Proceedings ArticleDOI
Generalized frame multiresolution analysis of abstract Hilbert spaces and their applications
Manos Papadakis
- Vol. 4119, pp 165-175
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TLDR
In this paper, the authors define a generic class of multiresolution analysis of abstract Hilbert spaces, which they call frame multi scaling vector set, and characterize the associated frame multi wavelet vector sets by generalizing the concept of the low and high pass filters and the Quadrature Mirror filter condition.Abstract:
We define a very generic class of multiresolution analysis of abstract Hilbert spaces. Their core subspaces have a frame produced by the action of an abelian unitary group on a perhaps infinite subset of the core subspace, which we call frame multi scaling vector set. We characterize the associated frame multi wavelet vector sets by generalizing the concept of the low and high pass filters and the Quadrature Mirror filter condition. We include an extensive overview of related work of other and we conclude with some examples.© (2000) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.read more
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Book ChapterDOI
The Double Density DWT
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Book ChapterDOI
Generalized Frame Multiresolution Analysis of Abstract Hilbert Spaces
TL;DR: In this paper, a generic class of multiresolution analysis of abstract Hilbert spaces is defined, where the core subspaces have a frame produced by the action of an abelian unitary group on a countable frame multiscaling vector set, which may be infinite.
Proceedings ArticleDOI
Riesz wavelets and multiresolution structures
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Dissertation
Generalized Multiresolution Analysis: Construction and Measure Theoretic Characterization
TL;DR: In this paper, the generalized multiresolution analysis (GFMRA, GMRA) theory was extended to d-dimensional Euclidean spaces, where the scaling functions of non-MRA wavelets have nonconstant dimension functions.
Wavelet packets on locally compact abelian groups
Firdous A. Shah,Abdul Wahid +1 more
TL;DR: In this paper, the authors construct wavelet packets associated with multiresolution analysis on locally compact Abelian groups and characterize the subcollections which form an orthonormal basis for L 2 (G).
References
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Journal ArticleDOI
The Theory of Multiresolution Analysis Frames and Applications to Filter Banks
John J. Benedetto,Shidong Li +1 more
TL;DR: In this paper, the concept of Frame Multi-Resolution Analysis (FMRA) is introduced, which is a natural extension to affine frames of the classical notion of a multiresolution analysis (MRA).
Journal ArticleDOI
Wavelets: Mathematics and Applications
TL;DR: In this article, Benedetto and Mitrea introduced the idea of irregular sampling in the construction of wavelet transform on Discrete Sets, and showed that the sampling theorem can be expressed as a regular sampling problem.
Book
Wandering Vectors for Unitary Systems and Orthogonal Wavelets
X. Dai,David R. Larson +1 more
TL;DR: In this article, the wavelet system and wavelet sets operator interpolation of wavelets are discussed. And examples of interpolation maps are given for examples of a wavelet interpolation map.
Book
A User's Guide to Operator Algebras
TL;DR: In this article, Von Neumann algebras are used to describe the structure of K-theory. But they do not describe the relation between K-Theory and structure theory.