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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.

References

Buckley, M. J., Eagleson, G. K. and Silverman, B. W. (1988) The estimation of residual variance in nonparametric regression. Biometrika 75, 189–199.Google Scholar
Gasser, T., Sroka, L. and Jennen-Steinmetz, C. (1986) Residual variance and residual pattern in nonlinear regression. Biometrika 73, 625–633.Google Scholar
Hall, P., Kay, J. W. and Titterington, D. M. (1990) Asymptotically optimal difference-based estimation of variance in nonparametric regression. Biometrika 77, 521–528.Google Scholar
Hall, P. and Titterington, D. M. (1986) On some smoothing techniques used in image restoration. J. R. Statist. Soc. 48, 330–343.Google Scholar
Hall, P. and Titterington, D. M. (1987) Common structure of techniques for choosing smoothing parameters in regression problems. J. R. Statist. Soc. 49, 184–198.Google Scholar
Hall, P. and Titterington, D. M. (1988) On confidence bands in density estimation and regression. J. Multivariate Analysis 27, 228–254.Google Scholar
Jin, Z. P. (1988) On the Multi-scale Iconic Representations for Low-level Computer Vision. Unpublished Ph.D. thesis. The Turing Institute and University of Strathclyde.Google Scholar
Kay, J. W. (1988) On the choice of regularisation parameter in image restoration. Lecture Notes in Computer Science 301, pp. 587–596. Springer-Verlag, Berlin.Google Scholar
Kuan, D. T., Sawchuk, A. A., Strand, T. C. and Chavel, P. (1986) Adaptive noise smoothing filter for images with signal-dependent noise. IEEE Trans. Pattern Analysis and Machine Intelligence 7, 165–177.Google Scholar
Lee, J.-S. (1981) Refined filtering of image noise using local statistics. Computer Graphics and Image Processing 15, 380–389.Google Scholar
Lee, J.-S. (1984) The sigma filter and its application to speckle smoothing of synthetic aperture radar images. Statistical Signal Processing , ed. Wegman, E. J. and Smith, J. G., pp. 445–459. Dekker, New York.Google Scholar
Müller, H.-G. and Stadtmüller, U. (1987) Estimation of heteroscedasticity in regression analysis. Ann. Statist. 15, 610–635.Google Scholar
Müller, H.-G. and Stadtmüller, U. (1989) Detecting dependencies in smooth regression models. Biometrika 75, 639–637.Google Scholar
Mowforth, P. H. and Jin, Z. P. (1986) Implementation for noise suppression in images. Image and Vision Computing 4, 29–37.Google Scholar
Serra, J. (1982) Image Analysis and Mathematical Morphology. Academic Press, London.Google Scholar
Thompson, A. M., Kay, J. W. and Titterington, D. M. (1989) Noise estimation in signal restoration using regularisation. In preparation.Google Scholar
Wahba, G. (1983) Bayesian ‘confidence intervals’ for the cross-validated smoothing spline. J. R. Statist. Soc. 45, 133–150.Google Scholar