Data compression and harmonic analysis
Information Theory, IEEE Transactions on, 44 (6):
2435--2476 (октября 1998)DOI: 10.1109/18.720544
Аннотация
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
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