基于结构容许覆盖的框架构造

摘要

Using the general theory of the structured admissible covering, a Ridgelet-type covering Q = {Qt}t∈et of the frequency space R2(￡) 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.%利用一般的结构容许覆盖理论,借助曲线波型框架的构造流程,得到了频域空间R2(ξ)中的脊波型覆盖Q={QT}T∈T,这里仿射变换T扮演着平移,膨胀和调制的作用.此外,通过联合正交脊波和所构造的脊波型覆盖构造了一些新的脊波型框架,即脊波型紧框架,对偶脊波型框架,以及单尺度对偶脊波型框架.与Candes的脊波紧框架相比,除了框架本身,其对偶框架也具有显式表达式.