Stability and Linear Independence Associated with Wavelet Decompositions
From MaRDI portal
Publication:4039317
DOI10.2307/2159543zbMath0770.42018OpenAlexW4253601690MaRDI QIDQ4039317
Jian-zhong Wang, Rong-Qing Jia
Publication date: 9 September 1993
Full work available at URL: https://doi.org/10.2307/2159543
stabilitymultiresolution analysisorthogonalityrefinement equationlinear independencewavelet decompositionsmask sequence
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Cites Work
- Unnamed Item
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- Unnamed Item
- Translates of multivariate splines
- A necessary and sufficient condition for the linear independence of the integer translates of a compactly supported distribution
- Ondelettes, analyses multirésolutions et filtres miroirs en quadrature. (Wavelets, multiscale analysis and quadrature mirror filters)
- Using the refinement equation for the construction of pre-wavelets
- A general framework of compactly supported splines and wavelets
- Orthonormal bases of compactly supported wavelets
- Stationary subdivision
- Ten Lectures on Wavelets
- Multiresolution Approximations and Wavelet Orthonormal Bases of L 2 (R)
- On linear independence for integer translates of a finite number of functions
- Wavelets and Dilation Equations: A Brief Introduction