Affine, Quasi-affine and Co-affine Frames

Frame theory has been the focus of active research for twenty years, both in theory and applications. Matrix Fourier multipliers send every orthonoamal wavelet to an orthonoamal wavelet. In this work, the notion of the bivariate generalized multiresolution structure (BGMS) of subspace is proposed. The characteristics of bivariate affine pseudoframes for subspaces is investigated. The construction of a GMS of Paley-Wiener subspace of is studied. The pyramid decomposition scheme is obtained based on such a GMS and a sufficient condition for its existence is provided. A constructive method for affine frames of based on a BGMS is established.

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Topological and geometric properties of refinable functions and MRA affine frames

Applied and Computational Harmonic Analysis ◽

10.1016/j.acha.2010.04.002 ◽

2011 ◽

Vol 30 (2) ◽

pp. 151-174 ◽

Cited By ~ 2

Author(s):

Deguang Han ◽

Qiyu Sun ◽

Wai-Shing Tang

Keyword(s):

Refinable Functions ◽

Geometric Properties ◽

Affine Frames

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A sufficient condition for affine frames with matrix dilation

Analysis in Theory and Applications ◽

10.1007/s10496-009-0166-0 ◽

2009 ◽

Vol 25 (2) ◽

pp. 166-174 ◽

Cited By ~ 4

Author(s):

Dengfeng Li ◽

Xianliang Shi

Keyword(s):

Sufficient Condition ◽

Matrix Dilation ◽

Affine Frames

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Bessel Sequences and Affine Frames

Applied and Computational Harmonic Analysis ◽

10.1006/acha.1993.1003 ◽

1993 ◽

Vol 1 (1) ◽

pp. 29-49 ◽

Cited By ~ 35

Author(s):

Charles K. Chui ◽

Xianliang Shi

Keyword(s):

Affine Frames ◽

Bessel Sequences

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The Nice Characters of Biorthogonal Four-Element Wavelet Packets with Two-Scale

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.460-461.351 ◽

2011 ◽

Vol 460-461 ◽

pp. 351-356

Author(s):

Yu Li ◽

Jin Shun Feng

Keyword(s):

Iteration Method ◽

Wavelet Packets ◽

Constructive Method ◽

Biorthogonal Wavelet ◽

New Approach ◽

Novel Approach ◽

Affine Frames

In this article, the notion of orthogonal nonseparable four-dimensional wavelet packets, which is the generalization of orthogonal univariate wavelet packets, is introduced. A new approach for constructing them is presented by iteration method. A novel approach for constructing two-directional biorthogonal wavelet packets is developed. The biorthogonality property of four-dimensional wavelet packets is discussed. Three biorthogonality formulas concerning these wavelet packets are estabished. A constructive method for affine frames of is proposed.

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The Characteristics of Affine Bivariate Pseudoframes of Subspace Associated with a Bivariate Filter Functions

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.439-440.926 ◽

2010 ◽

Vol 439-440 ◽

pp. 926-931

Author(s):

Yu Min Yu

Keyword(s):

Frame Theory ◽

Constructive Method ◽

Sufficient Condition ◽

Decomposition Scheme ◽

Affine Frames ◽

Active Research

Frame theory has been the focus of active research for twenty years, both in theory and applications. In this work, the notion of the bivariate generalized multiresolution structure (BGMS) of subspace is proposed. The characteristics of bivariate affine pseudoframes for subspaces is investigated. The construction of a GMS of Paley-Wiener subspace of is studied. The pyramid decomposition scheme is obtained based on such a GMS and a sufficient condition for its existence is provided. A constructive method for affine frames of based on a BGMS is established.

Download Full-text