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Cited by 21,372

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A theory for multiresolution signal decomposition: the wavelet representation

Mallat, S.G.·1989·IEEE Transactions on Pattern Analysis and Machine Intelligence

Abstract

Multiresolution representations are effective for analyzing the information content of images. The properties of the operator which approximates a signal at a given resolution were studied. It is shown that the difference of information between the approximation of a signal at the resolutions 2/sup j+1/ and 2/sup j/ (where j is an integer) can be extracted by decomposing this signal on a wavelet orthonormal basis of L/sup 2/(R/sup n/), the vector space of measurable, square-integrable n-dimensional functions. In L/sup 2/(R), a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi (x). This decomposition defines an orthogonal multiresolution representation called a wavelet representation. It is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters. Wavelet representation lies between the spatial and Fourier domains. For images, the wavelet representation differentiates several spatial orientations. The application of this representation to data compression in image coding, texture discrimination and fractal analysis is discussed.>

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Metadata

Authors
Mallat, S. G.
Venue
IEEE Transactions on Pattern Analysis and Machine Intelligence
Published
1989-07
Volume
11
Issue
7
Pages
674-693
ISSN
0162-8828 (ISSN-L)
OpenAlex
W2132984323
Cited by
21,372
References
3
FWCI
184.71
Type
journal article
Language
en
Open access
closed

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