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Data compression and harmonic analysis
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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.
- Subjects :
- sampling theorem
n-widths
Data_CODINGANDINFORMATIONTHEORY
Library and Information Sciences
Lossy compression
Information theory
Harmonic analysis
wavelet packets
cosine packets
Entropy (information theory)
block coding
non- Gaussian process
€- entropy
wavelet transform
Transform coding
Mathematics
Discrete mathematics
Wavelet transform
subband coding
Gabor transform
second-order statistics
scalar quantization
Gaussian proc- ess
Computer Science Applications
Besov spaces
Wilson bases
Sobolev spaces
Littlewood–Paley theory
Karhunen–Loève transform
Fourier transform
rate-distortion
Algorithm
transform coding
Information Systems
Image compression
Data compression
Subjects
Details
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- OpenAIRE
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- ResearcherID
- Accession number :
- edsair.doi.dedup.....0d02d91f25741bb63c08507a93b1491d