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  1. Journal of Fourier Analysis and Applications
  2. Journal of Fourier Analysis and Applications : Volume 3
  3. Journal of Fourier Analysis and Applications : Volume 3, Issue 5, September 1997
  4. Tight frames of multidimensional wavelets
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Journal of Fourier Analysis and Applications : Volume 23
Journal of Fourier Analysis and Applications : Volume 22
Journal of Fourier Analysis and Applications : Volume 21
Journal of Fourier Analysis and Applications : Volume 20
Journal of Fourier Analysis and Applications : Volume 19
Journal of Fourier Analysis and Applications : Volume 18
Journal of Fourier Analysis and Applications : Volume 17
Journal of Fourier Analysis and Applications : Volume 16
Journal of Fourier Analysis and Applications : Volume 15
Journal of Fourier Analysis and Applications : Volume 14
Journal of Fourier Analysis and Applications : Volume 13
Journal of Fourier Analysis and Applications : Volume 12
Journal of Fourier Analysis and Applications : Volume 11
Journal of Fourier Analysis and Applications : Volume 10
Journal of Fourier Analysis and Applications : Volume 9
Journal of Fourier Analysis and Applications : Volume 8
Journal of Fourier Analysis and Applications : Volume 7
Journal of Fourier Analysis and Applications : Volume 6
Journal of Fourier Analysis and Applications : Volume 5
Journal of Fourier Analysis and Applications : Volume 4
Journal of Fourier Analysis and Applications : Volume 3
Journal of Fourier Analysis and Applications : Volume 3, Issue 6, November 1997
Journal of Fourier Analysis and Applications : Volume 3, Issue 5, September 1997
From the original framer to present-day time-frequency and time-scale frames
On dualizing a multivariable Poisson summation formula
Stability theorems for Fourier frames and wavelet Riesz bases
Sampling multipliers and the Poisson Summation Formula
Tight frames of multidimensional wavelets
Perturbation of operators and applications to frame theory
Characterization of biorthogonal cosine wavelets
On a theorem of Ingham
From continuous to discrete Weyl-Heisenberg frames through sampling
Sampling and interpolating sequences for multiband-limited functions and exponential bases on disconnected sets
Affine systems inL 2 (ℝ d ) II: Dual systems
Interpolation and frames in certain Banach spaces of entire functions
Journal of Fourier Analysis and Applications : Volume 3, Issue 4, July 1997
Journal of Fourier Analysis and Applications : Volume 3, Issue 3, May 1997
Journal of Fourier Analysis and Applications : Volume 3, Issue 2, March 1997
Journal of Fourier Analysis and Applications : Volume 3, Issue 1, Supplement,January 1997
Journal of Fourier Analysis and Applications : Volume 3, Issue 1, January 1997

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Tight frames of multidimensional wavelets

Content Provider SpringerLink
Author Bownik, Marcin
Copyright Year 1997
Abstract In this paper we deal with multidimensional wavelets arising from a multiresolution analysis with an arbitrary dilation matrix A, namely we have scaling equations $$\varphi ^s (x) = \sum\limits_{k \in \mathbb{Z}^n } {h_k^s \sqrt {|\det A|} \varphi ^1 } (Ax - k) for s = 1, \ldots ,q,$$ where ϕ1 is a scaling function for this multiresolution and ϕ2, …, ϕq (q=|det A |) are wavelets. Orthogonality conditions for ϕ1, …, ϕq naturally impose constraints on the scaling coefficients $$\{ h_k^s \} _{k \in \mathbb{Z}^n }^{s = 1, \ldots ,q} $$ , which are then called the wavelet matrix. We show how to reconstruct functions satisfying the scaling equations above and show that ϕ2, …, ϕq always constitute a tight frame with constant 1. Furthermore, we generalize the sufficient and necessary conditions of orthogonality given by Lawton and Cohen to the case of several dimensions and arbitrary dilation matrix A.
Starting Page 525
Ending Page 542
Page Count 18
File Format PDF
ISSN 10695869
Journal Journal of Fourier Analysis and Applications
Volume Number 3
Issue Number 5
e-ISSN 15315851
Language English
Publisher Birkhäuser-Verlag
Publisher Date 1997-01-01
Publisher Place Boston
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Tight frame wavelets multiresolution analysis Abstract Harmonic Analysis Approximations and Expansions Fourier Analysis Partial Differential Equations Applications of Mathematics Signal, Image and Speech Processing
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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