基于结构容许覆盖的框架构造

Abstract

Abstract:

Using the general theory of the structured admissible covering, a Ridgelet-type covering Q={Q_T}_T∈T of the frequency space R²(ξ) is analogously introduced along with the constructed flow of Curvelet-type frame. The affine transformation T acts on the roles of dilation, translation, and modulation. Most of all, some different Ridgelet-type frames are given, such as Ridgelet-type tight frame, Dual Ridgelet-type frame, and Monoscale Dual Ridgelet-type frame, by combining the orthonomal Ridgelet with the constructed covering. Compared with Candes's Ridgelet tight frame, besides the analysis frames, their dual frames also have an explicit form.

Key words: Frame, Structured admissible covering, Ridgelet, Curvelet

CLC Number:

42C15

LIU Guo-Jun, FENG Xiang-Chu, ZHANG Wei-Bin. Construction of Frames Based on Structured Admissible Covering[J].Acta mathematica scientia,Series A, 2011, 31(3): 670-677.

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Construction of Frames Based on Structured Admissible Covering

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