Explicit Construction of Framelets
نویسندگان
چکیده
منابع مشابه
Explicit Construction of Framelets
We study tight wavelet frames associated with given refinable functions which are obtained with the unitary extension principles. All possible solutions of the corresponding matrix equations are found. It is proved that the problem of the extension may be always solved with two framelets. In particular, if symbols of the refinable functions are polynomials (rational functions), then the corresp...
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The projection method is a useful tool for analyzing various properties of multivariate refinable function vectors and for obtaining low-dimensional refinable function vectors and wavelets from high-dimensional ones. In this paper, we shall further study the projection method and its applications to multivariate wavelet and framelet systems. Examples will be given to illustrate the projection m...
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We study tight wavelet frames associated with symmetric compactly supported re-nable functions, which are obtained with the unitary extension principle. We give a criterion for existence of two symmetric or antisymmetric compactly supported framelets. All reenable masks of length up to 6, satisfying this criterion, are found.
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Suppose a real-valued function φ ∈ L2(R) satisfies the following conditions: (a) φ̂(2ω) = m0(ω)φ̂(ω), where m0 is an essentially bounded 2π -periodic function; and (b) limω→0 φ̂(ω) = (2π)−1/2; then the function φ is called refinable or scaling, m0 is called a symbol of φ, and the relation in item (a) is called a refinement equation. Every refinable function generates multiresolution analysis (MRA)...
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ژورنال
عنوان ژورنال: Applied and Computational Harmonic Analysis
سال: 2001
ISSN: 1063-5203
DOI: 10.1006/acha.2000.0337