剪切波系统的酉扩展原理
A Unitary Extension Principle for Shearlet Systems
AI总结：
本文提出自适应MRA结构，推导出滤波器设计的酉扩展原理，并将其应用于剪切波系统，实现快速分解算法与紧框架构造。
摘要：
本文首先引入自适应MRA（AMRA）结构的概念，它是经典MRA结构的一种变体，适用于在每个分解层根据数据自适应地进行快速灵活分解策略的主要目标。然后，我们针对仿射类系统的一般情况研究了这种新方法，并推导出了滤波器设计的酉扩展原理（UEP）。最后，我们将结果应用于剪切波的方向表示系统。这为与剪切波系统相关的快速分解算法提供了一个全面的理论，该理论涵盖了在AMRA结构内具有空间紧支撑生成元的紧剪切波框架。此外，还在此框架内研究了与抛物尺度化和最优接近旋转的单模矩阵相关的类剪切波系统以及3D剪切波系统。
英文摘要：
In this paper, we first introduce the concept of an adaptive MRA (AMRA) structure which is a variant of the classical MRA structure suited to the main goal of a fast flexible decomposition strategy adapted to the data at each decomposition level. We then study this novel methodology for the general case of affine-like systems, and derive a Unitary Extension Principle (UEP) for filter design. Finally, we apply our results to the directional representation system of shearlets. This leads to a comprehensive theory for fast decomposition algorithms associated with shearlet systems which encompasses tight shearlet frames with spatially compactly supported generators within such an AMRA structure. Also shearlet-like systems associated with parabolic scaling and unimodular matrices optimally close to rotation as well as 3D shearlet systems are studied within this framework.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
