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Two-direction Refinement Equations and Construction of Wavelets with Good Properties

Author: LinJunHong
Tutor: YangShouZhi
School: Shantou University
Course: Applied Mathematics
Keywords: Way multi - scale refinement Bidirectional high Vega fine Scaling function Orthogonal Approximation Filter Inseparable Regularity
CLC: O174.2
Type: Master's thesis
Year: 2010
Downloads: 21
Quote: 0
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Abstract


Wavelet analysis is based on the Fourier analysis developed rapidly emerging discipline , simultaneously in the time domain and frequency domain with good locality , it has profound theoretical and applied very wide range of dual significance of in-depth article about the direction refinement equations , multi- band wavelet and wavelet theory can not be separated on the basis of a finite non-negative coefficients way multi - scale refinement equation , two-way high- Vega fine equation L1 construed further research , and construct a class of arbitrarily high approximation order three -band orthogonal scaling function . Finally, a non- diagonal matrix expansion of high-dimensional configuration of non-separable orthogonal wavelet made ??two kinds of methods the main text frame is as follows: the first chapter briefly describes the brief history of the development of wavelet analysis the current research status , project sources , this paper outlines the main work second chapter introduces some related marks and L2 (Rd) in the multi-resolution analysis of the idea . third chapter studies with a limited two-way non- negative coefficients multi - scale refinement equation L1 solution to prove that all of these equations L1 solution set is supported by certain of its take on a constant symbol consisting of compactly supported function space, and the space is at most one -dimensional. finally give out of the equation has ( or does not have ) some non-trivial solution L1 sufficient conditions ( and these conditions are relatively easy to verify ) . fourth chapter studies with a limited two-way non- negative coefficients high Vega fine equation L1 Solutions noted All of these equations L1 solution set is supported by certain of its take on a constant symbol consisting of compactly supported function space, and the space is at most one -dimensional. finally study the equation with ( or without ) a nontrivial L1 solution conditions, including sufficient conditions , necessary conditions , necessary and sufficient conditions in the fifth chapter , we give a class with high approximation order of three orthogonal scaling function with compact support explicit structure , and gives the two tectonic example in Chapter VI , the main provider of non- diagonal stretch factor of high-dimensional orthogonal compactly supported wavelets two inseparable construction method whereby construct a class of L2 (Rr 1) of non-separable orthogonal wavelet group. concludes with a discussion of non-separable wavelets constructed some important properties .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Theory of functions > Fourier analysis ( classical harmonic analysis )
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