A theory for multiresolution signal decomposition: the wavelet representation (1989)
| Venue: | IEEE Transactions on Pattern Analysis and Machine Intelligence |
| Citations: | 1884 - 10 self |
BibTeX
@ARTICLE{Mallat89atheory,
author = {Stephane G. Mallat},
title = {A theory for multiresolution signal decomposition: the wavelet representation},
journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
year = {1989},
volume = {11},
pages = {674--693}
}
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Abstract
Abstract-Multiresolution representations are very effective for ana-lyzing 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 rep-resentation called a wavelet representation. It is computed with a py-ramidal algorithm based on convolutions with quadrature mirror lil-ters. 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, quadra-ture mirror filters, texture discrimination, wavelet transform.
