自适应方向细分格式与剪切波多尺度分析
Adaptive Directional Subdivision Schemes and Shearlet Multiresolution Analysis
AI总结：
本文通过构造自适应方向细分格式，解决了计算调和分析中具有方向分量的多尺度分析的基本问题，并建立了剪切波多尺度分析框架以实现快速分解。
摘要：
在本文中，我们为计算调和分析中的一个基本问题——即具有方向分量的多尺度分析的构造——提出了一个解决方案。我们将通过构造细分格式来实现，这些格式提供了一种将方向性纳入数据以及极限函数的方法。我们开发了一种新型的非平稳二元细分格式，允许在细分过程中根据方向性约束自适应调整，并推导了这些自适应方向细分格式收敛的掩模的完整刻画。此外，我们给出了几个数值例子来说明该格式的工作原理。其次，我们描述了与二维数据的稀疏方向表示系统相关的快速分解，重点放在最近引入的剪切波稀疏方向表示系统上。实际上，我们证明了所引入的自适应方向细分格式可以用作推导具有有限支撑滤波器的剪切波多尺度分析的框架，从而实现快速剪切波分解。
英文摘要：
In this paper, we propose a solution for a fundamental problem in computational harmonic analysis, namely, the construction of a multiresolution analysis with directional components. We will do so by constructing subdivision schemes which provide a means to incorporate directionality into the data and thus the limit function. We develop a new type of non-stationary bivariate subdivision schemes, which allow to adapt the subdivision process depending on directionality constraints during its performance, and we derive a complete characterization of those masks for which these adaptive directional subdivision schemes converge. In addition, we present several numerical examples to illustrate how this scheme works. Secondly, we describe a fast decomposition associated with a sparse directional representation system for two dimensional data, where we focus on the recently introduced sparse directional representation system of shearlets. In fact, we show that the introduced adaptive directional subdivision schemes can be used as a framework for deriving a shearlet multiresolution analysis with finitely supported filters, thereby leading to a fast shearlet decomposition.
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。
