共查询到10条相似文献,搜索用时 78 毫秒
1.
Wenchang Sun 《Mathematische Nachrichten》2010,283(10):1488-1505
The homogeneous approximation property (HAP) for wavelet frames was studied recently. The HAP is useful in practice since it means that the number of building blocks involved in a reconstruction of a function up to some error is essentially invariant under time‐scale shifts. In this paper, we prove the HAP for wavelet frames generated by admissible wavelet functions with arbitrary translation parameters and a class of dilation matrices. Moreover, we show that the approximation is uniform to some extent whenever wavelet functions satisfy moderate smooth and decaying conditions (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
2.
Bei Liu 《Numerical Functional Analysis & Optimization》2013,34(7-8):784-798
The homogeneous approximation property (HAP) for the continuous wavelet transform is useful in practice because it means that the measure of the building area involved in a reconstruction of a function up to some error is essentially invariant under timescale shifts. For the univariate case, it was shown that the pointwise HAP holds if and only if the Fourier transforms of both wavelets and the function to be reconstructed are compactly supported on ??{0}. In this paper, we study the HAP for multivariate wavelet transforms. We show that similar results hold for this case. However, the above condition is only sufficient but not necessary if the dimension of the variable is greater than 1, which is different from the univariate case. We also get a convergence result on the inverse of wavelet transforms, which improves similar results by Daubechies and Holschneider and Tchamitchain. 相似文献
3.
Wenchang Sun 《Monatshefte für Mathematik》2010,12(3):289-324
The homogeneous approximation property (HAP) of wavelet frames is useful in practice since it means that the number of building
blocks involved in a reconstruction of f up to some error is essentially invariant under time-scale shifts. In this paper, we show that every wavelet frame generated
with functions satisfying some moderate decay conditions possesses the HAP. Our result improves a recent work of Heil and
Kutyniok’s. Moreover, for wavelet frames generated with separable time-scale parameters, i.e., wavelet frames of the form
$\bigcup_{\ell=1}^r\{s^{-d/2}\psi_{\ell}(s^{-1}
\cdot - t):\, s\in S_{\ell}, t\in T_{\ell}\},$\bigcup_{\ell=1}^r\{s^{-d/2}\psi_{\ell}(s^{-1}
\cdot - t):\, s\in S_{\ell}, t\in T_{\ell}\}, 相似文献
4.
The homogeneous approximation property (HAP) for frames is useful in practice and has been developed recently. In this paper, we study the HAP for the continuous wavelet transform. We show that every pair of admissible wavelets possesses the HAP in L2 sense, while it is not true in general whenever pointwise convergence is considered. We give necessary and sufficient conditions for the pointwise HAP to hold, which depends on both wavelets and functions to be reconstructed. 相似文献
5.
Lili Zang 《Numerical Functional Analysis & Optimization》2013,34(9):1090-1101
One of the fundamental problems in the study of wavelet frames is to find conditions on the wavelet function and the dilation and translation parameters so that the corresponding wavelet system forms a frame. In this article, we obtain some inequalities for a discrete wavelet system to be a frame. Our result improves known ones by Chui, Shi, and Chen. 相似文献
6.
2-D NONSEPARABLE SCALING FUNCTIONINTERPOLATION AND APPROXIMATION 总被引:1,自引:0,他引:1
1 IntroductionWe begin witl1 two fundanlental questious of apprdriation theory Namely given sam-ples of a square iutegrable signal dyadically spaced in tin1e, is it possible to reconstruct thesignal?How close can the original signal be aPprokimated from the knowledge of the samples?There are many dtherent approaches to answer these questiolls. In [81, Wells and Zhoushowed that a wavelet approalmatiou theorem is valid for degree 1wavelet systenis in whichone obtains second-order approximation… 相似文献
7.
Quasi-interpolation has been audied in many papers, e.g. , [5]. Here we introduce nonseparable scal-ing function quasi-interpolation and show that its approximation can provide similar convergence propertiesas scalar wavelet system. Several equivalent statements of accuracy of nonseparable scaling function are alsogien. In the numerical experiments, it appears that nonseparable scaling function interpolation has betterconvergonce results than scalar wavelet systems in some cases. 相似文献
8.
EnbingLin LingYi 《逼近论及其应用》2002,18(3):65-78
Quasi-interpolation has been studied in many papers,e.g.,[5].Here we introduce nonseparable scaling function quasi-interpolation and show that its approximation can provide similar convergence properties as scalar wavelet system.Several equivalent statements of accuracy of nonseparable scaling function are also given.In the numerical experiments,it appears that nonseparable scaling function interpolation has better convergence results than scalar wavelet systems in some cases. 相似文献
9.
We investigate the construction of two-direction tight wavelet frames First, a sufficient condition for a two-direction refinable function generating two-direction tight wavelet frames is derived. Second, a simple constructive method of two-direction tight wavelet frames is given. Third, based on the obtained two-direction tight wavelet frames, one can construct a symmetric multiwavelet frame easily. Finally, some examples are given to illustrate the results. 相似文献
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