多小波子空间采样定理

Sampling Theorem for Multiwavelet Subspaces

该文基于再生核Hilbert空间理论,把小波子空间的Walter采样定理推广到多小波子空间,建立了多小波子空间的均匀采样定理,利用Zak变换给出了由尺度函数构造重构函数的公式。进一步针对采样点不均匀的情况,建立了多小波子空间的不规则采样定理。最后给出数值算例。

In this paper, the multiwavelet sampling theorem from Walter＇s wavelet sampling theorem by reproducing kernel is generalized. The reconstruction function can be expressed by multiwavelet using Zak transform. Then the general case of the irregular sampling is considered and the irregular sampling theorem for multiwavelet subspaces is established. Finally, the corresponding examples are given.