基于连续标架的方向性时频分析
Directional time frequency analysis via continuous frame
摘要：
Grafakos和Sansing \cite{GS}已经展示了如何在基于Gabor系统的$L^2(\mr^n)$中获得方向敏感的时间-频率分解。在$\ltr;$中，关键工具是“岭思想”，其将一元函数提升为多个变量的多元函数。我们推广他们的结果表明，类似的结果举行开始与一般的框架$L^2(\mr),$在设置的离散框架和连续框架。这允许将该理论应用于若干其他类别的帧，例如，小波框架和平移不变系统。我们将考虑应用到迈耶小波和复杂的B样条。在小波系统的特殊情况下，我们展示了如何离散的表示使用$ε$ -网。
英文摘要：
Grafakos and Sansing \cite{GS} have shown how to obtain directionally sensitive time-frequency decompositions in $L^2(\mr^n)$ based on Gabor systems in $\ltr;$ the key tool is the "ridge idea," which lifts a function of one variable to a function of several variables. We generalize their result by showing that similar results hold starting with general frames for $L^2(\mr),$ both in the setting of discrete frames and continuous frames. This allows to apply the theory for several other classes of frames, e.g., wavelet frames and shift-invariant systems. We will consider applications to the Meyer wavelet and complex B-splines. In the special case of wavelet systems we show how to discretize the representations using $ε$-nets.
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