Publication

Wavelets: approximation and compression--a review

Martin Vetterli
1999
Conference Papers

Abstract

In this paper, we briefly review the connection between subband coding, wavelet approximation and general compression problems. Wavelet or subband coding is successful in compression applications partly because of the good approximation properties of wavelets. First, we revisit some rate-distortion bounds for wavelet approximation of piecewise smooth functions. We contrast these results with rate-distortion bounds achievable using oracle based methods. We indicate that such bounds are achievable in practice using dynamic programming. Finally, we conclude with an outlook on open questions in the area of compression and representations.

Official source

https://infoscience.epfl.ch/entities/publication/ae97afeb-828a-41e9-8011-72f122e071c9

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Martin Vetterli
1999
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/ae97afeb-828a-41e9-8011-72f122e071c9

About this result

Related concepts (30)

Wavelet

A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the number and direction of its pulses. Wavelets are imbued with specific properties that make them useful for signal processing. For example, a wavelet could be created to have a frequency of Middle C and a short duration of roughly one tenth of a second.

Discrete wavelet transform

In numerical analysis and functional analysis, a discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, a key advantage it has over Fourier transforms is temporal resolution: it captures both frequency and location information (location in time). Haar wavelet The first DWT was invented by Hungarian mathematician Alfréd Haar. For an input represented by a list of numbers, the Haar wavelet transform may be considered to pair up input values, storing the difference and passing the sum.

Data compression

In information theory, data compression, source coding, or bit-rate reduction is the process of encoding information using fewer bits than the original representation. Any particular compression is either lossy or lossless. Lossless compression reduces bits by identifying and eliminating statistical redundancy. No information is lost in lossless compression. Lossy compression reduces bits by removing unnecessary or less important information.

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Wavelets: approximation and compression--a review

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