A pr 2 00 7 Multivariate Wavelet Frames 1
نویسنده
چکیده
We proved that for any matrix dilation and for any positive integer n, there exists a compactly supported tight wavelet frame with approximation order n. Explicit methods for construction of dual and tight wavelet frames with a given number of vanishing moments are suggested.
منابع مشابه
ar X iv : 0 70 4 . 14 87 v 1 [ m at h . C A ] 1 1 A pr 2 00 7 Wavelet frames , Bergman spaces and Fourier transforms of Laguerre functions
The Fourier transforms of Laguerre functions play the same canonical role in wavelet analysis as do the Hermite functions in Gabor analysis. We will use them as analyzing wavelets in a similar way the Hermite functions were recently by Gröchenig and Lyubarskii in Gabor frames with Hermite functions, C. R. Acad. Sci. Paris, Ser. I 344 157-162 (2007). Building on Seip ́s work Beurling type density...
متن کاملar X iv : m at h / 03 07 31 7 v 1 [ m at h . FA ] 2 3 Ju l 2 00 3 GROUPS , WAVELETS , AND WAVELET SETS
Wavelet and frames have become a widely used tool in mathematics, physics, and applied science during the last decade. This article gives an overview over some well known results about the continuous and discrete wavelet transforms and groups acting on R n. We also show how this action can give rise to wavelets, and in particular, MSF wavelets)in L 2 (R n).
متن کاملPopular Wavelet Families and Filters and Their Use
Glossary 5 Introduction 6 Definition of Wavelets 7 Definition of Filters 8 Multi-Resolution Analysis 9 Wavelet Decomposition and Reconstruction 10 Refinable Functions 11 Compactly Supported Orthonormal Wavelets 12 Parameterization of Orthonormal Wavelets 13 Biorthogonal Wavelets 14 Prewavelets 15 Tight Wavelet Frames 16 Tight Wavelet Frames over Bounded Domain 17 q-Dilated Orthonormal Wavelets ...
متن کاملar X iv : f un ct - a n / 97 04 00 5 v 1 2 1 A pr 1 99 7 A natural extension of a left invariant lower semi - continuous weight
In this paper, we describe a natural method to extend left invariant weights on C *-algebraic quantum groups. This method is then used to improve the invariance property of a left invariant weight. We also prove some kind of uniqueness result for left Haar weights on C *-algebraic quantum groups arising from algebraic ones.
متن کاملar X iv : 0 80 2 . 10 79 v 1 [ m at h . C A ] 8 F eb 2 00 8 p - ADIC MULTIRESOLUTION ANALYSIS AND WAVELET FRAMES
We study p-adic multiresolution analyses (MRAs). A complete characterisation of test functions generating MRAs (scaling functions) is given. We prove that only 1-periodic test functions may be taken as orthogonal scaling functions. We also suggest a method for the construction of wavelet functions and prove that any wavelet function generates a p-adic wavelet frame.
متن کامل