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On continuous image models and image analysis in the presence of correlated noise

Published online by Cambridge University Press:  01 July 2016

Peter Hall  and
Inge Koch
Peter Hall
Affiliation:
Australian National University
Inge Koch
Affiliation:
Australian National University
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Abstract

Most theoretical studies of image processing employ discrete image models. While that might be a good approximation to digital analysis, it severely restricts the class of tractable models for the blur component of image degradation, and concentrates excessive attention on specialized features of the pixel lattice. It is analogous to modelling all real statistical data using discrete distributions, which is clearly unnecessary. In this paper we study a continuous model for image analysis, in the presence of systematic degradation via a point spread function and stochastic degradation by a second-order stationary random field. Thus, we depart from the restrictive white-noise models which are commonly used in the theory of image analysis. We establish a general result which describes the performance of optimal image processing methods when the noise process has short-range dependence. Concise limits to resolution are derived, depending on image type, point spread function and noise correlation. These results are developed in important special cases, giving explicit formulae for optimal smoothing sets and convergence rates.

Keywords

IMAGE PROCESSINGPARTIAL FOURIER INVERSIONPOINT SPREAD FUNCTIONRANDOM FIELDSMOOTHING SET
Type
Research Article
Information
Advances in Applied Probability , Volume 22 , Issue 2 , June 1990 , pp. 332 - 349
Copyright
Copyright © Applied Probability Trust 1990 

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References

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