论文标题
具有高平衡订单的多元准紧密边框，这些订单源自任何紧凑的可改进矢量功能
Multivariate Quasi-tight Framelets with High Balancing Orders Derived from Any Compactly Supported Refinable Vector Functions
论文作者
论文摘要
通过添加所需的冗余和灵活性来概括小波，在许多应用中，诸如图像处理和数值算法等许多应用中都具有关注和重要性。框架的几种关键特性是稀疏多尺度表示的高消失力矩，快速帧转换以达到数值效率，以及可鲁棒性的冗余。然而，研究和构建多元不可分割的边框是一个具有挑战性的问题，这主要是由于它们与多元多项式矩阵的分解和syzygy模块的内在联系。在本文中，我们通过准确边框的方法来避免上述困难，这些框的表现几乎相同。从任意支持的$ \ dm $ -dm $ - 可依次的矢量功能$ ϕ $的多种多样的$ \ dm $ - $ ϕ $大于一个大于一个的情况下，我们可以始终从一个紧凑的多元变量 - 多变量的准界面列出，所有Fram fram Issement的最高序列均可（II）的最高序列（II），我们可以使用fram的最高序列（ii），我们可以始终列出了所有的最高序列（II） with the highest balancing order.For a refinable scalar function $ϕ$, the above item (ii) often cannot be achieved intrinsically but we show that we can always construct a compactly supported OEP-based multivariate quasi-tight framelet derived from $ϕ$ satisfying item (i).This paper provides a comprehensive investigation on OEP-based multivariate quasi-tight multiframelets and their associated framelet transforms with high balancing订单。这加深了我们对多元准密码多帧及其相关快速多膜变换的理论理解。
Generalizing wavelets by adding desired redundancy and flexibility,framelets are of interest and importance in many applications such as image processing and numerical algorithms. Several key properties of framelets are high vanishing moments for sparse multiscale representation, fast framelet transforms for numerical efficiency, and redundancy for robustness. However, it is a challenging problem to study and construct multivariate nonseparable framelets, mainly due to their intrinsic connections to factorization and syzygy modules of multivariate polynomial matrices. In this paper, we circumvent the above difficulties through the approach of quasi-tight framelets, which behave almost identically to tight framelets. Employing the popular oblique extension principle (OEP), from an arbitrary compactly supported $\dm$-refinable vector function $ϕ$ with multiplicity greater than one, we prove that we can always derive from $ϕ$ a compactly supported multivariate quasi-tight framelet such that (i) all the framelet generators have the highest possible order of vanishing moments;(ii) its associated fast framelet transform is compact with the highest balancing order.For a refinable scalar function $ϕ$, the above item (ii) often cannot be achieved intrinsically but we show that we can always construct a compactly supported OEP-based multivariate quasi-tight framelet derived from $ϕ$ satisfying item (i).This paper provides a comprehensive investigation on OEP-based multivariate quasi-tight multiframelets and their associated framelet transforms with high balancing orders. This deepens our theoretical understanding of multivariate quasi-tight multiframelets and their associated fast multiframelet transforms.
