A theory for multiresolution signal decomposition: the waveletrepresentation
Mallat, S.G.
Dept. of Comput. Sci., New York Univ., NY;
This paper appears in: Pattern Analysis and Machine Intelligence, IEEE Transactions on
Publication Date: Jul 1989
Volume: 11,
Issue: 7
On page(s): 674-693
ISSN: 0162-8828
References Cited: 44
CODEN: ITPIDJ
INSPEC Accession Number: 3466263
Digital Object Identifier: 10.1109/34.192463
Current Version Published: 2002-08-06
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 2j+1 and 2j (where j is an
integer) can be extracted by decomposing this signal on a wavelet
orthonormal basis of L2(Rn), the
vector space of measurable, square-integrable n-dimensional
functions. In L2(R), a wavelet orthonormal
basis is a family of functions which is built by dilating and
translating a unique function ψ(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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