Frames, modular functions for shift-invariant subspaces and FMRA wavelet frames
Frames, modular functions for shift-invariant subspaces and FMRA wavelet frames
复制标题
框架、平移不变子空间的模块化函数和 FMRA 小波框架
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
D. Han
中科院分区：
文献类型：
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作者：
Qing Gu;D. Han
引入了平移不变子空间的模函数概念，并证明了它与平移不变子空间的框架生成元的选择无关。我们将利用它来研究任意可扩展整数矩阵A的小波标架的维度函数与一般多分辨分析(GMRA)的重数函数之间的关系。在给定框架多分辨率分析(FMRA)的情况下，我们证明了标准的正交多分辨率分析小波的构造公式不会产生小波框架，除非基础的FMRA是多分辨率分析。利用框架尺度函数和低通滤波器，给出了一种改进的FMRA小波框架的显式构造公式。
We introduce the concept of the modular function for a shift-invariant subspace that can be represented by normalized tight frame generators for the shift-invariant subspace and prove that it is independent of the selections of the frame generators for the subspace. We shall apply it to study the connections between the dimension functions of wavelet frames for any expansive integer matrix A and the multiplicity functions for general multiresolution analysis (GMRA). Given a frame mutiresolution analysis (FMRA), we show that the standard construction formula for orthonormal multiresolution analysis wavelets does not yield wavelet frames unless the underlying FMRA is an MRA. A modified explicit construction formula for FMRA wavelet frames is given in terms of the frames scaling functions and the low-pass filters.