基于冗余滤波器系统的Parseval小波构造
Construction of Parseval wavelets from redundant filter systems
摘要：
我们考虑L^2（R^d）中具有广义多分辨的小波。这意味着L^2（R^d）中的初始分辨子空间V_0不是单独生成的。结果，限制于V_0的整数格Z^d的表示具有非平凡的重数函数。我们展示了如何相应的分析和合成，这些小波可以理解的酉矩阵值函数作用于一定的向量丛的环面。具体来说，我们展示了如何在R^d上的小波函数可以直接从广义小波滤波器构造。
英文摘要：
We consider wavelets in L^2(R^d) which have generalized multiresolutions. This means that the initial resolution subspace V_0 in L^2(R^d) is not singly generated. As a result, the representation of the integer lattice Z^d restricted to V_0 has a nontrivial multiplicity function. We show how the corresponding analysis and synthesis for these wavelets can be understood in terms of unitary-matrix-valued functions on a torus acting on a certain vector bundle. Specifically, we show how the wavelet functions on R^d can be constructed directly from the generalized wavelet filters.
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