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On the amount of detail that can be recovered from a degraded signal

Published online by Cambridge University Press:  01 July 2016

Peter Hall
Peter Hall*
Affiliation:
University of Glasgow
*
∗This research was carried out while the author was on leave from the Department of Statistics, Faculty of Economics and Commerce, Australian National University, GPO Box 4, Canberra ACT 2601, Australia.
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Abstract

Motivated by applications in digital image processing, we discuss information-theoretic bounds to the amount of detail that can be recovered from a defocused, noisy signal. Mathematical models are constructed for test-pattern, defocusing and noise. Using these models, upper bounds are derived for the amount of detail that can be recovered from the degraded signal, using any method of image restoration. The bounds are used to assess the performance of the class of linear restorative procedures. Certain members of the class are shown to be optimal, in the sense that they attain the bounds, while others are shown to be sub-optimal. The effect of smoothness of point-spread function on the amount of resolvable detail is discussed concisely.

Keywords

DEFOCUSINFORMATIONLINEAR IMAGE RESTORATIONLINES PER MILLIMETREMEAN SQUARED ERRORNOISEPOINT-SPREADRESOLUTIONTEST-PATTERN
Type
Research Article
Information
Advances in Applied Probability , Volume 19 , Issue 2 , June 1987 , pp. 371 - 395
Copyright
Copyright © Applied Probability Trust 1987 

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Reference added in proof

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