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A theory for multiresolution signal decomposition : the wavelet representation (1989)
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| Venue: | IEEE Transaction on Pattern Analysis and Machine Intelligence |
| Citations: | 3531 - 12 self |
BibTeX
@ARTICLE{Mallat89atheory,
author = {G. Mallat},
title = {A theory for multiresolution signal decomposition : the wavelet representation},
journal = {IEEE Transaction on Pattern Analysis and Machine Intelligence},
year = {1989}
}
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Abstract
Abstract-Multiresolution representations are very effective for analyzing the information content of images. We study the properties of the operator which approximates a signal at a given resolution. We show that the difference of information between the approximation of a signal at the resolutions 2 ’ + ’ and 2jcan be extracted by decomposing this signal on a wavelet orthonormal basis of L*(R”). In LL(R), a wavelet orthonormal basis is a family of functions ( @ w (2’ ~-n)),,,“jEZt, which is built by dilating and translating a unique function t+r (xl. This decomposition defines an orthogonal multiresolution representation called a wavelet representation. It is computed with a pyramidal algorithm based on convolutions with quadrature mirror lilters. For images, the wavelet representation differentiates several spatial orientations. We study the application of this representation to data compression in image coding, texture discrimination and fractal analysis. Index Terms-Coding, fractals, multiresolution pyramids, quadrature mirror filters, texture discrimination, wavelet transform. I I.
Keyphrases
wavelet representation multiresolution signal decomposition texture discrimination wavelet orthonormal basis multiresolution pyramid image coding quadrature mirror filter abstract-multiresolution representation index terms-coding pyramidal algorithm orthogonal multiresolution representation fractal analysis several spatial orientation quadrature mirror lilters unique function wavelet transform information content
