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An inequality for pairs of martingales and its application to fractal image coding

Part of: Communication, information Stochastic processes

Published online by Cambridge University Press:  14 July 2016

F. M. Dekking
F. M. Dekking*
Affiliation:
Technische Universiteit Delft
*
∗Postal address: Faculteit der Technische Wiskunde en Informatica, Technische Universiteit Delft, Mekelweg 4, 2628 CD Delft, The Netherlands.
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Abstract

We prove a monotonicity property for a function of general square integrable pairs of martingales which is useful in fractal-based algorithms for compression of image data.

Keywords

MARTINGALESQUAD TREESFRACTAL IMAGE COMPRESSION

MSC classification

Primary: 60G42: Martingales with discrete parameter
Secondary: 94A99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 4 , December 1996 , pp. 968 - 973
Copyright
Copyright © Applied Probability Trust 1996 

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References

[1] Bedford, T., Dekking, F. M., Breeuwer, M., Keane, M. S., and Van Schooneveld, D. (1994) Fractal coding of monochrome images. Signal Process: Image Communication 6, 405–419.Google Scholar
[2] Bedford, T., Dekking, F. M. and Keane, M. S. (1992) Fractal image coding techniques and contraction operators. Nieuw Arch. Wisk. 10, 185–217.Google Scholar
[3] Fisher, Y. (1995) Fractal image compression with quad trees. In Fractal Image Compression. ed. Fisher, Y. Springer, New York.CrossRefGoogle Scholar
[4] Jacquin, A. E. (1989) A fractal theory of iterated Markov operators with applications to digital image coding. PhD thesis. Georgia Institute of Technology.Google Scholar
[5] Kelly, M. D. (1971) Edge detection in pictures by computer using planning. Machine Intelligence 6, 397–409.Google Scholar