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

  • Peter Hall (a1) and Inge Koch (a1)


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.


Corresponding author

Postal address for both authors: Statistics Research Section, School of Mathematical Sciences, The Australian National University, GPO Box 4, Canberra, ACT 2601, Australia.


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[1] Hall, P. (1987a) On the amount of detail that can be recovered from a degraded signal. Adv. Appl. Prob. 19, 371395.
[2] Hall, P. (1987b) On the processing of a motion-blurred image. SIAM J. Appl. Math. 47, 441453.
[3] Hall, P. (1989) Optimal convergence rates in signal recovery. Ann. Prob.
[4] Prakasa Rao, B. L. S. (1983) Nonparametric Functional Estimation. Academic Press, New York.
[5] Rosenfeld, A. and Kak, A. C. (1982) Digital Picture Processing, Vol. 1, 2nd edn. Academic Press, New York.
[6] Serra, J. P. (1982) Image Analysis and Mathematical Morphology. Academic Press, New York.


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

  • Peter Hall (a1) and Inge Koch (a1)


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