DocumentCode :
1434581
Title :
Data compression and harmonic analysis
Author :
Donoho, David L. ; Vetterli, Martin ; DeVore, R.A. ; Daubechies, Ingrid
Author_Institution :
Stanford Univ., CA, USA
Volume :
44
Issue :
6
fYear :
1998
fDate :
10/1/1998 12:00:00 AM
Firstpage :
2435
Lastpage :
2476
Abstract :
In this paper we review some recent interactions between harmonic analysis and data compression. The story goes back of course to Shannon´s R(D) theory in the case of Gaussian stationary processes, which says that transforming into a Fourier basis followed by block coding gives an optimal lossy compression technique; practical developments like transform-based image compression have been inspired by this result. In this paper we also discuss connections perhaps less familiar to the information theory community, growing out of the field of harmonic analysis. Recent harmonic analysis constructions, such as wavelet transforms and Gabor transforms, are essentially optimal transforms for transform coding in certain settings. Some of these transforms are under consideration for future compression standards. We discuss some of the lessons of harmonic analysis in this century. Typically, the problems and achievements of this field have involved goals that were not obviously related to practical data compression, and have used a language not immediately accessible to outsiders. Nevertheless, through an extensive generalization of what Shannon called the “sampling theorem”, harmonic analysis has succeeded in developing new forms of functional representation which turn out to have significant data compression interpretations. We explain why harmonic analysis has interacted with data compression, and we describe some interesting recent ideas in the field that may affect data compression in the future
Keywords :
Gaussian processes; block codes; data compression; harmonic analysis; image coding; information theory; reviews; signal sampling; time-frequency analysis; transform coding; Fourier basis; Gabor transforms; Gaussian stationary processes; Shannon theory; block coding; data compression; harmonic analysis; information theory; optimal lossy compression technique; review; sampling theorem; transform coding; wavelet transforms; Block codes; Contracts; Data compression; Fourier transforms; Harmonic analysis; Image coding; Quantization; Transform coding; Wavelet packets; Wavelet transforms;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/18.720544
Filename :
720544
Link To Document :
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