop methods for estimating the variance of white noise in a two-dimensional degraded signal. We discuss optimal configurations of pixels for difference-based estimation, and describe asymptotically optimal selection of weights for the component pixels. After extensive analysis of possible configurations we recommend averaging linear configurations over a variety of different orientations (usually two or four). This approach produces estimators with properties of both statistical and numerical efficiency.

Keywords

COMBINATORIALCONFIGURATIONDIFFERENCEEFFICIENCYIMAGE PROCESSING
Type
Research Article
Information
Advances in Applied Probability , Volume 23 , Issue 3 , September 1991 , pp. 476 - 495
Copyright
Copyright © Applied Probability Trust 1991 

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Footnotes

Research carried out while this author was visiting the University of Glasgow.

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