Wavelets pp 247-252 | Cite as

Construction of Wavelets on Open Sets

  • S. Jaffard
Conference paper
Part of the inverse problems and theoretical imaging book series (IPTI)


We shall describe a way to construct wavelets on an open set Ω of R n (this construction is a joint work with Y.MEYER and can be found in (1) ;the reader should look there for precisions),then we shall give a more explicit description of the two following points that are important for possible applications: The asymptotic behavior (wavelets that are localized around very small cubes which are far from the boundary of Ω are numerically identical to the ”corresponding” wavelet on R n ) and the fast decomposition algorithms (which are of a similar kind as in R n except that the storage of more filters is needed).


Orthonormal Basis Asymptotic Estimate Multiresolution Analysis Riesz Basis Unconditional Basis 
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  1. 1.
    S. Jaffard et Y. Meyer, Bases d’ondelettes dans des ouverts de Rn to appear in Journal des Mathématiques pures et appliquéesGoogle Scholar
  2. 2.
    S. Mallat, A theory for multiresolution signal decomposition: The wavelet representation. Dept of computer science, University of Pennsylvania, PA 19104–6389,USAGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • S. Jaffard
    • 1
    • 2
  1. 1.CMAPEcole PolytechniquePalaiseau CedexFrance
  2. 2.CERMA (ENPC)France

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