research-article

A Theory for Multiresolution Signal Decomposition: The Wavelet Representation

Author:

S. G. MallatAuthors Info & Claims

IEEE Transactions on Pattern Analysis and Machine Intelligence, Volume 11, Issue 7

Pages 674 - 693

https://doi.org/10.1109/34.192463

Published: 01 July 1989 Publication History

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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Index Terms

A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
1. Computing methodologies
  1. Computer graphics
    1. Image compression
  2. Machine learning

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cover image IEEE Transactions on Pattern Analysis and Machine Intelligence

IEEE Transactions on Pattern Analysis and Machine Intelligence Volume 11, Issue 7

July 1989

109 pages

ISSN:0162-8828

Editor:
S. L. Tanimoto
Univ. of Washington, Seattle

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Copyright © Copyright © 1989 IEEE. All Rights Reserved.

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IEEE Computer Society

United States

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Published: 01 July 1989

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