Hostname: page-component-848d4c4894-tn8tq Total loading time: 0 Render date: 2024-06-19T04:06:46.406Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Hall, P. (1987a) On the amount of detail that can be recovered from a degraded signal. Adv. Appl. Prob. 19, 371–395.Google Scholar
[2] Hall, P. (1987b) On the processing of a motion-blurred image. SIAM J. Appl. Math. 47, 441–453.Google Scholar
[3] Hall, P. (1989) Optimal convergence rates in signal recovery. Ann. Prob. Google Scholar
[4] Prakasa Rao, B. L. S. (1983) Nonparametric Functional Estimation. Academic Press, New York.Google Scholar
[5] Rosenfeld, A. and Kak, A. C. (1982) Digital Picture Processing, Vol. 1, 2nd edn. Academic Press, New York.Google Scholar
[6] Serra, J. P. (1982) Image Analysis and Mathematical Morphology. Academic Press, New York.Google Scholar