论文标题
紧凑的支持多元双重多帧，具有较高的消失时刻和高平衡订单
Compactly supported multivariate dual multiframelets with high vanishing moments and high balancing orders
论文作者
论文摘要
与单变量的三角体相比，研究多元框架涉及的主要挑战是，我们必须处理分解多元多项式矩阵的高度非平凡的问题。结果，多变量的三角体的研究要比文献中的单变量框架要少得多。在现有关于多元火与的作品中，多变量多帧群被认为与被研究的标量框架相比，要少得多。因此，多火心远非众所周知。在本文中，我们专注于通过流行的倾斜扩展原理（OEP）获得的多元双重多帧（或双重矢量印度群），这些原理称为基于OEP的双重多帧。我们将证明，从任何给定的紧凑型可改进的向量函数中，人们始终可以构建一个基于OEP的双重MLTiframelet，以便其生成器的生成器可能是消失的矩的最高顺序。此外，相关的离散帧转换是紧凑而稀疏的。
Comparing with univariate framelets, the main challenge involved in studying multivariate framelets is that we have to deal with the highly non-trivial problem of factorizing multivariate polynomial matrices. As a consequence, multivariate framelets are much less studied than univariate framelets in the literature. Among existing works on multivariate framelets, multivariate multiframelets are much less considered comparing with the exitensively studied scalar framelets. Hence multiframelets are far from being well understood. In this paper, we focus on multivariate dual multiframelets (or dual vector framelets) obtained through the popular oblique extension principle (OEP), which are called OEP-based dual multiframelets. We will show that from any given pair of compactly supported refinable vector functions, one can always construct an OEP-based dual mltiframelet, such that its generators have the highest possible order of vanishing moments. Moreover, the associated discrete framelet transform is compact and sparse.
