Representation of Signal in Tight Wavelet Frame and Best Wavelet Base
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摘要: 探讨了信号的小波标架表示与最佳小波基选择问题.首先对信号的小波标架表示与小波基表示的关系进行了描述,这个关系对于分析信号的小波标架表示是非常有用的;其次推导了周期小波标架的分解与重构的Mallat-塔式算法并证明了标架界为1的紧小波标架的周期化仍为标架界为1的紧小波标架;最后给出了基于小波标架算法和极小化加性代价函数的最佳小波基选择算法.Abstract: The subject on the representation of signal in tight wavelet frame and the selection of the best wavelet base was discussed. The relation between the wavelet frame representation and the wavelet base representations, which is very useful for interpreting the wavelet frame representation, is described. then the Mallat-pyramid algorithm for periodic tight wavelet frame decomposition and reconstruction is derived and it is proven that periodic wavelet frame by periodizing the tight wavelet frame with bound 1 in is a tight wavelet frame with bound 1. Finally based on the wavelet frame algorithm and criterion of minimizing an additive cost function, the selecting best wavelet base algorithm is proposed.
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