小波参数化与小波神经网络研究
摘要
多小波和非分离小波是小波分析的研究热点。正交、紧支撑、对称性、消失矩、平衡性、时频局域性等是小波理论和应用研究广泛关注的性质。将他们参数化以建立统一的多小波或非分离小波函数库，能使不同应用对象针对不同应用要求选取最优小波基函数，对促进小波应用意义重大。
小波神经网络是近年发展起来的一种高效的非线性信号处理新模型，根据被处理问题自适应最优化小波神经网络的系统性能，能为神经网络广泛的实际应用提供科学的模型设计指南和系统的理论保证。
本课题拟对比较广泛的一类多小波及相对特殊但具有十分强烈应用背景的几类非分离小波建立关于小波各种内在性质的参数化函数库，并试图揭示非分离小波的本质特征；通过最优化小波元和小波基函数，建立面向问题的自适应小波神经网络系统，并应用于相关的信号处理问题。
In recent years,the research in the field of wavelets analysis has focused on Multiwavelets and Nonseparable wavelets. Symmetry,Orthogonality,Vanishing moment,Balacing and finite supported are the properties concerned widely of the wavelets theory and their applied research.
It is significant for the application of wavelts to parameterize them and construct a class of function banks of Multiwavelets and Nonseparable wavelets which could supply the most optimized bases of wavelets based on the different applied object and the different applied demands.
The Wavelets Neural Network is the novel and efficient model of nonlinear signal processing developed in latest years. Optimized wavelet networks adaptively according to the handled question could offer the scientific guide of model design and the systemic theoretic guarantee.
This project intends to construct a parameterized function banks about the internal properties of wavelets aimed at a extensive kind of Multi-wavelets and some categories of relatively specific Non-separable wavelets with significant practical background, and disclose the essential characters of Non-separable wavelets. Through optimizing the bases of wavelets, it will build a problems oriented system of self-adaptive Wavelets Neural Network and apply it to the relative problems of signal processing.
小波神经网络是近年发展起来的一种高效的非线性信号处理新模型，根据被处理问题自适应最优化小波神经网络的系统性能，能为神经网络广泛的实际应用提供科学的模型设计指南和系统的理论保证。
本课题拟对比较广泛的一类多小波及相对特殊但具有十分强烈应用背景的几类非分离小波建立关于小波各种内在性质的参数化函数库，并试图揭示非分离小波的本质特征；通过最优化小波元和小波基函数，建立面向问题的自适应小波神经网络系统，并应用于相关的信号处理问题。
In recent years,the research in the field of wavelets analysis has focused on Multiwavelets and Nonseparable wavelets. Symmetry,Orthogonality,Vanishing moment,Balacing and finite supported are the properties concerned widely of the wavelets theory and their applied research.
It is significant for the application of wavelts to parameterize them and construct a class of function banks of Multiwavelets and Nonseparable wavelets which could supply the most optimized bases of wavelets based on the different applied object and the different applied demands.
The Wavelets Neural Network is the novel and efficient model of nonlinear signal processing developed in latest years. Optimized wavelet networks adaptively according to the handled question could offer the scientific guide of model design and the systemic theoretic guarantee.
This project intends to construct a parameterized function banks about the internal properties of wavelets aimed at a extensive kind of Multi-wavelets and some categories of relatively specific Non-separable wavelets with significant practical background, and disclose the essential characters of Non-separable wavelets. Through optimizing the bases of wavelets, it will build a problems oriented system of self-adaptive Wavelets Neural Network and apply it to the relative problems of signal processing.
引文
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[21] P.Teffen, P.N.Heller, R. A. Gopinath and C.S. Burrus. Theory of regular mrand wavelet bases. IEEE. Trans. signal processing, 1993,41(12)
[22] W.Lawton. Necessary and sufficient conditions for constructing orthonormal wavelet bases. J.Math.Phys, 1993,32:57-61
[23] Xieping Gao, Jian Wang, Jianshe Yu (高协平、王键、庚建设). Parameterization of univariate orthogonal wavelets with any finite support. preprint, 2003
[24] 朱长青，小波分析理论与影像分析．测绘出版社，1988
[25] 秦前清，杨宗凯，实用小波分析．西安电子科技大学出版社，1994
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[32] I.W. Selesnick. Multiwavelets bases with extra approximation properties. IEEE Trans. Signal Process,1998,46:2898-2908
[33] I.W. Selesnick. Balanced multiwavelet bases based on symmetric FIR filters. IEEE Trans. Signal Process,2000,48:184-191
[34] J.Lebrun and M.Vetterli.Balanced muitiwavelets, In:Proc. IEEE. Int. Conf. Aconst. Speech, Signal Process.(ICASSP).Munich, Germany, 1997
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[37] Qingtang J.On the design ofmultifiiter banks and orthonormal multiwavelet bases. IEEE Trans. Signal Process,1998,46(12):3292-3302
[38] Qingtang J. Paramerzations of symmetric orthogonal muitifilter banks with different filter lengths. Linear Algebra and its Applications, 2000,311:79-96
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