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Directional time frequency analysis via continuous frame (1402.3682v1)

Published 15 Feb 2014 in math.FA

Abstract: Grafakos and Sansing \cite{GS} have shown how to obtain directionally sensitive time-frequency decompositions in $L2(\mrn)$ 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 $L2(\mr),$ 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 $\epsilon$-nets.

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