Super-Wavelets and Decomposable Wavelet Frames
Super-Wavelets and Decomposable Wavelet Frames
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DOI：
10.1007/s00041-005-5005-x
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发表时间：
2005-11
影响因子：
1.2
通讯作者：
Qing Gu;D. Han
中科院分区：
文献类型：
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作者：
Qing Gu;D. Han
当一个小波框架等价于一个长度大于1的超小波框架时，称它是可分解的。可分解小波框架与超小波的一些问题密切相关。本文首先给出了Parseval小波框架可分解的充分必要条件。作为这些条件的一个应用，我们证明了对任意n> 1，存在一个Parseval小波框架，它对任意1 <m ≤ n是m-可分解的，但对任意k> n不是k-可分解的.此外，存在一个超小波，其分量是不可分解的。同样地，我们还证明了对于每个n> 1，存在一个Parseval小波框架，它可以扩展到长度为m的超小波，对任意1 <m ≤ n，但不能扩展到长度为k的超小波，对任意k> n.研究了可分解Parseval小波框架与超小波之间的联系，给出了可扩Parseval小波框架的一些充要条件。
A wavelet frame is called decomposable whenever it is equivalent to a superwavelet frame of length greater than one. Decomposable wavelet frames are closely related to some problems on super-wavelets. In this article we first obtain some necessary or sufficient conditions for decomposable Parseval wavelet frames. As an application of these conditions, we prove that for each n > 1 there exists a Parseval wavelet frame which is m-decomposable for any 1 < m ≤ n, but not k-decomposable for any k > n. Moreover, there exists a super-wavelet whose components are non-decomposable. Similarly we also prove that for each n > 1, there exists a Parseval wavelet frame that can be extended to a super-wavelet of length m for any 1 < m ≤ n, but can not be extended to any super-wavelet of length k with k > n. The connection between decomposable Parseval wavelet frames and super-wavelets is investigated, and some necessary or sufficient conditions for extendable Parseval wavelet frames are given.