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A theory for multiresolution signal decomposition: the wavelet representation

Stéphane Mallat · IEEE Transactions on Pattern Analysis and Machine Intelligence · 1989

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Author / responsible party
Stéphane Mallat
Publisher
IEEE Transactions on Pattern Analysis and Machine Intelligence
Year
1989
Language
English

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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.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

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APA 7

Mallat, S. (1989). A theory for multiresolution signal decomposition: the wavelet representation. https://doi.org/10.1109/34.192463

MLA

Mallat, Stéphane. "A theory for multiresolution signal decomposition: the wavelet representation." 1989. https://doi.org/10.1109/34.192463.

Chicago

Mallat, Stéphane. 1989. "A theory for multiresolution signal decomposition: the wavelet representation.". https://doi.org/10.1109/34.192463.

Harvard

Mallat, S. 1989, A theory for multiresolution signal decomposition: the wavelet representation, IEEE Transactions on Pattern Analysis and Machine Intelligence, available at: https://doi.org/10.1109/34.192463 [Accessed 7 Aug. 2026].

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Resource details

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Title
A theory for multiresolution signal decomposition: the wavelet representation
Author / contributors
Stéphane Mallat
Publisher
IEEE Transactions on Pattern Analysis and Machine Intelligence
Publication year
1989
Language
English

Subjects

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Orthonormal basis; Wavelet; Wavelet transform; Mathematics; Multiresolution analysis; Pattern recognition (psychology); Artificial intelligence; Representation (politics); Basis function; Square-integrable function; Algorithm; Discrete wavelet transform
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