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Showing papers on "Multiresolution analysis published in 1989"


Journal ArticleDOI
TL;DR: In this paper, 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.
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. >

20,028 citations


Book ChapterDOI
Ingrid Daubechies1
01 Jan 1989
TL;DR: This work focuses on orthonormal bases of wavelets, in particular bases ofwavelets with finite support, and defines wavelets and the wavelet transform.
Abstract: We define wavelets and the wavelet transform. After discussing their basic properties, we focus on orthonormal bases of wavelets, in particular bases of wavelets with finite support.

72 citations


Book ChapterDOI
R.R. Coifman1
06 Sep 1989
TL;DR: In this article, the scale is allowed to change at various points in space, as well as the analyzing wavelets, and various versions of wavelet analysis valid in a non-translation-invariant setting are described.
Abstract: Summary form only given, as follows. Various versions of wavelet analysis valid in a non-translation-invariant setting are described. Here, the scale is allowed to change at various points in space, as well as the analyzing wavelets. Such a generalized time (space) frequency analysis could find uses in a variety of signal and image processing contexts, as well as in the study of partial differential operators with variable coefficients arising in a nonhomogeneous medium, and gives rise to fast numerical algorithms. This multiresolution analysis, say for an edge detection problem, takes into account the variable geometry and sensitivity of the receptors. >

9 citations